When two objects are separated by a distance then gravitational attraction between them is 1.36 × 10^-9 N.
Given,
m = 1.5 × 10^5 kg
M = 8.5 × 10^2 kg
r = 2500 m
F=GmM/r^2
Here G = 6.67 × 10^-11 N.m^2/kg^2 is the value of the gravitational constant
F = 1.36 × 10^-9 N
Every body in the universe attracts every other body with a gravitational force that decreases with distance as 1/r2. But actually he knew more about the gravitational force: from the fact that bodies of different masses near the earth’s surface accelerate downwards at the same rate, using F = ma (Second Law).
If two bodies of different masses have the same acceleration they must be feeling forces in the same ratio as their masses (so a body twice as massive feels twice the gravitational force), that is, the gravitational force of attraction a body feels must be proportional to its mass.
Newton’s first clue that gravitation between bodies fell as the inverse-square of the distance may have come from comparing a falling apple to the falling moon, but important support for his idea was provided by a detailed description of planetary orbits constructed half a century earlier by Johannes Kepler.
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What measuring device should you use to determine that the internal potential energy of a substance has changed?
A calorimeter is a device which is used to measure and define the internal energy of a system.
A calorimeter is a device used to measure the heat of chemical processes or physical changes, as well as heat capacity. Among the most frequent varieties are differential scanning calorimeters, isothermal micro calorimeters, titration calorimeters, and accelerated rate calorimeters.
A basic calorimeter is just a thermometer attached to a metal container filled with water that is suspended above a combustion chamber. It is a type of measuring instrument used in the study of thermodynamics, chemistry, and biochemistry.
To calculate the enthalpy change per mole of substance A in a reaction involving two compounds A and B, the substances are individually introduced to a calorimeter and the beginning and final temperatures (before and after the reaction) are recorded.
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Draw conclusions: Objects falling through air are slowed by the force of air resistance. Which objects were slowed the most by air resistance
Due to this air resistance, Galileo discovered that heavier or more dense things fall more quickly than less dense ones. Together, a brick and a feather fell. The feather falls more slowly due to air resistance.
Descending against air resistance an object often experiences some air resistance as it falls through the air. The leading surface of the object collides with air molecules, creating air resistance. Several variables affect how much air resistance the object really experiences.
Therefore, heavier things fall quicker than lighter ones because the force of gravity acting on them is greater. As a result, heavier objects accelerate at faster speeds until the force of air resistance acts on them.
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4. A railcar of mass m and speed v collides and sticks to another identical, stationary railcar. The speed of the center of mass of the two-railcar system will be
The required speed of the centre of mass of the two-railcar system after the collision will be half as much as it was before the collision.
One of the railroads has zero motion prior to the collision. Following it, both railroads move at the same speed. By the conservation of the total momentum of the system, we have,
m vi = m vf + m vf
m vi = 2 m vf
vi = 2 vf
vf = 1/2 vi
vf is the velocity after collision
vi is the velocity before collision
Thus, the speed of the railroad together after the collision is calculated to be half of that before collision.
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How do you think the speed a satellite fall towards Earth compares to the speed it is moving forward
The speed a satellite fall towards Earth compares to the speed it is moving forward If the speed drops, it will fall toward the earth.
We can say that satellite speed has a significant impact on satellite motion because if a satellite's speed is reduced by half, it will fall towards the earth because it is drawn in by the earth's gravitational pull. However, if a satellite's speed is doubled, it will travel into space because the earth's gravitational pull will no longer hold it in orbit.
When a satellite is moving quickly, the force of gravity may not be able to hold it in orbit. If it moves slowly, it won't make enough progress to resist gravity's pull and collide with the object it is orbiting.
Rockets are used to put the majority of satellites into orbit. When the pull of Earth's gravity and the satellite's speed are equal, the satellite circled the planet. Without this equilibrium, the satellite would either fall back to Earth or shoot off into space in a straight path.
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1. What is the
momentum of a 1.5 × 103-kilogram car
as it travels at 30. meters per second due east for 60.
seconds?
A) 4.5 x 104 kg m/s, east
B) 4.5 x 104 kg.m/s, west
C) 4.5 x 106 kg•m, east
D) 4.5 x 106 kg•m, west
A 1.5 x 103 kg car's momentum is equal to 4.5 x 104 kg m/s east if it moves at a speed of 30 m/s for 60 seconds while traveling straight east.
What is momentum ?Momentum is a property of an object or system that describes its tendency to move or stay in motion. It is equal to the product of the mass of the object and its velocity. Momentum is conserved, meaning that the total momentum of an isolated system remains constant, regardless of any changes or interactions within the system. Momentum is an important concept in classical mechanics, and is directly related to forces, energy, and angular momentum. Momentum is an essential factor for describing the behavior of objects in motion.
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What pressure, in pascals, can you create by exerting a force of 480 N with your tooth on an area of 0.95 mm2
According to the given statement The pressure exerted by the tooth is 506,315.78 Pa.
What is pressure?Pressure is a measure of the force exerted on a surface per unit area. It is a scalar quantity and is measured in units of force per unit area, such as pascals (Pa), pounds per square inch (psi), or atmospheres (atm).
It can be calculated using the formula:
Pressure (Pa) = Force (N) / Area (m²)
Given that the force exerted is 480 N and the area of contact with the tooth is 0.95 mm^2, we can use the formula to find the pressure exerted:
Pressure (Pa) = 480 N / (0.95 x 10⁻³ m²)
To convert mm² to m², we divide by 10⁶
Pressure (Pa) = 480 N / (0.95 x 10⁻³ m²) = 506,315.78 Pa
Hence, the pressure exerted by the tooth is approximately 506,315.78 Pa.
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How Tyler mentally reacts toward himself when he swings and misses the ball, is called _____.
A) self-talk
B) feedback
C) solution focused
Answer:
A)Self-Talk
Explanation:
Not really sure
A. Self talk
he is mentally reacting to HIMSELF
if energy of 10 watts is transferred into a conatiner of helium, how long does it take to vaporize 1 kg of liquid helium
Consider how much energy is required to melt one kilogram of ice at zero degrees to produce one kilogram of water at zero degrees.
The energy required to melt one kilogram of ice is determined by Q = mLf = (1.0 kg)(334 kJ/kg) = 334 kJ using the equation for a change in temperature and the value for water from Table 1. Water is converted from a liquid to a gas by the process of evaporation, which requires a significant amount of energy. The amount of energy needed to cause the state change is known as the latent heat of vaporization. At 1 atmosphere of pressure, the latent heat of vaporization is 539 calories per gram of water.
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Does temperature or mass affect thermal energy more?
If the temperature doesn't change but the mass of the object increases, the thermal energy in the object increases.
About Thermal energyThermal energy, which is referred to as heat energy, is produced when there is an increase in temperature. Due to the increase in temperature, the molecules and atoms will move faster. Thermal energy, which is referred to as thermal energy, is generated when there is an increase in temperature. Due to the increase in temperature, the molecules and atoms will move faster.
In fact, they would collide even more quickly. In other words, heat energy can be thought of as a form of energy, which is produced when a substance in which atoms and molecules vibrate at a faster rate, due to an increase in temperature.
How is Thermal Energy GeneratedWith that in mind, you need to understand how thermal energy is produced. That's where you need to dive deeper and look at the definition of thermal energy. In the case of matter, atoms and molecules are moving all the time. When the substance is heated, there will be an increase in temperature. It can force particles to move at a faster speed. As a result, you will be able to see how they meet each other. Heat energy can be said to be a form of energy that comes out of a heated substance.
If a substance is hotter, the science of defining heat energy explains how more particles are moving. As a result, you can also get higher heat energy output.
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name the instrument that can be used to measure specific heat capacity
Answer:
thermomiter
Explanation:
Answer:
A thermometer is specifically made to measure on point heat or coldness of a item,
Un avioncito de control remoto viaja con una velocidad constante de 20 km/hr el tiempo en que se realiza el vuelo es de 25 minutos antes que se agote la pila. ¿Qué distancia en pies y kilómetros recorrió el avioncito?
Answer:
Distancia = 27559.06 pies
Explanation:
Dados los siguientes datos;
Velocidad = 20 km/hr
Tiempo = 25 minutos
Conversión de minutos a horas;
60 minutos = 1 hora
25 minutos = 0.42 horas
Para encontrar la distancia;
Distancia = velocidad * tiempo
Distancia = 20 * 0.42
Distancia = 8.4 km
Conversión de kilómetros a pies;
1 km = 3280.84 pies
8.4 kilometros = 8.4 * 3280,84 = 27559,06
Distancia = 27559.06 pies
How do you solve a torque problem in physics?
Calculate the angle between the vector connecting the force's application point and the pivot point and the direction of the applied force. You may calculate the torque by multiplying r by F and sin.
How does physics explain torque?The force that can cause an object to revolve around an axis is measured in torque. Torque accelerates an object in an angular direction, much like force does in linear kinematics.
An easy explanation of torqueAn angular force known as a torque tends to produce rotation along an axis, which could be the center of mass or a fixed point. Torque can also be thought of as a thing's capacity in order to overcome turning resistance, such as a shaft or a gear, that is rotating.
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Calculate the power of a light bulb that uses 40J of electricity in 4 seconds.
Answer:
power=work done /time
power=40J/4s
power=10wat
Suppose the particles in the preceding problem have masses The velocities of the particles are (a) Calculate the angular momentum of each particle about the origin. (b) What is the total angular momentum of the four-particle system about the origin?
Part A: The angular momentum of each particle about the origin
The angular momentum of the first particle is -0.4 kg.m²/s.The angular momentum of the second particle is 0.The angular momentum of the third particle is 1.3 kg.m²/s.The fourth particle's angular momentum is 0.Part B: The total angular momentum of the four-particle system is 0.95 kg.m²/s.
The expression used to calculate angular momentum L is:
L = r x mv
Here, r is the position vector of the object m is the mass and v is the velocity vector.
According to the superposition principle, the resultant angular momentum due to many particles is the vector sum of the individual angular momentum.
L = L₁ + L₂ + L₃ + ...
Here, L₁ is the angular momentum of a particle, L₂ is the angular momentum of the particle, and so on.
In the question
Mass of a particle = 5.0 kg
vector r = (2.0i - 3.0j) m
vector v = (3.0i) m/s
Part A (seen in the picture for instruction)
For particle 1
The position vector is 2.0j m
Substitute 0.10 kg from m₁, 2.0j from r, and 2.0i m/s for v₁ in the expression of angular momentum
L = r x mv
L₁ = (2.0jm) x [(0.10 kg)( 2.0i m/s)]
L₁ = -4.0 kg.m²/s
The angular momentum for the first particle is -4.0 kg.m²/s.
For particle 2
Position vector is (2.0i - 2.0j) m
Substitute 0.20 kg from m₂, (2.0i - 2.0j) m from r, and (3.0i - 3.0j)m/s for v₂ in the expression of angular momentum
L₂ = (2.0i - 2.0j) m x [ (0.20 kg) (3.0i - 3.0j) m/s]
L₂ = 0
The angular momentum for the second particle is 0
For particle 3
The position vector is (-3.0i + 1.0j) m.
Substitute 0.30 kg from m₃, (-3.0i + 1.0j) m from r, and -5.0j m/s for v₃ in the expression of angular momentum
L₃ = (-3.0i + 1.0j) m x [((-3.0i + 1.0j) m) ( -5.0j m/s)]
L₃ = 1.35 kg.m²/s
The angular momentum for three particles is 1.35 kg.m²/s.
For particle 4
The position vector is 4.01i m.
Substitute 0.40 kg from m₄, 4.0i m from r, and -4.0i m/s for v₄ in the expression of angular momentum
L₄ = (4.0i m) x [(0.40 kg) (-4.0i m/s)
L₄ = 0
The angular momentum for four particles is 0.
Part B
Formula used: L = L₁ + L₂ + L₃ + L₄
The total angular momentum of the four-particle system is calculated as follows:
By superposition principle
L = L₁ + L₂ + L₃ + L₄
L = -4.0 kg.m²/s + 0 + 1.35 kg.m²/s + 0
L = 0.95 kg.m²/s
Hence, the total angular momentum of the four-particle system is 0.95 kg.m²/s.
Your question is incomplete but most probably your full question was:
Suppose the particles in the preceding problem have masses m₁ =0.10 kg, m₂=0.20 kg, m₃ = 0.30 kg, m₄ = 0.40 kg. The velocities of the particel are v₁= 2.0i m/s,v₂= (3.0i - 3.0j) m/s, v₃= - 1.5j m/s, v₄= -4i m/s.
(a) Calculate the angular momentum of each particle about the origin.
(b) What is the total angular momentum of the four-particle system about the origin?
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The sound that reaches the ears after bouncing off a wall or a floor is called _____.
(a) direct sound
(b) indirect sound
(c) virtual sound
(d) harmonics.
The correct option is B, the sound that reaches the ears after bouncing off a wall or a floor is called indirect sound.
Indirect sound is a type of sound that is not heard directly by the listener. Instead, it is heard through reflections of the original sound off of nearby surfaces. This sound is more muffled, as the reflections tend to lose some of the original sound's energy as it is reflected from wall to wall. Indirect sound is often used in recording studios and concert halls, as it can create a more natural or realistic sounding environment.
This is due to the fact that in real life, the sound is rarely heard directly by the listener, but rather bounces off of nearby surfaces. By using indirect sound, a more natural sound can be created for the listener. Indirect sound is also used in sound reinforcement systems, as it can help distribute sound more evenly throughout a space. This can help to create a more uniform sound.
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It is known that a damped oscillator has a maximum displacment that is 13.5% of the original amplitude after 0.60 s. What is the value of the time constant
The value of the time constant is = 0.2996 s. Due to the fluid's dampening effect, the oscillations' amplitudes reduce. ma=−bv−kx.
How long does it take for the damped oscillations' amplitude to decrease to half of what it was initially?Its amplitude decreases by half after every ten oscillations. Find the starting time at which the amplitude becomes 11000 times as large as it was initially: Q. A damped harmonic oscillator's displacement is determined by the equation x(t)=e01.
How do amplitude and oscillation relate to one another?In an oscillating system, the amplitude is the amount by which the oscillating variable changes with each oscillation. For instance, sound waves in the air oscillate the atmospheric pressure, and the amplitude of each oscillation is proportional to the variation in the pressure.
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you work at a Dave's donut shop the shop sells a dozen donuts for 6.99 dollars Dave redesigned the Box used to hold one dozen donuts you have been asked to determine whether the company should use the new box or keep the original box the table shows the dimensional of each box and the cost per square foot of cardboard to make each box box original length in 10 waste in six height in three cost per square foot dollar 0.22 new length in 15 waste it with in 11 ties into cost per square foot dollar 0.15 what is the surface area in square inches of the original box? please help I really need help with my work
Answer:
The original box is 180 Inches², the new box is 330 inches²
In 2009, there were 3,494 radio stations across the united states. Radio became a common device for transmitting and receiving signals?
In the United States, there were 3,494 radio broadcasting stations in 2009. Radio reaches approximately 68 percent of American customers aged 12 and older on average each day, and 236 million people listen to radio every week, according to records.
Since their beginnings at the turn of the 20th century, radio stations in the United States have changed. Following the establishment of 8MK in Detroit in 1920, thousands of private and public radio stations have operated across the country. There are several different ways to organise the lists of radio stations in the US.
The Federal Communications Commission oversees radio transmission in the US (FCC). Various broadcasting services, including the following, have been produced under the AM broadcast band, which runs from 540 to 1700 kHz, is where radio transmission initially gained popularity in the 1920s.
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A child whirls a ball at the end of a rope, in a uniform circular motion. Which of the following 19. statements is NOT true? (A) The radius of the circle remains constant the entire time the ball is moving in a circular path. (B) The direction of the tension exerted by the string on the ball is directed towards the center of the Cular path. The magnitude of the ball's acceleration is directly proportional to the length of the string. The velocity of the ball is constant the entire time the ball is moving in a circular path.
The velocity of the ball is constant the entire time the ball is moving in a circular path at the end of a rope, in a uniform circular motion.
Hence, Option D is correct.
A particular kind of motion in which an object moves in a circle at a fixed speed is known as uniform circular motion. Any point on a propeller, for instance, that is rotating at a consistent speed is doing uniform circular motion. Other examples include the watch's second, minute, and hour hands.Because velocity depends on the direction of travel, and in circular motion the object's direction changes at each point, for a body moving in uniform circular motion, the speed the object reaches will remain constant, not the velocity. Acceleration will remain constant as long as speed doesn't change.To know more about Circular motion here
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An ambulance racing down the highway has 14,600,000 J of energy. It is moving 34 m/s. What is the mass of the ambulance? (Round
your answer to two decimal places) KE=1/2mva^2
The ambulance weighs 16.97 tons, and the kinetic energy of an object is given by the formula KE = 1/2mv2, where m is the object's mass, v is its velocity, and KE is the kinetic energy.
What is kinetic energy and above explanation?Kinetic energy is the energy an object possesses due to its motion, and it is calculated as 1/2mv^2, where m is the mass of the object and v is its velocity. It represents the ability of an object to do work by virtue of its motion.Given that the ambulance has 14,600,000 J of energy and is moving at 34 m/s, we can use this formula to find the mass of the ambulance:KE = 1/2mv^214,600,000 J = 1/2m(34 m/s)^2To solve for mass, we can divide both sides of the equation by (1/2)(34 m/s)^2:m = (14,600,000 J) / [(1/2)(34 m/s)^2]m = 14,600,000 J / (1/2)(1156 m^2/s^2)m = 14,600,000 J * (2/1156 m/s^2)m = 16.97 tonSo the mass of the ambulance is approximately 16.97 ton.
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How much heat is required to be removed from a 8kg liquid water at 33 °C to be transformed into ice at 0 °C?
The Total heat required to transform 8 kg of liquid water at 33 °C to the ice at 0 °C is 13,019 J.
The heat required to be removed from a liquid to transform it into a solid is called the heat of fusion. For water, the heat of fusion is approximately 334 J/g. To calculate the amount of heat required to transform 8 kg of liquid water at 33 °C to the ice at 0 °C, we'll need to take into account both the heat of fusion and the heat required to lower the temperature of the water from 33 °C to 0 °C.
First, we'll calculate the heat required to lower the temperature of the water from 33 °C to 0 °C. This can be calculated using the formula:
Q = mcΔT
where Q is the heat required, m is the mass of the water (8 kg), c is the specific heat capacity of water (4.186 J/g·°C), and ΔT is the change in temperature (3temperature change
Q = (8 kg)(4.186 J/g·°C)(33 °C) = 10,347 J
Next, we'll calculate the heat of fusion by multiplying the heat of fusion of water (334 J/g) by the mass of the water (8 kg).
Q = (334 J/g)(8 kg) = 2672 J
To sum up, the total heat required to transform 8 kg of liquid water at 33 °C to ice at 0 °C, is equal to the heat required to lower the temperature + heat of fusion which is 10,347 J + 2672 J = 13,019 J
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PLEASE ANSWER 100 POINTS!!
Juan drives his car around a curve at a speed of 17.0 m/s. Assume the curve can be approximated by an arc of a circle of radius 122.0 m. If a force of 7380 N is required to maintain the car’s circular motion, what is the car’s mass?
In ∑ F = m v^2r , both m and r are unknown but remain constant
What is the centripetal force that allows a car to move around a sharp curve in a roadway?
Any force, or set of forces, can accelerate an object radially or centripetally. A few examples include the tension in a tether ball's rope, the gravitational pull of the Earth on the Moon, the friction between roller skates and a rink's floor, the force of a banked road on a car, and the forces on a centrifuge's tube.
A centripetal force is any net force that produces uniform circular motion. The centripetal force and centripetal acceleration both point in the direction of the centre of curvature. Newton's second equation of motion states that net force equals mass times acceleration, or net F = m a.
The centripetal acceleration—a = a c—determines the rate of acceleration for uniform circular motion.
Consequently, the size of
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If you move 50 meters in 10 seconds, what is your specd?
HERE
Answer:
5 meters per second
Explanation:
To find the unit speed, divide the distance, 50 meters, by the time, 10 seconds.
[tex]\frac{50}{10} =5[/tex]
You moved 5 meters per second. We can check this by seeing how far you move at this rate in 10 seconds. Multiply 5 by 10.
[tex]5\cdot 10=50[/tex]
So, your speed is 5 meters per second.
Good luck ^^
Questions and problems 1) Why at the maximum height, the acceleration of projected object does not equal to zero? 2) What is meant by freely fall acceleration is equal to 9.8m/s²? 3) Describe the characteristics of uniform motion 4) Define these terms. a) distance 5) Explain the difference between distance and displacement. b) displacement d) speed d) velocity e) motion f) rest 6) Distinguish between average speed and instantaneous speed. 7) Give reason when an object falls freely from rest increases its velocity. 8) A car has covered a distance of 600 km in 10 hours. What is its average speed? 9) A body moves at speed of 180 km/h. Calculate the distance it covers in a minute. 10) Calculate the average velocity in km/h for an athlete who covered a distance of 4000 m in 30 minutes.
When an item is projected vertically upward, its velocity is assumed to be zero at its highest point, yet it still experiences acceleration from the gravity of 9.8 m/s^2.
What is meant by freely fall acceleration being equal to 9.8m/s²?This means that anything that is drawn toward the center of the earth has a 9.8-meter acceleration per second as it "falls" to the earth. As a result, each second that such a body is dragged towards the earth, its velocity (the speed with direction) increases by around 9.8 meters per second.
Describe the characteristics of uniform motion.The velocity is constant in uniform motion. In terms of time, neither its magnitude nor its direction change.
Explain the difference between distance and displacement.Distance is the length of any path connecting any two places. When measured along the shortest path between any two points, displacement is the direct distance between them. The direction is ignored when calculating distance. The direction is accounted for in the displacement calculation.
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If your vehicle plunges into deep water, but does not sink immediately, you should escape through a:
If this situation ever happens, you should always try to escape through an open window first because it is your best option.
How do you classify a vehicle?There are several ways to categorize automobiles; in North America, trucks and passenger vehicles are separated by rated rating and total interior capacity, respectively (GVWR). In the European Union, vehicle segments employ linear metrics to represent size.
Why are vehicles important?The private automobile has changed contemporary civilization for more than a century by enabling autonomy and freedom of movement. Due to the growing distances between places like home, work, educational establishments, retail malls, and recreational facilities, mobility has become more and more crucial.
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A tsunami hits northern California at a frequency of 0.25 Hz and a wavelength of 8000 m. What is the speed of the wave?
Answer:
2000 m/s
Explanation:
The speed of a wave is it's frequency * wavelength. In this case, the frequency is 0.25 Hz (waves per second) and the wavelength is 8000m. So the speed of the wave will be 0.25Hz * 8000m which is 2000 meters per second.
A tsunami when hits north California, its speed will be 2000m/s.
What is tsunami?The tsunami caused by the movement of tectonic plates at the sea or ocean floor or due to large volcanic activities . These are high energy waves that can destroy everything.
What is speed?Speed was the pace as well as the direction of an object's movement, whereas speed would be the time rate whereby an object is traveling along a path. In other words, velocity is just a vector, whereas speed would be a scalar value.
In the question, given data is ,
frequency (n) = 0.25 Hz.
Wavelength (λ) = 8000msince
speed of wave (v) = n.λ
on putting values.
v = 0.25×8000 =2000m/s
Hence, the speed of the wave is 2000m/s.
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Suppose two dinosaurs with masses of 80. 0 kg and 120. 0 kg sat on the middle and the far end, respectively, of a tree branch. The dinosaurs produced a net counterclockwise torque of 9,400N•m about the end of the branch that was attached to the tree. What was the length of the branch?
The dinosaurs produced a net counterclockwise torque of 9,400Nm about the end of the branch that was attached to the tree. The length of the branch is 4.7m.
τ = Σr × F = rmg
where g is the acceleration caused by gravity, m is the mass, and r is the distance.
Torque has a direct relationship with -
1.the object's mass, in m
2. The mass's separation, r, from the location where the torque is being calculated.
Therefore, the torque will change whether we increase or reduce them.
Therefore, increasing mass will result in an increase in torque, but since we must retain the same torque, we must reduce mass's distance from the location of the torque.
As a result, the mass should be moved closer to the location of the torque.
Total Mass = (80 + 120)kg
= 200kg
Torque = 9400N
τ = Σr × F = rmg
τ = 200 × r × 10
9400 = 200 × r × 10
r = 9400 / 2000
r = 4.7m
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-----PLZ HELP ME-----Plants use energy from sunlight, water, and carbon dioxide to produce sugar. Which structureis found only in plant cells and helps plants capture energy from sunlight?
A. Vacuole
B. Nucleus
C. Chloroplast
D. Cell membrane
Answer:
c. Chloroplas
Explanation:
A lighthouse that rises 49 feet above the surface of the water sits on a rocky cliff that extends 19 feet from the base. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 30.0 degrees about the horizontal.
If the sailor’s eye level is 14 feet above the water, how far is the ship from the rocks?
If the sailor’s eye level is 14 feet above the water, So the ship from the rocks is 41.62 feet far from the sailor.
The main concepts required to solve this problem are the trigonometric properties and the distance. Later, use the tangent function and substitute the values. Finally, rearrange the tangent equation to calculate the distance of the ship from the rocks.
tan30.0°=35ft./19ft.+x
1/√3=35ft./19ft.+x
x=(35ft.) ([Equation]3)-19ft.
=41.62ft.
A tangent equation is an equation that describes a line that touches a given curve at a single point. It is usually expressed in the form y=mx+b, where m is the slope of the line and b is the y-intercept. To find the equation of a tangent, one must calculate the slope of the line at the point of tangency. This can be done by taking the derivative of the equation of the curve at that point.
The derivative will be the slope of the tangent, so this can be substituted into the tangent equation. The y-intercept can be found by plugging the x-coordinate of the point of tangency into the equation of the curve and solving for y. This will give you the y-intercept of the tangent equation. Through this process, one can find the equation of a tangent to any given curve.
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A light rope is wrapped several times around a large wheel of radius 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis. The free end of the rope is tied to a suitcase of mass 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.5 m/s when it reaches the ground. Calculate (a) the angular velocity of the wheel when the suitcase reaches the ground and (b) the moment of inertia of the wheel.
Answer:
a) ω = 8.75 rad/s
b) I = 12.9 kgm^2
Explanation:
Given data:
Radius of the wheel r = 0.400 m
Speed of the suitcase v = 3.50 m/s
Height h = 4.00 m
Mass of the suitcase m = 15 kg
a) To determine angular velocity of the wheel when the suitcase reaches the ground is
we know that , ω = v / r
ω = (3.50 m/s) / (0.400 m )
ω = 8.75 rad/s
b) From the conservation of energy
we have KEi + Ui = KEf + Uf
where KEi , KEf are initial and final kinetic energies and Ui and Uf are initial and final potentail energies.
We know that KEi = 0 and Uf = 0
Ui = KEf
mgh = (1/2)mv^2 + (1/2) Iω^2
I = moment of inertia of wheel to determined
15×9.8×4 = (1/2) (15)(3.5)^2 + (1/2) I (8.75)^2
Calculating we get
I = 12.9 kgm^2
A force that acts on a body moving in a circular path and is directed toward the center around which the body is moving.
According to the question, The formula is used to find the omega is:-
[tex]w =\frac{v}{r}[/tex]
[tex]w= \frac{3.50}{0.400}[/tex]
Hence, the omega is ω = 8.75 rad/s
From the conservation of energy we have KEi + Ui = KEf + Uf
where Kei, KEf are initial and final kinetic energies and Ui and Uf are initial and final potential energies.
We know that KEi = 0 and Uf = 0
So, therefore the Ui = KEf
Hence [tex]mgh = \frac{1}{2}mv^{2} + \frac{1}{2} Iw^{2}[/tex]
After putting the value:-
[tex]15*9.8*4 = \frac{1}{2}*15*3.5^{2} + \frac{1}{2}*I*8.75^{2}[/tex]
Hence the value of I is[tex]12.9 kgm^2[/tex]
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