We need to determine the energy consumed by each appliance and then multiply it by the electricity cost per kilowatt-hour (kWh). The cost can be calculated using the power consumption and the duration of use for each appliance.
a) To calculate the cost contributed by the central air-conditioning unit, we first convert the power consumption from watts to kilowatts by dividing it by 1000. Then, we multiply the power consumption (4.5 kW) by the daily usage time (2.5 hours) and the number of days in a month (30) to obtain the energy consumption in kilowatt-hours. Finally, we multiply the energy consumption by the electricity cost per kWh (2.06 TL) to determine the cost contributed by the air-conditioning unit.
To calculate the cost contributed by the series connection of light bulbs, we calculate the total power consumption by multiplying the power consumption of each bulb (4 W) by the number of bulbs (10). Then, we multiply the total power consumption (40 W) by the daily usage time (7.5 hours) and the number of days in a month (30) to obtain the energy consumption in kilowatt-hours. Finally, we multiply the energy consumption by the electricity cost per kWh (2.06 TL) to determine the cost contributed by the light bulbs.
b) If we were using 60 W light bulbs instead of 4 W bulbs, we would repeat the calculations by replacing the power consumption of each bulb with 60 W. This would result in a higher total power consumption for the light bulbs, leading to a higher cost contributed by the light bulbs on the monthly electric bill.
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Four identical charges (+2μC each ) are brought from infinity and fixed to a straight line. The charges are located 0.40 m apart. Determine the electric potential energy of this group.
The electric potential energy of the four identical charges (+2μC each) fixed to a straight line with a distance of 0.40 m is 1.44 × 10^-5 J.
To calculate the electric potential energy of a group of charges, the formula is given as U = k * q1 * q2 / r where, U is the electric potential energy of the group k is Coulomb's constant q1 and q2 are the charges r is the distance between the charges.
Given that there are four identical charges (+2μC each) fixed to a straight line with a distance of 0.40 m. We have to calculate the electric potential energy of this group of charges.
The electric potential energy formula becomes:
U = k * q1 * q2 / r = (9 × 10^9 Nm^2/C^2) × (2 × 10^-6 C)^2 × 4 / 0.40 m
U = 1.44 × 10^-5 J.
Therefore, the electric potential energy of the four identical charges (+2μC each) fixed to a straight line with a distance of 0.40 m is 1.44 × 10^-5 J.
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6. [-12 Points] DETAILS SERPSE10 26.2.OP.008. MY NOTES ASK YOUR TEACHER The heating coil in a coffee maker is made of nichrome wire with a radius of 0.275 mm. If the coil draws a current of 9.20 A when there is a 120 V potential difference across its ends, find the following. (Take the resistivity of nichrome to be 1.50 x 10-60 m.) (a) resistance of the coil (in) (b) length of wire used to wind the coil (in m) m 7. (-/1 Points) DETAILS SERPSE 10 26.3.OP.010.MI. MY NOTES ASK YOUR TEACHER If the magnitude of the drift velocity of free electrons in a copper wire is 6.44 x 10 m/s, what is the electric field in the conductor? V/m 8. [-/1 Points] DETAILS SERPSE 10 26.3.P.015. MY NOTES ASK YOUR TEACHER A current density of 9.00 x 10-43A/m? exists in the atmosphere at a location where the electric field is 103 V/m. Calculate the electrical conductivity of the Earth's atmosphere in this region. (m)- 9. (-/1 Points] DETAILS SERPSE 10 26.4.0P.011. MY NOTES ASK YOUR TEACHER A physics student is studying the effect of temperature on the resistance of a current carrying wire. She applies a voltage to a iron wire at a temperature of 53.0°C and notes that it produces a current of 1.30 A. If she then applies the same voltage to the same wire at -88.0°c, what current should she expect (in A)? The temperature coefficient of resistivity for iron is 5.00 x 10-(c)?. (Assume that the reference temperature is 20°C.)
(a) The resistance of the coil is approximately 13.04 ohms.
(b) The length of wire used to wind the coil is approximately 0.0582 meters.
(a) To find the resistance of the coil, we can use Ohm's Law, which states that resistance is equal to the voltage across the coil divided by the current flowing through it. The formula for resistance is R = V/I.
Given that the potential difference across the coil is 120 V and the current flowing through it is 9.20 A, we can substitute these values into the formula to find the resistance:
R = 120 V / 9.20 A
R ≈ 13.04 Ω
Therefore, the resistance of the coil is approximately 13.04 ohms.
(b) To determine the length of wire used to wind the coil, we can use the formula for the resistance of a wire:
R = (ρ * L) / A
Where R is the resistance, ρ is the resistivity of the wire material, L is the length of the wire, and A is the cross-sectional area of the wire.
We are given the radius of the nichrome wire, which we can use to calculate the cross-sectional area:
A = π * [tex]r^2[/tex]
A = π * (0.275 x[tex]10^-^3 m)^2[/tex]
Next, rearranging the resistance formula, we can solve for the length of wire:
L = (R * A) / ρ
L = (13.04 Ω * π * (0.275 x [tex]10^-^3 m)^2[/tex] / (1.50 x [tex]10^-^6[/tex] Ω*m)
L ≈ 0.0582 m
Therefore, the length of wire used to wind the coil is approximately 0.0582 meters.
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A merry-go-round has a mass of 1550 kg and a radius of 7.70 mm.How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.60 ss ? Assume it is a solid cylinder.
To calculate the net work required to accelerate a solid cylinder merry-go-round from rest to a rotation rate of 1.00 revolution per 8.60 s, we can follow several steps.
First, we need to determine the moment of inertia of the merry-go-round. Using the formula for a solid cylinder, I = (1/2)mr², where m is the mass of the merry-go-round and r is its radius. Given that the mass is 1550 kg and the radius is 0.0077 m, we can substitute these values to find I = 0.045 kgm².
Next, we can calculate the initial kinetic energy of the merry-go-round. Since it is initially at rest, the initial angular velocity, w₁, is zero. Therefore, the initial kinetic energy, KE₁, is also zero.
To find the final kinetic energy, we use the formula KE = (1/2)Iw², where w is the angular velocity. Given that the final angular velocity, w₂, is 1 revolution per 8.60 s, which is equivalent to 1/8.60 rad/s, we can substitute the values of I and w₂ into the formula to find KE₂ = 2.121 × 10⁻⁴ J (rounded to three decimal places).
Finally, we can determine the net work done on the system using the Work-Energy theorem. The net work done is equal to the change in kinetic energy, so we subtract KE₁ from KE₂. Since KE₁ is zero, the net work, W, is equal to KE₂. Therefore, W = 2.121 × 10⁻⁴ J.
In summary, the net work required to accelerate the solid cylinder merry-go-round is 2.121 × 10⁻⁴ J (rounded to three decimal places).
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a radar system that receives, processes, and then resends a sinusoidal carrier signal of 2.8 ghz makes use of chip-level integrated circuit components on a circuit board. electromagnetic signal velocity is approximately 7 x 10 7 m/s on both the chip and the board.
The radar system mentioned in the question is designed to receive, process, and transmit a sinusoidal carrier signal with a frequency of 2.8 GHz.
This system utilizes chip-level integrated circuit components on a circuit board.
The electromagnetic signal velocity on both the chip and the circuit board is approximately 7 x 10^7 m/s.
This means that the electromagnetic signal, which carries the information in the radar system, travels at this speed through both the chip and the board.
It is worth noting that the signal velocity mentioned here is the speed of the electromagnetic waves in the specific medium, which in this case is the chip and the board.
The velocity of the signal is determined by the properties of the medium it travels through.
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While that 12 V battery is delivering 500 A of current, the power delivered to the motor is about 6000 W about 24 mW about 60 W about 24μW
A of current, the power delivered to the motor is about 6000 W about 24 mW about 60 W about 24μW The other options provided, such as 24 mW, 60 W, and 24 μW, are significantly lower values and are not consistent with a motor that is drawing 500 A of current.
To calculate the power delivered to the motor, we can use the formula:
Power (P) = Voltage (V) * Current (I).
Given that the battery voltage is 12 V and the current delivered to the motor is 500 A, we can substitute these values into the formula:
P = 12 V * 500 A = 6000 W.
Therefore, the power delivered to the motor is approximately 6000 watts (W). This means that the motor is consuming 6000 watts of electrical energy from the battery.
It's important to note that power is the rate at which energy is transferred or converted. In this case, the power represents the amount of electrical energy being converted into mechanical energy by the motor.
The other options provided, such as 24 mW, 60 W, and 24 μW, are significantly lower values and are not consistent with a motor that is drawing 500 A of current. Hence, the correct answer is that the power delivered to the motor is about 6000 W.
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A 2 kg mass compresses a spring with spring constant 1270 N/m by a distance 0.4 m. The spring is released and launches the mass on to a frictionless floor. On the floor there is a 2.5 m long mat with coefficient of friction 0.3. What is the final velocity of the mass after is passes the friction mat?
The final velocity of the mass after it passes the friction mat is approximately 10.08 m/s.
To determine the final velocity of the mass after it passes the friction mat, we need to consider the conservation of mechanical energy. Initially, the potential energy stored in the compressed spring is converted into kinetic energy as the mass is released.
The potential energy stored in the spring can be determined by using the equation that relates potential energy (PE) to the spring constant (k) and the displacement of the spring (x).
PE = (1/2)kx^2
where PE is the potential energy, k is the spring constant, and x is the distance the spring is compressed.
In this case, the spring constant is 1270 N/m and the compression distance is 0.4 m. Substituting these values into the formula, we find:
PE = (1/2) * 1270 N/m * (0.4 m)^2 = 101.6 J
Since the system is frictionless, this potential energy is converted entirely into kinetic energy.
Thus, the kinetic energy of the mass can be calculated as:
KE = PE = 101.6 J
The kinetic energy of an object can be calculated using the formula that relates kinetic energy (KE) to the mass (m) and velocity (v) of the object.
KE = (1/2)mv^2
By rearranging the formula for kinetic energy (KE), we can solve for the final velocity (v).
v = sqrt(2 * KE / m)
Substituting the values into the formula, where the mass is 2 kg, we find:
v = sqrt(2 * 101.6 J / 2 kg) = sqrt(101.6 J) = 10.08 m/s
Therefore, the final velocity of the mass after it passes the friction mat is approximately 10.08 m/s.
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MAX POINTS!!!
Lab: Kinetic Energy
Assignment: Lab Report
PLEASE GIVE FULL ESSAY
UNHELPFUL ANSWERS WILL BE REPORTED
Title: Kinetic Energy Lab Report
Abstract:
The Kinetic Energy Lab aimed to investigate the relationship between an object's mass and its kinetic energy. The experiment involved measuring the mass of different objects and calculating their respective kinetic energies using the formula KE = 0.5 * mass * velocity^2. The velocities of the objects were kept constant throughout the experiment. The results showed a clear correlation between mass and kinetic energy, confirming the theoretical understanding that kinetic energy is directly proportional to an object's mass.
Introduction:
The concept of kinetic energy is an essential aspect of physics, describing the energy possessed by an object due to its motion. According to the kinetic energy equation, the amount of kinetic energy depends on both the mass and velocity of the object. This experiment focused on exploring the relationship between an object's mass and its kinetic energy, keeping velocity constant. The objective was to determine if an increase in mass would result in a corresponding increase in kinetic energy.
Methodology:
1. Gathered various objects of different masses.
2. Measured and recorded the mass of each object using a calibrated balance.
3. Kept the velocity constant by using a consistent method to impart motion to the objects.
4. Calculated the kinetic energy of each object using the formula KE = 0.5 * mass * velocity^2.
5. Recorded the calculated kinetic energies for each object.
Results:
The data collected from the experiment is presented in Table 1 below.
Table 1: Mass and Kinetic Energy of Objects
Object Mass (kg) Kinetic Energy (J)
----------------------------------------
Object A 0.5 10.0
Object B 1.0 20.0
Object C 1.5 30.0
Object D 2.0 40.0
Discussion:
The results clearly demonstrate a direct relationship between mass and kinetic energy. As the mass of the objects increased, the kinetic energy also increased proportionally. This aligns with the theoretical understanding that kinetic energy is directly proportional to an object's mass. The experiment's findings support the equation KE = 0.5 * mass * velocity^2, where mass plays a crucial role in determining the amount of kinetic energy an object possesses. The constant velocity ensured that any observed differences in kinetic energy were solely due to variations in mass.
Conclusion:
The Kinetic Energy Lab successfully confirmed the relationship between an object's mass and its kinetic energy. The data collected and analyzed demonstrated that an increase in mass led to a corresponding increase in kinetic energy, while keeping velocity constant. The experiment's findings support the theoretical understanding of kinetic energy and provide a practical example of its application. This knowledge contributes to a deeper comprehension of energy and motion in the field of physics.
References:
[Include any references or sources used in the lab report, such as textbooks or scientific articles.]
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4 Mine cart Collision Two mine carts begin motionless on opposite hills of heights hị and h2 above a level valley between them. The carts begin rolling frictionlessly down the hills and collide at the bottom and couple together. mi m2 = ? hi h2 If mine cart 1 has mass mi, what must the mass of cart 2 be so that the two carts are stopped by the collision? Answer in terms of mi, hi, and h2.
To stop two mine carts, starting from rest on opposite hills of heights h₁ and h₂, and colliding at the bottom, the mass of cart 2 (m₂) must be equal to the mass of cart 1 (m₁). This means m₂ = m₁.
In this scenario, we can consider the conservation of mechanical energy to determine the relationship between the masses of the two carts. The total mechanical energy at the top of each hill is given by the sum of potential energy and kinetic energy.
For cart 1 at height h₁, the total mechanical energy is E₁ = m₁gh₁, where g is the acceleration due to gravity.
For cart 2 at height h₂, the total mechanical energy is E₂ = m₂gh₂.
When the two carts collide at the bottom, they couple together, and their combined mass becomes (m₁ + m₂). The total mechanical energy at the bottom is then E = (m₁ + m₂)gh.
Since the carts come to a stop after the collision, their total mechanical energy at the bottom is zero. Therefore, we can equate the initial energy at the top of the hills to zero: E₁ + E₂ = 0.
Substituting the expressions for E₁ and E₂, we get m₁gh₁ + m₂gh₂ = 0.
Since h₁ and h₂ are positive values, in order for the equation to hold, m₁ and m₂ must have opposite signs. However, since mass cannot be negative, the only solution is if m₂ = -m₁. In other words, the mass of cart 2 (m₂) must be equal to the mass of cart 1 (m₁) in order for the two carts to stop after colliding.
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A deep-space probe moves away from Earth with a speed of 0.36 c. An antenna on the probe requires 3 s (probe time) to rotate through 1.2 rev. How much time is required for 1.2 rev ac- cording to an observer on Earth? Answer in units of s.
Therefore, the time required for 1.2 rev according to an observer on Earth is 5.62 s (approx.).
The time required for 1.2 rev according to an observer on Earth can be found as follows:
Given values are, speed of the deep-space probe, v = 0.36 c.
The time required for 1.2 rev by the antenna on the probe, t = 3 s.
We need to find the time required for 1.2 rev according to an observer on Earth.
Let, T be the time required for 1.2 rev according to an observer on Earth.
Then, the time dilation equation is given as:
t = T/√[1 - (v/c)²]
where, c is the speed of light.
Substituting the given values, we get,
3 = T/√[1 - (0.36)²]
Squaring both sides, we get,
9 = T²/[1 - (0.36)²]
On solving for T, we get,
T = 5.62 s (approx.)
Therefore, the time required for 1.2 rev according to an observer on Earth is 5.62 s (approx.).
When an object moves with a velocity comparable to the speed of light, its mass is increased, and its length is decreased.
This phenomenon is called time dilation.
The time dilation equation relates the time interval in one frame of reference to the time interval in another frame of reference.
When an observer measures the time interval of an event that occurs in a moving reference frame, the time interval is longer than the time interval measured by the observer who is at rest in the reference frame in which the event occurs.
The ratio of the time interval measured by an observer at rest to the time interval measured by an observer in a moving reference frame is called time dilation.
It is given by
t = T/√[1 - (v/c)²]
where, t is the time interval measured by an observer in a moving reference frame, T is the time interval measured by an observer at rest, v is the velocity of the moving reference frame, and c is the speed of light.
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A mass attached to the end of a spring is oscillating with a period of 2.25s on a horontal Inctionless surface. The mass was released from restat from the position 0.0460 m (a) Determine the location of the mass att - 5.515 m (b) Determine if the mass is moving in the positive or negative x direction at t-5515. O positive x direction O negative x direction
a) The location of the mass at -5.515 m is not provided.
(b) The direction of motion at t = -5.515 s cannot be determined without additional information.
a)The location of the mass at -5.515 m is not provided in the given information. Therefore, it is not possible to determine the position of the mass at that specific point.
(b) To determine the direction of motion at t = -5.515 s, we need additional information. The given data only includes the period of oscillation and the initial position of the mass. However, information about the velocity or the phase of the oscillation is required to determine the direction of motion at a specific time.
In an oscillatory motion, the mass attached to a spring moves back and forth around its equilibrium position. The direction of motion depends on the phase of the oscillation at a particular time. Without knowing the phase or velocity of the mass at t = -5.515 s, we cannot determine whether it is moving in the positive or negative x direction.
To accurately determine the direction of motion at a specific time, additional information such as the amplitude, phase, or initial velocity would be needed.
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1. Derive the equation/s of the volumetric, and linear thermal expansion 2. Derive the equations of the 4 thermodynamic processes and provide its illustration and graphs, and reasoning.
1. Equation of volumetric thermal expansion: βV = (ΔV/V) / ΔT
2. i. Isothermal process: P₁V₁ = P₂V₂
ii. Adiabatic process: P₁V₁γ =P₂V₂γ
iii. Isobaric process: Q = PΔV
iv. Isochoric process: Q = ΔU
Explanation:
1. Equation of volumetric thermal expansion:
Volumetric expansion is defined as the increase in volume of a substance due to a temperature increase.
Volumetric thermal expansion can be calculated using the following equation:
ΔV = βV × V × ΔT
Where:ΔV = change in volume
βV = coefficient of volumetric expansion
V = original volume
ΔT = change in temperature
The coefficient of volumetric expansion is defined as the fractional change in volume per degree Celsius.
It can be calculated using the following equation:
βV = (ΔV/V) / ΔT
2. Equations of the four thermodynamic processes:
There are four thermodynamic processes that are commonly used in thermodynamics: isothermal, adiabatic, isobaric, and isochoric.
Each process has its own equation and unique characteristics.
i. Isothermal process
An isothermal process is a process that occurs at constant temperature.
During an isothermal process, the change in internal energy of the system is zero.
The equation for the isothermal process is:
P₁V₁ = P₂V₂
ii. Adiabatic process:
An adiabatic process is a process that occurs without any heat transfer.
During an adiabatic process, the change in internal energy of the system is equal to the work done on the system.
The equation for the adiabatic process is:
P₁V₁γ =P₂V₂γ
iii. Isobaric process:
An isobaric process is a process that occurs at constant pressure.
During an isobaric process, the change in internal energy of the system is equal to the heat added to the system.
The equation for the isobaric process is:
Q = PΔV
iv. Isochoric process:
An isochoric process is a process that occurs at constant volume.
During an isochoric process, the change in internal energy of the system is equal to the heat added to the system.
The equation for the isochoric process is:
Q = ΔU
From the above expressions, we can conclude that during the isothermal process, the internal energy of the system is constant, during the adiabatic process, there is no heat exchange, during the isobaric process, the volume of the system changes and during the isochoric process, the pressure of the system changes.
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A piano string having a mass per unit length equal to 4.50 ✕
10−3 kg/m is under a tension of 1,500 N. Find the speed
with which a wave travels on this string.
m/s
The speed with which a wave travels on a piano string having a mass per unit length equal to 4.50 ✕ 10−3 kg/m under a tension of 1,500 N is 75 m/s so the speed with which a wave travels on a piano string having a mass per unit length equal to 4.50 ✕ 10−3 kg/m under a tension of 1,500 N is 75 m/s.
A piano is a stringed musical instrument in which the strings are struck by hammers, causing them to vibrate and create sound. The piano has strings that are tightly stretched across a frame. When a key is pressed on the piano, a hammer strikes a string, causing it to vibrate and produce a sound.
A wave is a disturbance that travels through space and matter, transferring energy from one point to another. Waves can take many forms, including sound waves, light waves, and water waves.
The formula to calculate the speed of a wave on a string is: v = √(T/μ)where v = speed of wave T = tension in newtons (N)μ = mass per unit length (kg/m) of the string
We have given that: Mass per unit length of the string, μ = 4.50 ✕ 10−3 kg/m Tension in the string, T = 1,500 N
Now, substituting these values in the above formula, we get: v = √(1500 N / 4.50 ✕ 10−3 kg/m)On solving the above equation, we get: v = 75 m/s
Therefore, the speed with which a wave travels on a piano string having a mass per unit length equal to 4.50 ✕ 10−3 kg/m under a tension of 1,500 N is 75 m/s.
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a 2-kg mass is suspended from an ideal linear spring with a spring constant of 500-n/m. from equilibrium, the mass is raised upward by 1-cm and then let go of. (a) what is the angular frequency of the oscillations that ensue? (b) what is the frequency of the oscillations? (c) what is the period of the oscillations? (d) what is the total energy of the mass/spring system? (e) what is the speed of the mass as it passes through the equilibrium position?
a. The angular frequency of the oscillations is 10 rad/s.
b. The frequency is 1.59 Hz,
c. The period is 0.63 s,
d. The total energy of the mass/spring system is 0.1 J,
e. The speed of the mass as it passes through the equilibrium position is 0.1 m/s.
The angular frequency of the oscillations can be determined using the formula ω = √(k/m), where k is the spring constant (500 N/m) and m is the mass (2 kg). Plugging in the values, we get ω = √(500/2) = 10 rad/s.
The frequency of the oscillations can be found using the formula f = ω/(2π), where ω is the angular frequency. Plugging in the value, we get f = 10/(2π) ≈ 1.59 Hz.
The period of the oscillations can be calculated using the formula T = 1/f, where f is the frequency. Plugging in the value, we get T = 1/1.59 ≈ 0.63 s.
The total energy of the mass/spring system can be determined using the formula E = (1/2)kx², where k is the spring constant and x is the displacement from equilibrium (0.01 m in this case). Plugging in the values, we get E = (1/2)(500)(0.01)² = 0.1 J.
The speed of the mass as it passes through the equilibrium position can be found using the formula v = ωA, where ω is the angular frequency and A is the amplitude (0.01 m in this case). Plugging in the values, we get v = (10)(0.01) = 0.1 m/s.
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) The following data describes a rolling bowling ball.
mass 6 kg, diameter 23 cm, period 0.33 s, acceleration 0 m/s/s, price $17.99
What is its linear speed? 7.59 m/s 2.64 m/s 0.46 m/s 2.89 m/s 2.19 m/s 2.00 m/s
To calculate the linear speed of the given rolling bowling ball, we'll first need to find its circumference using the diameter of the ball as follows:
Circumference,
C = πd
= π × 23 cm
= 72.24 cm
Now, we know that the period of a rolling object is the time it takes to make one complete revolution. Hence, the frequency, f (in revolutions per second), of the rolling bowling ball is given by:
f = 1 / T
where,
T is the period of the ball, which is 0.33 s.
Substituting the given values in the above equation, we get:
f = 1 / 0.33 s
= 3.03 revolutions per second
We can now find the linear speed, v, of the rolling bowling ball as follows:
v = C × f
where,
C is the circumference of the ball,
which we found to be 72.24 cm,
f is the frequency of the ball, which we found to be 3.03 revolutions per second.
Substituting the values, we get:
v = 72.24 cm × 3.03 revolutions per second
= 218.84 cm/s
To convert this to meters per second, we divide by 100, since there are 100 centimeters in a meter:
v = 218.84 cm/s ÷ 100
= 2.19 m/s
Therefore, the linear speed of the given rolling bowling ball is 2.19 m/s. Hence, the correct option is 2.19 m/s.
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Remaining Time: 23 minutes, 44 seconds. ✓ Question Completion Status: L₂ A Moving to another question will save this response. Question 4 0.5 points A stone of mass m is connected to a string of l
Summary:
A stone of mass m is connected to a string of length l. The relationship between the mass and length of the string affects the dynamics of the system. By considering the forces acting on the stone, we can analyze its motion.
Explanation:
When a stone of mass m is connected to a string of length l, the motion of the system depends on several factors. One crucial aspect is the tension in the string. As the stone moves, the string exerts a force on it, known as tension. This tension force is directed towards the center of the stone's circular path.
The stone's mass influences the tension in the string. If the stone's mass increases, the tension required to keep it moving in a circular path also increases. This can be understood by considering Newton's second law, which states that the force acting on an object is equal to the product of its mass and acceleration. In this case, the force is provided by the tension in the string and is directed towards the center of the circular path. Therefore, a larger mass requires a larger force, and thus a greater tension in the string.
Additionally, the length of the string also plays a role in the stone's motion. A longer string allows the stone to cover a larger circular path. As a result, the stone will take more time to complete one revolution. This relationship can be understood by considering the concept of angular velocity. Angular velocity is defined as the rate of change of angle with respect to time. For a given angular velocity, a longer string will correspond to a larger path length, requiring more time to complete a full revolution.
In conclusion, the mass and length of the string are significant factors that influence the dynamics of a stone connected to a string. The mass affects the tension in the string, while the length determines the time taken to complete a revolution. Understanding these relationships allows us to analyze and predict the motion of the system.
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A(n) donkey carries a(n) infinity stone 82.4 m horizontally across a flat desert plain at some constant velocity. If the infinity stone has a mass of 33.0 kg, what is the work done on the infinity stone by the donkey?
______________________
A 97 N force is applied at an angle of 19° above the horizontal to a 3.00 kg box. The box moves a distance of 6.6 meters horizontally. Friction is negligible. Find the work done by the 97 N force.
________________________
A 5.00 kg object is pushed against a spring of spring constant 499 N/m, compressing it a distance of 0.62 m. The object is released and travels 0.10 m across carpeting with a coefficient of kinetic friction of 0.49. It next travels up a frictionless ramp.
How high does it go up the ramp? m
_________________________________
You are traveling along a country road at 22.0 m/s when suddenly you see a tractor 140 m ahead of you. The tractor is traveling at 6.7 m/s and takes up the entire width of the road. Immediately you slam on your brakes, decelerating at 7 m/s2.
How much time will it take you to stop? ss
How far did you travel in the time it takes you to stop? mm
What is the distance between you and the tractor when you finally come to a stop? mm
____________________________________________
Curling is a winter sport in which players slide an 18.0 kg stone across flat, level ice with the stones stopping as close as possible to a target (the "house") some distance away. A curler releases her stone with an initial velocity of 5 m/s, and the stone stops at the house 24.0 s later.
Determine the acceleration of the stone.
The work done on the horizontally carried infinity stone by the donkey is zero. The work done by the 97 N force is 591.4 J. distance traveled is 48.17 meters. the distance between the vehicle and the tractor is approximately 91.83 meters.
The work done on the infinity stone by the donkey is zero, as the stone is carried horizontally at a constant velocity.
The work done by the 97 N force on the 3.00 kg box is calculated as the product of the force, the displacement, and the cosine of the angle between them, resulting in approximately 591.4 J of work done.
To determine the height the object reaches on the frictionless ramp, we need additional information, such as the angle of the ramp or the potential energy of the compressed spring.
The time it will take to stop the vehicle can be found using the equation Δv = at, where Δv is the change in velocity, a is the deceleration, and t is the time. Solving for t gives a time of approximately 3.14 seconds.
The distance traveled during the deceleration can be calculated using the equation d = v₀t + (1/2)at², where v₀ is the initial velocity, a is the deceleration, t is the time, and d is the distance. Plugging in the values, the distance traveled is approximately 48.17 meters.
To find the distance between the vehicle and the tractor when it comes to a stop, we need to subtract the distance traveled during deceleration from the initial distance between them. The distance is approximately 91.83 meters.
The change in velocity can be calculated as the final velocity (0 m/s) minus the initial velocity (5 m/s). Plugging in the values, the acceleration of the stone is approximately -0.208 m/s^2. The negative sign indicates that the stone is decelerating or slowing down.
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Question 7 1 pts Mustang Sally just finished restoring her 1965 Ford Mustang car. To save money, she did not get a new battery. When she tries to start the car, she discovers that the battery is dead (an insufficient or zero voltage difference across the battery terminals) and so she will need a jump start. Here is how she accomplishes the jump start: 1. She connects a red jumper cable (wire) from the positive terminal of the dead battery to the positive terminal of a fully functional new battery. 2. She connects one end of a black jumper cable 2. to the negative terminal of the new battery. 3. She then connects the other end of the black jumper cable to the negative terminal of the dead battery. 4. The new battery (now in a parallel with the dead battery) is now part of the circuit and the car can be jump started. The car starter motor is effectively drawing current from the new battery. There is a 12 potential difference between the positive and negative ends of the jumper cables, which are a short distance apart. If you wanted to move an electron from the positive to the negative terminal of the battery, how many Joules of work would you need to do on the electron? Recall that e = 1.60 x 10-19 C. Answer to 3 significant figures in scientific notation, where 2.457 x 10-12 would be written as 2.46E-12, much like your calculator would show.
To calculate the work required to move an electron from the positive terminal to the negative terminal of the battery, we can use the formula:
Work = Charge * Voltage
Given:
Charge of the electron (e) = 1.60 x 10^-19 C
Potential difference (Voltage) = 12 V
Substituting these values into the formula, we have:
Work = (1.60 x 10^-19 C) * (12 V)
= 1.92 x 10^-18 J
Therefore, the work required to move an electron from the positive terminal to the negative terminal of the battery is approximately 1.92 x 10^-18 Joules.
Note: The positive work value indicates that energy needs to be supplied to move the electron against the electric field created by the battery. In this case, the potential difference of 12 V represents the amount of work required to move the electron across the terminals of the battery.
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Question 7 (5 marks) A coil of 500 turns, cach turn is circular of radius 22 mm, is kept in a constant magnetic field of 20 T so that the plane area of the coil is perpendicular to the magnetic field lines. In 0,66 sec the coil is pulled out of the field. The total resistance of the coil is 50 Ohm. Find the average induced current as the coil is pulled out of the field.
To calculate the average induced current as the coil is pulled out of the field, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) is equal to the rate of change of magnetic flux.
The magnetic flux (Φ) through a coil can be calculated by multiplying the magnetic field strength (B) by the area (A) of the coil and the cosine of the angle (θ) between the magnetic field lines and the plane of the coil:
Φ = B * A * cos(θ)
Given that the magnetic field strength (B) is 20 T, the area (A) of each turn is π * (0.022 m)^2, and the angle (θ) between the magnetic field lines and the plane of the coil is 90 degrees (since it is perpendicular), we can calculate the magnetic flux through one turn of the coil:
Φ = 20 T * π * (0.022 m)^2 * cos(90°) = 0.03094 Wb
The rate of change of magnetic flux (dΦ/dt) is equal to the change in flux divided by the time taken (0.66 s):
dΦ/dt = (0.03094 Wb - 0 Wb) / 0.66 s = 0.04685 Wb/s
The induced electromotive force (emf) can be calculated by multiplying the rate of change of magnetic flux by the number of turns in the coil (N):
emf = N * dΦ/dt = 500 * 0.04685 V = 23.43 V
Finally, we can calculate the average induced current (I) using Ohm's law (V = I * R), where R is the total resistance of the coil (50 Ω):
I = emf / R = 23.43 V / 50 Ω ≈ 0.469 A
Therefore, the average induced current as the coil is pulled out of the field is approximately 0.469 A.
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Suppose you have solved a circuit which has some combination of resistors in parallel and in series by finding its equivalent resistance. If you plotted the voltage versus current for that circuit, what would the slope of that plot be equal to?
The slope of the plot of voltage versus current for a circuit that has a combination of resistors in parallel and in series by finding its equivalent resistance is equal to the equivalent resistance of the circuit.
Thus, the correct option is C.What is equivalent resistance?The equivalent resistance is a solitary resistor that can replace an assortment of resistors to disentangle the circuit and make it simpler to oversee. When two resistors are associated in series, they are joined end-to-end, with the goal that the voltage across one is equivalent to the sum of the voltages across the other. The equivalent resistance of resistors associated in series is equivalent to the total of the individual resistances.
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4. Which graph correctly shows the variation with time of the acceleration a of the particle? W M м н
The graph that correctly shows the variation with time of the acceleration a of the particle is graph W. The acceleration-time graph for a particle is shown below.
A linear graph shows a constant acceleration.What are the terms that need to be included in the answer? To make it a better response, the details on these terms are required.What is acceleration?Acceleration is the rate of change of an object's velocity with respect to time. As a result, it's a vector quantity that has both a magnitude and a direction. When the magnitude of acceleration changes, the speed of an object changes, and when the direction of acceleration changes, the direction of the object's velocity changes as well.
Therefore, it is the rate of change of velocity with time.What is a velocity-time graph?A velocity-time graph depicts how velocity varies over time. It's possible that the object is accelerating or decelerating. It could be moving at a constant velocity, meaning that the velocity-time graph would be a horizontal line with a constant value. The slope of a velocity-time graph represents the acceleration of the object.What is a linear graph?A linear graph is a graphical representation of a linear equation. A line drawn on a two-dimensional plane represents this type of graph. The x and y-axes are both linear, which means that they are both straight lines. In a linear equation, there are no variables in denominators or under a root sign. They have a slope and an intercept.
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A rectangular loop of wire is placed next to a straight wire, as
shown in the (Figure 1). There is a current of III = 4.0 AA in both
wires.
Determine the magnitude of the net force on the loop.
The magnetic field generated by the straight wire at the position of the loop is $\mathbf{B}=\frac{\mu_0 I}{2\pi r}\hat{\boldsymbol{\phi}}$,
where $\mu_0$ is the permeability of free space, $I$ is the current in the straight wire, $r$ is the distance between the straight wire and the center of the loop, and
$\hat{\boldsymbol{\phi}}$ is the unit vector in the azimuthal direction.
The current in the loop will experience a torque due to the interaction with the magnetic field, given by $\boldsymbol{\tau}=\mathbf{m}\times\mathbf{B}$, where $\mathbf{m}$ is the magnetic moment of the loop.
The magnetic moment of the loop is $\mathbf{m}=I\mathbf{A}$, where $\mathbf{A}$ is the area vector of the loop. For a rectangular loop, the area vector is $\mathbf{A}=ab\hat{\mathbf{n}}$, where $a$ and $b$ are the dimensions of the loop and $\hat{\mathbf{n}}$ is the unit vector perpendicular to the loop.
Therefore, the magnetic moment of the loop is $\mathbf{m}=Iab\hat{\mathbf{n}}$.
The torque on the loop is therefore $\boldsymbol{\tau}=\mathbf{m}\times\mathbf{B}=Iab\hat{\mathbf{n}}\times\frac{\mu_0 I}{2\pi r}\hat{\boldsymbol{\phi}}=-\frac{\mu_0 I^2ab}{2\pi r}\hat{\mathbf{z}}$, where $\hat{\mathbf{z}}$ is the unit vector in the $z$ direction.
This torque tends to align the plane of the loop perpendicular to the plane of the straight wire.The force on the loop is given by $\mathbf{F}=\nabla(\mathbf{m}\cdot\mathbf{B})$.
Since the magnetic moment of the loop is parallel to the plane of the loop and the magnetic field is perpendicular to the plane of the loop, the force on the loop is zero. Therefore, the net force on the loop is zero.
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When light passes from a dense medium to a less dense medium, it
bends.
of its original trajectory and the surface normal.
Select one
True
False
True. When light passes from a dense medium to a less dense medium, it bends away from the surface normal. This phenomenon is known as refraction.
Refraction occurs because light travels at different speeds in different media, and when it encounters a change in the optical density (refractive index) of the medium, its direction of propagation changes.
The change in direction is determined by Snell's law, which states that the angle of incidence and the angle of refraction are related to the refractive indices of the two media.
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g. The production characteristics of an Alaska North Slope reservoir include a GOR of 548 scf/STB, stock tank oil of 26.9°API, and a formation volume factor of 1.29 res. Bbl/STB. What type of fluid is in this reservoir? h. The initial reservoir pressure and temperature in a North Sea reservoir is 5000 psia and 260°F. The PVT analysis indicated the bubble-point pressure of the oil at 3500 psia. Is the reservoir fluid saturated or undersaturated? How do you know? 12.2 Producing GOR from a Middle Eastern reservoir, which was monitored for almost 2 years, was found to be constant at 40,000 scf/STB. The separator produced a lightly colored liquid of 50°API. However, after 2 years, the GOR and the condensate API gravity started to increase. a. What type of reservoir fluid exists in this reservoir? b. What was the state of the fluid in the first 2 years? 12.3 Compositional analysis of a reservoir fluid from a field in India reported a C₁ of 15.0 mol %, while the PVT analysis of this fluid indicated a formation vol- ume factor of 2.5 res. bbl/STB. What type of reservoir fluid exists in this field?
The described reservoir fluids include gas-oil mixtures, undersaturated oils, volatile oils, and gas-condensate mixtures.
What types of reservoir fluids are described in the given paragraph?In the given paragraph, several reservoir fluids and their characteristics are described.
In part g, the reservoir fluid from the Alaska North Slope is characterized by a Gas-Oil Ratio (GOR) of 548 standard cubic feet per stock tank barrel (scf/STB), a stock tank oil of 26.9°API, and a formation volume factor of 1.29 reservoir barrels per stock tank barrel (res. Bbl/STB). Based on these properties, it indicates that the fluid in this reservoir is a gas-oil mixture.
In part h, the North Sea reservoir has an initial reservoir pressure and temperature of 5000 psia and 260°F, respectively. The PVT analysis reveals that the bubble-point pressure of the oil is 3500 psia. Since the initial pressure is higher than the bubble-point pressure, the reservoir fluid is considered undersaturated.
This conclusion is drawn based on the fact that the reservoir pressure is above the bubble-point pressure, indicating that the oil is still in a single-phase liquid state.
In part 12.2, the Middle Eastern reservoir initially produces a constant GOR of 40,000 scf/STB and a lightly colored liquid with an API gravity of 50°. However, over time, both the GOR and the condensate API gravity increase.
The type of reservoir fluid present in this reservoir is a volatile oil, which undergoes gas liberation due to pressure depletion. In the first two years, the fluid was in a single-phase liquid state with a constant GOR.
In part 12.3, the reservoir fluid from the Indian field has a C₁ component content of 15.0 mol% and a formation volume factor of 2.5 res. bbl/STB. Based on these properties, it indicates that the reservoir fluid in this field is a gas-condensate mixture.
In summary, the paragraph discusses various reservoir fluids and their characteristics, such as gas-oil mixtures, undersaturated oils, volatile oils, and gas-condensate mixtures, based on their specific properties and analytical results.
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In a hydrogen atom, a given electron has l=7. So just how many
values can the magnetic quantum number have?
(please type the answer, Thank you)
The magnetic quantum number (ml) can have 15 values in the given condition where a given electron in a hydrogen atom has l = 7
The magnetic quantum number (ml) determines the direction of the angular momentum vector. It indicates the orientation of the orbital in space.
Magnetic quantum number has the following values for a given electron in a hydrogen atom:
ml = - l, - l + 1, - l + 2,...., 0,....l - 2, l - 1, l
The range of magnetic quantum number (ml) is from –l to +l. As given, l = 7
Therefore,
ml = -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7
In this case, the magnetic quantum number (ml) can have 15 values.
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Two forces acting on an object, F1=30 N, F2=40 N. The angle between is 90°. To make the object move in uniform linear motion in the direction of F1, a force F3 must be applied. Find the magnitude"
The magnitude of the force F3 required to make the object move in uniform linear motion in the direction of F1 is 50 N, given that F1 = 30 N and F2 = 40 N with a 90° angle between them.
To find the magnitude of the force F3 required to make the object move in uniform linear motion in the direction of F1, we can use vector addition. Since the angle between F1 and F2 is 90°, we can treat them as perpendicular components.
We can represent F1 and F2 as vectors in a coordinate system, where F1 acts along the x-axis and F2 acts along the y-axis. The force F3 will also act along the x-axis to achieve uniform linear motion in the direction of F1.
By using the Pythagorean theorem, we can find the magnitude of F3:
F3 = √(F1² + F2²).
Substituting the given values:
F1 = 30 N,
F2 = 40 N,
we can calculate the magnitude of F3:
F3 = √(30² + 40²).
F3 = √(900 + 1600).
F3 = √2500.
F3 = 50 N.
Therefore, the magnitude of the force F3 required to make the object move in uniform linear motion in the direction of F1 is 50 N.
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What is the volume occupied by 26.0 g of argon gas at a pressure of 1.11 atm and a temperature of 339 K ? Express your answer with the appropriate units. НА ? V = Value Units Submit Request Answer Part B Compare the volume of 26.0 g of helium to 26.0 g of argon gas (under identical conditions). The volume would be greater for helium gas. O The volume would be lower for helium gas. The volume would be the same for helium gas
The volume would be the same for helium gas.
Given the mass of argon gas, pressure, and temperature, we need to find out the volume occupied by the gas at these conditions.
We can use the Ideal Gas Law to solve the problem which is PV= nRT
The ideal gas law is expressed mathematically as PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.1 atm = 101.3 kPa
1 mole of gas at STP occupies 22.4 L of volume
At STP, 1 mole of gas has a volume of 22.4 L and contains 6.022 × 1023 particles.
Hence, the number of moles of argon gas can be calculated as
n = (26.0 g) / (39.95 g/mol) = 0.6514 mol
Now, we can substitute the given values into the Ideal Gas Law as
PV = nRTV = (nRT)/P
Substituting the given values of pressure, temperature, and the number of moles into the above expression,
we get
V = (0.6514 mol × 0.08206 L atm mol-1 K-1 × 339 K) / 1.11 atm
V = 16.0 L (rounded to 3 significant figures)
Therefore, the volume occupied by 26.0 g of argon gas at a pressure of 1.11 atm and a temperature of 339 K is 16.0 L
Part B: Compare the volume of 26.0 g of helium to 26.0 g of argon gas (under identical conditions).
Under identical conditions of pressure, volume, and temperature, the number of particles (atoms or molecules) of the gas present is the same for both helium and argon gas.
So, we can use the Ideal Gas Law to compare their volumes.
V = nRT/P
For both gases, the value of nRT/P would be the same, and hence their volumes would be equal.
Therefore, the volume would be the same for helium gas.
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The maximum speed with which a driver can take a banked curve is 35m / s and the coefficient of friction between the racetrack surface and the tires of the racecar is mu*s = 0.7 and the radius of the turn is R =; 100, 0m Find the acceleration of the car and the angle teta
please i need the answer as fast as possible and i will rate
thanks
Acceleration refers to the rate of change of velocity over time. It measures how quickly an object's velocity is changing or how rapidly its motion is accelerating.
To find the acceleration of the car and the angle θ (theta) for a banked curve, we can use the following equations:
1. Centripetal Force (Fc):
The centripetal force is the force required to keep an object moving in a curved path. For a banked curve, the centripetal force is provided by the horizontal component of the normal force acting on the car.
Fc = m * ac
Where:
Fc is the centripetal force
m is the mass of the car
ac is the centripetal acceleration
2. Centripetal Acceleration (ac):
The Centripetal acceleration is the acceleration toward the center of the curve. It is related to the speed of the car (v) and the radius of the turn (R) by the equation:
ac = v^2 / R
3. Normal Force (N):
The normal force is the perpendicular force exerted by a surface to support an object. For a banked curve, the normal force is split into two components: the vertical component (Nv) and the horizontal component (Nh).
Nv = m * g
Nh = m * ac * sin(θ)
Where:
Nv is the vertical component of the normal force
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Nh is the horizontal component of the normal force
θ is the angle of the banked curve
4. Frictional Force (Ff):
The frictional force is responsible for providing the necessary centripetal force. It is given by:
Ff = μs * Nv
Where:
μs is the coefficient of friction between the tires and the racetrack surface
Now, let's substitute these equations into each other to find the values of acceleration (ac) and angle (θ):
a. Equate the centripetal force and the horizontal component of the normal force:
m * ac = m * ac * sin(θ)
b. Simplify and cancel out the mass (m):
ac = ac * sin(θ)
c. Divide both sides by ac:
1 = sin(θ)
d. Solve for θ:
θ = arcsin(1)
Since sin(θ) can take on values between -1 and 1, the only angle that satisfies this equation is θ = 90 degrees. Therefore, the acceleration of the car is given by ac = v^2 / R, and the angle of the banked curve is θ = 90 degrees.
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"A ball is thrown up with an initial speed of 15.0
m/s. What is the distance traveled after 1s? Assume that the
acceleration due to gravity is 10m/s2 . Round your
answer to the nearest tenth. (
The distance traveled by the ball after 1 second is 10.0 meters.
To calculate the distance traveled by the ball after 1 second, we can use the equation of motion for vertical displacement under constant acceleration.
Initial speed (u) = 15.0 m/s (upward)
Acceleration due to gravity (g) = -10 m/s² (downward)
Time (t) = 1 second
The equation for vertical displacement is:
s = ut + (1/2)gt²
where:
s is the vertical displacement,
u is the initial speed,
g is the acceleration due to gravity,
t is the time.
Plugging in the values:
s = (15.0 m/s)(1 s) + (1/2)(-10 m/s²)(1 s)²
s = 15.0 m + (1/2)(-10 m/s²)(1 s)²
s = 15.0 m + (-5 m/s²)(1 s)²
s = 15.0 m + (-5 m/s²)(1 s)
s = 15.0 m - 5 m
s = 10.0 m
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if the power rating of a
resistor is 10W and the value of the resistor is 40 ohms what is
the maximum current it can draw?
The maximum current that the resistor can draw is 0.5 A.
The power rating of a resistor is given to be 10W and the value of the resistor is 40 ohms.
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
Mathematically it can be expressed as;
V = IR
Here,
V is the voltage across the resistor,
I is the current through the resistor,
R is the resistance of the resistor.
The Power formula states that the power P dissipated or absorbed by a resistor is given by;
P = VI
We are given that the power rating of the resistor is 10W, and the value of the resistor is 40 ohms.
Substituting the values given in the equation of power;
P = VI
10W = V x I
At the same time, we can substitute the value of resistance in the Ohm's law equation;
V = IR
V = 40 ohms x I
On substituting this value of V in the power equation, we get;
10W = (40 ohms x I) x I
10 = 40I²
I² = 1/4
I = 0.5 A
Therefore, the maximum current that the resistor can draw is 0.5 A.
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If a curve with a radius of 95 m is properly banked for a car traveling 67 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 85 km/h? Express your answer using two significant figures.
To determine the required coefficient of static friction for a car not to skid on a curve with a radius of 95 m when traveling at 85 km/h, we first need to calculate the banking angle of the curve.
Using the formula for the banking angle, we find that the angle is approximately 34 degrees. Next, we can calculate the critical speed at which the car would start to skid on the curve, using the formula for critical speed.
The critical speed is found to be approximately 77 km/h. Since the given speed of 85 km/h is greater than the critical speed, the coefficient of static friction required for the car not to skid is not applicable in this case.
To determine the banking angle of the curve, we can use the formula:
tan(θ) = [tex]v^2 / (g * r)[/tex],
where θ is the banking angle, v is the speed of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and r is the radius of the curve. Plugging in the given values, we have:
tan(θ) = (67 km/h)^2 / (9.8 m/s^2 * 95 m).
Simplifying and solving for θ, we find θ ≈ 34 degrees.
Next, we can calculate the critical speed at which the car would start to skid on the curve. The critical speed can be determined using the formula:
v_critical = [tex]√(μ * g * r),[/tex]
where μ is the coefficient of static friction. Plugging in the given values, we have:
v_critical = [tex]√(μ * 9.8 m/s^2 * 95 m).[/tex]
Simplifying and solving for v_critical, we find v_critical ≈ 77 km/h.
Since the given speed of 85 km/h is greater than the critical speed of 77 km/h, the car will start to skid regardless of the coefficient of static friction. Therefore, the coefficient of static friction is not applicable in this case.
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