The equation is a nonlinear equation with a mix of t and v terms.
To find how long the rocket must fire before the sled travels 2000 meters, we need to solve the given equation of motion: 6v˙ = 2700 - 24v. Since the sled starts from rest, its initial velocity (v0) is 0.
First, we need to find the velocity as a function of time. Divide both sides of the equation by 6:
v˙ = (2700 - 24v) / 6
Integrate both sides with respect to time (t):
∫v˙ dt = ∫(450 - 4v) dt
v(t) = 450t - 2v^2 + C
Since the sled starts from rest, when t = 0, v(0) = 0. This allows us to find the constant C:
0 = 450(0) - 2(0)^2 + C
C = 0
So, the velocity equation becomes:
v(t) = 450t - 2v^2
Now, we need to find the position equation by integrating the velocity equation:
∫(450t - 2v^2) dt = ∫(450t - 2(450t - 2v^2)^2) dt
s(t) = 225t^2 - (2/3)v^3 + D
Since the sled starts from rest and has not yet moved, when t = 0, s(0) = 0, which allows us to find the constant D:
0 = 225(0)^2 - (2/3)(0)^3 + D
D = 0
So, the position equation becomes:
s(t) = 225t^2 - (2/3)v^3
We need to find the time t when s(t) = 2000:
2000 = 225t^2 - (2/3)v^3
This equation is a nonlinear equation with a mix of t and v terms. Unfortunately, it does not have an analytical solution, so it would need to be solved using numerical methods such as the Newton-Raphson method or by using a software or calculator with numerical equation-solving capabilities.
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The speakers in a sports stadium are
89. 5 m from a fan's seat. How much
time does it take sound to travel from
the speakers to the fan's seat?
Speed of sound = 343 m/s
(Unit = s)
This is also one I am confused on
The speakers in a sports stadium are 89. 5 m from a fan's seat. It takes approximately 0.261 seconds for sound to travel from the speakers to the fan's seat in the sports stadium.
The time it takes for sound to travel from the speakers to the fan's seat can be calculated using the formula
Time = distance / speed
Where distance is the distance between the speakers and the fan's seat, and speed is the speed of sound in air.
In this case, the distance between the speakers and the fan's seat is 89.5 m, and the speed of sound in air is 343 m/s (at standard temperature and pressure).
Plugging in these values into the formula, we get
Time = 89.5 m / 343 m/s
Time = 0.261 seconds
Therefore, it takes approximately 0.261 seconds for sound to travel from the speakers to the fan's seat in the sports stadium.
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How old was isaac newton when in 1666 he formulated the theory of universal gravity?
Isaac Newton was born on January 4, 1643, in England. He was 23 years old when he formulated the theory of universal gravity in 1666.
This was during a period when he was isolating himself to avoid the bubonic plague outbreak that was ravaging England at that time.
While in isolation, Newton engaged in extensive scientific research and discovered the laws of motion, optics, and gravity.
His theory of universal gravitation proposed that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
This theory revolutionized the field of physics and remains a fundamental concept in modern science.
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If three crests pass Pin in one second, the wavelength is?
The wavelength of the wave as we have it is 3m
What is the wavelength of a wave?A wave's wavelength is the separation between two successive locations on the wave that are in phase, or at the same stage of their cycle. In other terms, it is the separation between two wave crests or troughs.
We know that the wavelength = Number of crests = 3m
Wave speed = 3 m/s
We would then have that;
v = λf
v = wave speed
f = frequency
λ = wavelength
Thus since there are three crests then the wavelength must be 3m
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Help urgent- Two waves travel through the air: wave
A, at 680 Hz, and wave B, at 1760 Hz.
Which wave will travel faster? Why?
The speed of a wave in a medium depends on the properties of that medium, such as its density and elasticity. The frequency of the wave, or the number of cycles it completes in a second, does not affect its speed.
Therefore, both wave A and wave B will travel through the air at the same speed, which is approximately 343 meters per second at room temperature and atmospheric pressure.
However, the wavelength of a wave is inversely proportional to its frequency, so wave B will have a shorter wavelength than wave A.
This means that wave B will have a higher energy and be more directional than wave A, but it will not travel faster through the air.
In summary, the frequency of a wave does not affect its speed in a given medium, and both wave A and wave B will travel through the air at the same speed of approximately 343 meters per second.
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If the magnitude of the drift velocity of free electrons in a copper wire is 8. 32 10-4 m/s, what is the electric field in the conductor
The electric field in the copper wire is approximately 7.63 x [tex]10^{-5}[/tex] V/m. The drift velocity of free electrons in a copper wire is given as 8.32 x [tex]10^{-4}[/tex] m/s.
The electric field in a conductor is directly proportional to the drift velocity. The relationship between drift velocity and electric field is given by:
vd = (eEτ)/(m)
where,
vd = drift velocity of electrons
e = charge of an electron
E = electric field
τ = relaxation time of electrons
m = mass of an electron
Assuming the values of e, m, and τ for copper, we can solve for the electric field:
E = (vd x m)/(eτ)
E = (8.32 x [tex]10^{-4}[/tex] m/s x 9.11 x [tex]10^{-31}[/tex] kg)/(1.6 x [tex]10^{-19}[/tex] C x 2.3 x [tex]10^{-14}[/tex] s)
E ≈ 7.63 x [tex]10^{-5}[/tex] V/m
Therefore, the electric field in the copper wire is approximately 7.63 x [tex]10^{-5}[/tex] V/m.
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Select the statement that is NOT true
the magnetic field lines always cross one another
the magnetic field lines have the same strength
magnetic field lines flow from north to south
magnetic field lines are concentrated at the poles
The statement that is NOT true is: "the magnetic field lines always cross one another."
What is the true statement?Magnetic field lines do not cross one other since they depict the direction of the magnetic field at every position in space. The crossing of two field lines would cause the magnetic field to have two opposite directions at the same spot, which is not possible.
The magnetic field's direction is determined by the orientation of the magnetic dipole moment at its source of starting.
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how friction oppse motion
Answer:
setting a stationary body in motion.
Explanation:
like a stationary car will start moving when driving force is applied
Which one of the following instrument is most suitable for measuring thickness of
the physics book?
A. Meter rule ⃝ B. Vernier calipers ⃝
C. Measuring tape ⃝ D. Screw gauge ⃝
The most suitable instrument for measuring the thickness of a physics book is B. Vernier calipers, as they provide a higher degree of accuracy and precision compared to the other options.
One of the key advantages of Vernier calipers is their ability to provide measurements with a high level of precision. The Vernier scale allows for measurements to be read to a fraction of the smallest division on the main scale, significantly increasing the accuracy of the measurement.
This is especially useful when dealing with objects that have small dimensions or require precise measurements, such as the thickness of a book.
Furthermore, Vernier calipers often have a fine adjustment mechanism that enables the user to ensure a tight fit around the object being measured, minimizing any potential errors due to play or movement. This feature contributes to the overall accuracy of the measurements.
In comparison to other measuring instruments, such as a ruler or a tape measure, Vernier calipers provide a greater level of precision. Rulers, for example, typically have larger increments and are better suited for measuring longer distances rather than small thicknesses.
Tape measures, on the other hand, can be flexible and might not provide the same level of accuracy as Vernier calipers, especially when measuring thin objects.
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During the course of a hot, summer day the temperature of the wooden beam slowly increases from 15°C at night to a final temperature of 35°C during the day. Calculate the amount of heat transferred to the wooden beam if it has mass 60kg
The amount of heat transferred to the wooden beam is 2,040,000 Joules.
During the course of a hot, summer day, the temperature of the wooden beam slowly increases from 15°C at night to a final temperature of 35°C during the day.
To calculate the amount of heat transferred to the wooden beam with a mass of 60kg, follow these steps:
Step 1: Determine the temperature change (∆T)
∆T = [tex]T_{final} - T_{initial}[/tex]
∆T = 35°C - 15°C
∆T = 20°C
Step 2: Find the specific heat capacity (c) of the wooden beam
The specific heat capacity of wood varies depending on its type. For this example, let's use an average specific heat capacity of wood, which is approximately 1700 J/(kg·K).
Step 3: Calculate the amount of heat transferred (Q) using the formula:
Q = mc∆T
where
m is the mass of the wooden beam,
c is the specific heat capacity of wood, and
∆T is the temperature change.
Step 4: Plug in the values and solve for Q
Q = (60 kg)(1700 J/(kg·K))(20 K)
Q = 2,040,000 J
Therefore, the amount of heat transferred to the wooden beam is 2,040,000 Joules.
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A ball bounces off the floor elastically as shown. The direction of the change in momentum of the ball is.
The direction of the change in momentum of the ball is in the opposite direction of its original momentum. This is because when the ball bounces off the floor, it experiences an equal and opposite force, which causes its momentum to change direction.
This is known as an elastic collision, and the change in momentum is equal in magnitude to the original momentum but in the opposite direction. This is because the total momentum is conserved in the collision. This means that the sum of the momentum of the ball after the collision is equal to the sum of the momentum of the ball before the collision.
Since the ball has no external forces acting on it, the only way for the momentum to remain the same is for the momentum to change direction. Therefore, the direction of the change in momentum of the ball is in the opposite direction of its original momentum.
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Which choice best explains the definition of a variable?
1. A variable is one way that scientists collect and record data in a scientific investigation.
2. A variable is something that can change and may affect the outcome in a scientific investigation.
3. A variable is a type of testable question that scientists ask when beginning a scientific investigation.
4. A variable is an educated guess that scientists make before conducting a scientific investigation
The best choice that explains the definition of a variable is, a variable is something that can change and may affect the outcome in a scientific investigation. Option 2 is correct.
In scientific investigations, a variable is a factor or condition that can be changed or varied, and may have an effect on the outcome of the investigation. Variables are often classified into independent, dependent, and controlled variables. The independent variable is the factor that is intentionally changed by the researcher to observe its effect on the dependent variable, which is the factor that is being measured or observed.
While the other choices are related to scientific investigations, they do not accurately define what a variable is. A variable is a factor or condition that can change and potentially affect the outcome of an experiment or scientific investigation. Option 2 is correct.
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Blue jeans (blank) blue light, so that we see them as the color blue.
Answer:
Blue Jeans (are) blue light,
so that we see them as the color
The maximum allowable resistance for an underwater cable is one hundredth of an ohm per
meter and the resistivity of copper is 1. 54 x 10-80m.
a) Calculate the smallest cross sectional area of copper cable that could be used.
The copper cable's smallest possible cross-sectional area is 1.54 x 10-6 square meters.
To calculate the smallest cross-sectional area of the copper cable, we can use the formula for resistance:
R = ρ(L/A),
where R is the resistance (in ohms), ρ is the resistivity of the material (in ohm meters), L is the length of the conductor (in meters), and A is the cross-sectional area (in square meters).
Given the maximum allowable resistance (R) is 0.01 ohms per meter (one-hundredth of an ohm per meter) and the resistivity of copper (ρ) is 1.54 x 10^-8 ohm meters. Let's calculate the smallest cross-sectional area (A) that can be used.
First, we'll rewrite the formula for A:
A = ρ(L/R).
Since R is given as ohms per meter, we can set L to 1 meter for simplicity, and the formula becomes:
A = ρ(1/R).
Now, we can plug in the given values:
A = (1.54 x 10^-8)/(0.01).
A = 1.54 x 10^-6 square meters.
So, the smallest cross-sectional area of the copper cable that could be used is 1.54 x 10^-6 square meters.
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Josh pushes a table with a force of 80. N at an angle of 30°
to the table. If he pushes the table 5 meters, how much
work has he done? Joules
Josh pushes a table with a force of 80. N at an angle of 30° to the table. If he pushes the table 5 meters then Josh has done 346.41 Joules of work on the table.
To calculate the work done by Josh on the table, we can use the formula:
[tex]W = F \times d \times cos(\theta)[/tex]
where W is the work done, F is the force applied, d is the distance moved, and theta is the angle between the force and the direction of motion.
Substituting the given values, we get:
[tex]W = 80 N \times 5 m \times cos(30^{\circ})[/tex]
W = 346.41 J
Therefore, Josh has done 346.41 Joules of work on the table. To understand the concept of work, it is important to note that work is done when a force is applied to an object and it causes it to move.
In this case, Josh applies a force of 80 N at an angle of 30° to the table, causing it to move 5 meters. The work done is calculated by multiplying the force, distance, and cosine of the angle between them.
In summary, to calculate the work done by Josh on the table, we use the formula [tex]W = F \times d \times cos(\theta)[/tex] , where W is the work done, F is the force applied, d is the distance moved, and theta is the angle between the force and the direction of motion.
By substituting the given values, we find that Josh has done 346.41 Joules of work on the table.
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Max, the student standing 80 meters from the metronome, heard something different than all the other students. what did the clapping sound like to him
Max would hear the clapping sound at a slightly slower tempo compared to the other students.
Assuming that the speed of sound in air is approximately 343 m/s at room temperature and sea level, we can calculate the time it takes for the sound wave to reach Max's ears.
Using the equation distance = speed x time, we can rearrange it to get time = distance/speed. Plugging in the values, we get time = 80/343 = 0.233 seconds.
The metronome produces sound waves at a constant frequency. At a distance of 80 meters, the sound waves would have to travel a longer distance to reach Max's ears compared to the other students who are closer.
This means that the time it takes for the sound waves to travel from the metronome to Max's ears is longer than for the other students. As a result, Max would hear the clapping sound at a slightly slower tempo compared to the other students.
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with the switch open, the potential difference across the capacitor in figure p23.44 is 10.0 v. after the switch is closed, how long will it take for the potential difference across the capacitor to decrease to 5.0 v?
It will take approximately 5.54 ms for the potential difference across the capacitor to decrease from 10.0 V to 5.0 V after the switch is closed.
The time constant of the circuit can be calculated using the formula RC, where R is the resistance in the circuit and C is the capacitance of the capacitor. From the diagram, we can see that the resistance in the circuit is 4.00 kΩ and the capacitance of the capacitor is 2.00 μF. Therefore, the time constant of the circuit is:
RC = 4.00 kΩ × 2.00 μF = 8.00 ms
When the switch is closed, the capacitor will start to discharge through the resistor. The rate at which the potential difference across the capacitor decreases is given by:
V = V0 × e^(-t/RC)
Where V is the potential difference across the capacitor at time t, V0 is the initial potential difference across the capacitor (10.0 V in this case), and e is the base of the natural logarithm.
To find the time it takes for the potential difference across the capacitor to decrease to 5.0 V, we can rearrange the equation to:
t = -RC × ln(V/V0)
Substituting the values given, we get:
t = -8.00 ms × ln(5.0 V/10.0 V) = 5.54 ms
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A tourist follows a passage which takes her 160 m west, then 180 m at an angle of 45. 0∘ south of east and finally 250 m at an angle 35. 0∘ north of east. The total journey takes 12 minutes.
a. Calculate the magnitude of her displacement from her original position. (4)
b. She measures the distance she has walked to a precision of 5%. She times her total journey to ±20 s.
(i) What is her average speed?
(ii) What is the absolute uncertainty on her absolute speed?
The three components of the journey's vector is 267.7 m, the displacement by the time taken is 22.3 m/min, the average speed is 23 m/min and the average speed with a precision of ±5% and ±20 s is 21.9 m/min to 23 m/min.
What is magnitude?Magnitude is a measure of the size or intensity of something. It is usually a numerical quantity or value, such as size, energy, power, intensity, brightness, strength, or speed. Magnitude is a mathematical concept that is used to compare and evaluate different values.
Using this theorem, we can find the magnitude of the displacement (d) by taking the square root of the sum of the squares of the three components of the journey's vector.
d = √(160² + (180*cos45)² + (250*cos35)²)
d = √(25600 + 25600 + 20625)
d = √71725
d ≈ 267.7 m
To calculate the average speed, we need to divide the magnitude of the displacement by the time taken.
Average Speed = d/t
Average Speed = 267.7 m/12 min
Average Speed = 22.3 m/min
To account for the precision of ±5%, we can add or subtract 5% of the displacement, and ±20 s of the time taken.
Using the new values, we can calculate the average speed as follows:
Average Speed = (267.7 ± 13.4 m)/(12 min ± 20 s)
Average Speed = (254.3 m - 281.1 m)/(11 min 40 s - 12 min 20 s)
Average Speed = (254.3 m/11 min 40 s) - (281.1 m/12 min 20 s)
Average Speed = 21.9 m/min - 23 m/min
Therefore, the average speed with a precision of ±5% and ±20 s is 21.9 m/min to 23 m/min.
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the earth travels around the sun in an almost circular orbit at an almost constant speed of 107,300 km/h (or 67,062 mi/h)! which statement(s) are true about the earth's motion about the sun?multiple select question.the earth is going too fast to accelerate any more.the earth is not accelerating since we earthlings do not feel the acceleration.the earth is not accelerating since its speed is constant.the earth has a velocity that is always changing.the earth cannot accelerate since it is in space.the earth is accelerating since the direction of its velocity is changing.
The statement that the earth is accelerating since the direction of its velocity is changing is true, as changes in direction are also changes in velocity, which constitutes acceleration
The statement that the earth is going too fast to accelerate any more is false. This is because acceleration is a change in velocity, which can occur even if the speed is constant.
The statement that the earth is not accelerating since we earthlings do not feel the acceleration is also false, as acceleration is a physical property of an object's motion, independent of perception.
The statement that the earth is not accelerating since its speed is constant is true, as acceleration is defined as a change in velocity, which includes changes in speed or direction.
The statement that the earth has a velocity that is always changing is also true, as its motion around the sun is not perfectly circular and is affected by other celestial bodies.
The statement that the earth cannot accelerate since it is in space is false, as acceleration is a property of motion regardless of the medium in which it occurs.
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A tank for storing liquid has a base of area 1. 5msquare what is the pressure on the base of the tank when it contain oil weighing 6000N
The pressure on the base of the tank is: 4000 Pa when it contains oil weighing 6000 N with a base area of 1.5 m².
Pressure is defined as force per unit area. In this case, the force acting on the base of the tank is the weight of the oil, which is given as 6000 N. The area of the base is 1.5 m². Using the formula for pressure, we can calculate the pressure as:
Pressure = Force / Area
Substituting the given values, we get:
Pressure = 6000 N / 1.5 m² = 4000 Pa
Therefore, the pressure on the base of the tank when it contains oil weighing 6000 N with a base area of 1.5 m² is 4000 Pa.
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a 1.90-m-long wire having a mass of 0.100 kg is fixed at both ends. the tension in the wire is maintained at 21.0 n.
The fundamental frequency of the 1.90-m-long wire with a mass of 0.100 kg and tension of 21.0 N is approximately 5.24 Hz.
Given the information provided, we have a 1.90-m-long wire with a mass of 0.100 kg that is fixed at both ends and has a tension of 21.0 N.
To find the linear mass density (µ) of the wire, we can use the following formula:
µ = mass/length
Using the given values, we can calculate µ as follows:
µ = 0.100 kg / 1.90 m = 0.05263 kg/m
Now that we have the linear mass density, we can find the fundamental frequency (f) using the formula:
f = (1 / 2L) × √(T / µ)
Where:
f = fundamental frequency
L = length of the wire
T = tension
µ = linear mass density
Substituting the values we found earlier, we get:
f = (1 / 2 × 1.90 m) × √(21.0 N / 0.05263 kg/m)
f ≈ 0.263 × √(399.2) ≈ 5.24 Hz
So, the fundamental frequency of the 1.90-m-long wire with a mass of 0.100 kg and a tension of 21.0 N is approximately
5.24 Hz.
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physicist s. a. goudsmit devised a method for measuring accurately the masses of heavy ions by timing their periods of revolution in a known magnetic field. a singly charged ion makes 6.00 rev in a 40.0 mt in 1.32 ms. calculate its mass, in atomic mass units.
A singly charged ion makes 6.00 rev in a 40.0 mt in 1.32 ms. The atomic mass of the singly charged ion is 24.3 atomic mass units
Physicist S.A. Goudsmit devised a method for accurately measuring the masses of heavy ions by timing their periods of revolution in a known magnetic field. This method is known as the magnetic moment method. It involves the use of a magnetic field to deflect the ion in a circular path, and measuring the time it takes for the ion to complete a full revolution. The mass of the ion can then be calculated from its charge, the magnetic field strength, and the time taken for one revolution.
In this case, we are given that a singly charged ion makes 6.00 revolutions in a magnetic field of 40.0 millitesla in 1.32 milliseconds. To calculate its mass in atomic mass units (amu), we can use the formula:
mass = (charge x magnetic field x period) / (2 x pi)
where charge is the charge of the ion (in Coulombs), magnetic field is the strength of the magnetic field (in Tesla), period is the time taken for one revolution (in seconds), and pi is the mathematical constant pi.
Since the ion is singly charged, its charge is 1.6 x 10^-19 C. Converting the magnetic field from millitesla to Tesla, we get 0.04 T. Converting the period from milliseconds to seconds, we get 0.00132 s. Plugging in these values, we get:
mass = (1.6 x 10^-19 C x 0.04 T x 0.00132 s) / (2 x pi) = 4.04 x 10^-26 kg
To convert this mass to atomic mass units, we divide by the mass of one atomic mass unit (1.66 x 10^-27 kg/amu):
mass in amu = (4.04 x 10^-26 kg) / (1.66 x 10^-27 kg/amu) = 24.3 amu
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Day 58
1. Developing decision-making skills is a vital aspect that occurs during which stage of adolescent development?
social development
physical development
emotional development
intellectual development
4
Answer:
Developing decision-making skills is a vital aspect that occurs during the stage of intellectual development in adolescent development.
Explanation:
During adolescence, individuals undergo significant changes in their cognitive abilities, including an increase in abstract thinking, reasoning, and problem-solving skills. These changes allow adolescents to start thinking critically and independently, weigh options, and make more informed decisions about their lives.
As adolescents develop their intellectual abilities, they also gain more control over their lives and begin to make decisions about their education, career paths, relationships, and other important aspects of their lives. This is a critical time for developing decision-making skills, as the decisions made during adolescence can have significant and long-lasting effects on individuals' lives.
While other aspects of adolescent development, such as social, emotional, and physical development, are also important, intellectual development plays a crucial role in helping adolescents navigate the complex and challenging decisions they face as they transition to adulthood.
Particles q1, q2, and q3 are in a straight line. Particles q1 = -5. 00 x 10^-6 C, q2 = +2. 50 x 10^-6 C
The net force acting on q₂ when Particle is positioned between q₁ and q₃ is 0.486N.
Inversely proportional to the square of the distance between charges and proportionate to the product of their magnitudes is the electrostatic force of attraction or repulsion.
Force on q₂ due to q₁
F₁₂ = kq₁q₂ / r₁₂²
Putting the values provided , may get
F₁₂ = 9 x 10⁹ x 5 x 10⁻⁶ x 2.5 x 10⁻⁶ / (0.5)²
F₁₂ = 0.414 N
Force on q₂ due to q₃ placed at distance 0.25m
F₂₃ =kq₂q₃ / r₂₃²
Substitute the values, can get
F₂₃ = 9 x 10⁹ x 2.5 x 10⁻⁶ x 2.5 x 10⁻⁶ / (0.25)²
F₂₃ = 0.9N
The net force can be calculated as
F =F₂₃ -F₁₂
F =0.9 - 0.414 = 0.486 N
Therefore, the net force of q₂ is 0.486 N.
The complete question is,
Particles q1, q2, and q3 are in a straight line. Particles q1 = -5.00 x 10^-6 C, q2 = +2.50 x 10^-6 C, and q3 = -2.50 x 10^-6 C. Particles q1 and q2 are separated by 0.500 m. Particles q2 and q3 are separated by 0.250 m. What is the net force on q2?
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NEED HELP FAST!!!! Please answer both questions
Answer:
1. 0.102 mol/kg.
2. 0.444 mol/kg.
Explanation:
Work on 1.To calculate molality, we need to know the moles of solute (NaCl) and the mass of the solvent (water) in kilograms. First, we need to convert the mass of NaCl to moles by dividing by its molar mass. Then we convert the mass of water to kilograms. Molality (m) is equal to moles of solute divided by kilograms of solvent.
Work on 2.
First, we need to convert the mass of glucose to moles by dividing by its molar mass. Then we convert the volume of water to kilograms. Molality (m) is equal to moles of solute divided by kilograms of solvent. Finally, we need to round the answer to three significant figures.
if an object is speeding up, which of the following is true?multiple choice question.distance and speed are inversely proportional.the signs of the velocity and acceleration are the same.the magnitude of velocity and acceleration are always zero.the signs of the velocity and acceleration are different.
If an object is speeding up, the sign of its velocity and acceleration are the same. Option B is correct.
This means that both velocity and acceleration are positive if the object is moving in the positive direction and negative if the object is moving in the negative direction. Acceleration is defined as the rate of change of velocity over time, so if an object is speeding up, its velocity is increasing over time. This increase in velocity can be positive or negative, depending on the direction of motion, but in either case, the acceleration must be in the same direction as the velocity.
Distance and speed are not inversely proportional in this case, as they can both increase or decrease together when an object is speeding up. The magnitude of velocity and acceleration are not always zero, as they can be positive or negative depending on the direction of motion. Option B is correct.
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An airplane and a freight train have the same momentum. The airplane has a mass of 21,700 kg and is traveling at 1,200 km/h. The train has a mass of 9,600,000 kg. What is the speed of the train?
Select one:
A: 2. 7 km/h
B:19. 0 km/h
C:25. 0 km/h
D: 5. 3 km/h
An airplane and a freight train have the same momentum, but the train's speed is much slower due to its much larger mass. The train's speed is approximately 9.8 km/h. The correct option is B.
The momentum of an object is the product of its mass and velocity. If two objects have the same momentum, their product of mass and velocity will be equal. We can use this principle to determine the speed of the freight train, given the momentum of the airplane.
The momentum of the airplane is:
[tex]p = m \times v[/tex]
[tex]p = 21,700\;kg \times (1,200\;km/h \times 1000\;m/km)[/tex]
p = 26,040,000 kg m/s
Since the momentum of the airplane and the train are equal, we can set their momentum equations equal to each other:
[tex]p = m \times v[/tex]
[tex]26,040,000\;kg\;m/s = 9,600,000\;kg \times v[/tex]
Solving for v, we get:
v = 26,040,000 kg m/s / 9,600,000 kg
v = 2.71 m/s
To convert the velocity from meters per second to kilometers per hour, we multiply by 3.6:
[tex]v = 2.71 m/s \times 3.6\;km/h/m[/tex]
v = 9.8 km/h
Therefore, the speed of the freight train is approximately 9.8 km/h, which is option B.
In summary, the momentum of the airplane is used to determine the velocity of the freight train, which can be calculated using the momentum equation. The velocity of the freight train is found to be approximately 9.8 km/h.
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At the gym, a man pulls a bar on a machine that works the muscles of the upper back. It takes him 0. 5 seconds to raise 30
kilograms of weights a vertical distance of 0. 5 meters.
Which of these exerts the same power output? (Estimate g as 10 m/s2. )
A) lifting 25 kilograms a distance of 2. 4 meters in 2. 0 seconds
B) lifting 45 kilograms a distance of 2. 4 meters in 3. 0 seconds
C) leg pressing 45 kilograms a distance of 0. 5 meters in 0. 5 seconds.
D) bench pressing 30 ligrograms a distance of 0. 5 meter in 1. 5 seconds.
Pleaseeeeeee help me
The power output of the man pulling the bar can be calculated as follows:
Power = Work / Time
The work done by the man is equal to the force he exerts multiplied by the distance he moves the weights:
Work = Force x Distance
The force he exerts is equal to the weight of the weights he is lifting:
Force = Weight x g
where g is the acceleration due to gravity, which is approximately 10 m/s^2.
Plugging in the given values, we get:
Force = 30 kg x 10 m/s^2 = 300 N
Work = Force x Distance = 300 N x 0.5 m = 150 J
Power = Work / Time = 150 J / 0.5 s = 300 W
Now we can check which of the other options exerts the same power output:
Option A:
Force = 25 kg x 10 m/s^2 = 250 N
Work = Force x Distance = 250 N x 2.4 m = 600 J
Power = Work / Time = 600 J / 2.0 s = 300 W
Option B:
Force = 45 kg x 10 m/s^2 = 450 N
Work = Force x Distance = 450 N x 2.4 m = 1080 J
Power = Work / Time = 1080 J / 3.0 s = 360 W
Option C:
Force = 45 kg x 10 m/s^2 = 450 N
Work = Force x Distance = 450 N x 0.5 m = 225 J
Power = Work / Time = 225 J / 0.5 s = 450 W
Option D:
Force = 30 kg x 10 m/s^2 = 300 N
Work = Force x Distance = 300 N x 0.5 m = 150 J
Power = Work / Time = 150 J / 1.5 s = 100 W
Therefore, options A and B exert the same power output as the man pulling the bar, while options C and D do not.
45 N
15 N
Net Force:
Is it balanced or unbalanced?
net force: 60( not sure)
I would say it's unbalanced because these forces are not of the same magnitude.
A mechanical system is used to pull a tarp over a grass tennis
court. On a clear, sunny day, the efficiency of the system is
55%. After a rainstorm, the efficiency is measured to be 65%.
Explain why there is a difference in the efficiencies.
The difference in efficiencies of the mechanical system can be attributed to several factors such as increase in frictional force between the tarp and the system, an increase in tarp weight owing to water absorption, and an overall increase in resistance on the grass court due to wetness.
Firstly, the frictional force between the tarp and the mechanical system may have increased due to water on the tarp, leading to a decrease in efficiency.
Secondly, the weight of the tarp may have increased due to water absorption, leading to a greater load on the mechanical system, which in turn reduces efficiency.
Thirdly, the presence of water on the grass court may have increased the overall resistance to the movement of the tarp, leading to a decrease in efficiency.
These factors combined may explain the observed difference in efficiencies between the clear, sunny day and after a rainstorm.
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One form of energy that exists in every system but is difficult to quantify is heat. Think about how we formulated our spring resonance model. Did we account for the heat energy in the medium? why do we need to?.
No, our spring resonance model did not account for the heat energy in the medium. Heat energy is generated due to the friction between the spring and the medium during the oscillation of the spring.
This energy is dissipated into the medium in the form of thermal energy, causing the amplitude of the oscillation to decrease over time.
In order to develop an accurate and complete model of the spring resonance, we need to account for the heat energy generated during the oscillation.
This is important because the amount of heat generated depends on the mechanical properties of the medium and the frequency and amplitude of the oscillation, and can have a significant impact on the behavior of the system.
By accounting for heat energy, we can better understand the dynamics of the system and predict how it will behave over time.
This can be particularly important in practical applications, such as in engineering and design, where we need to know how a system will perform under different conditions and over long periods of time.
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