Work done by friction (rolling resistance)

In summary, the carriage and its passengers start at rest at A and the maximum speed is 20ms-1. At B, the bottom of the ride, the speed is reduced to 10ms-1. There is a vertical distance of 110m between A and B. The length of the track between A and B is 510m. The mass of the carriage and the passengers is 4000kg. By considering the energy changes from A to B, the average frictional force is determined to be 6900 N.
  • #1
Rumplestiltskin
97
3

Homework Statement


The carriage and its passengers start at rest at A. At B, the bottom of the ride, the maximum speed of the carriage is 20ms-1. The vertical distance between A and B is 110m. The length of the track between A and B is 510m. The mass of the carriage and the passengers is 4000kg.

By considering the energy changes from A to B, determine the average frictional force acting on the carriage.

Homework Equations


The Attempt at a Solution



GPE at A = mgh = 4000 * 9.81 * 110 = 4316400 J
KE at B = 0.5 * 4000 * 202 = 800000 J
4316400 - 800000 = 3516400 J work done.
W = Fx. 3516400 = F * 510
F = 6900 N?

 
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  • #2
Rumplestiltskin said:

Homework Statement


The carriage and its passengers start at rest at A. At B, the bottom of the ride, the maximum speed of the carriage is 20ms-1. The vertical distance between A and B is 110m. The length of the track between A and B is 510m. The mass of the carriage and the passengers is 4000kg.

By considering the energy changes from A to B, determine the average frictional force acting on the carriage.

Homework Equations


3. The Attempt at a Solution [/B]

GPE at A = mgh = 4000 * 9.81 * 110 = 4316400 J
KE at B = 0.5 * 4000 * 202 = 800000 J
4316400 - 800000 = 3516400 J work done.
W = Fx. 3516400 = F * 510
F = 6900 N?
Your arithmetic looks fine, but sadly the question is wrong. You do not have enough information to determine the average force.
Average force is ##\Delta p/\Delta t##, where p is momentum and t is time. This comes out the same as ##\Delta E/\Delta s## when the force is constant, but in not general.
See section 3 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/ for a fuller discussion.
 
  • #3
haruspex said:
Your arithmetic looks fine, but sadly the question is wrong. You do not have enough information to determine the average force.
Average force is ##\Delta p/\Delta t##, where p is momentum and t is time. This comes out the same as ##\Delta E/\Delta s## when the force is constant, but in not general.
See section 3 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/ for a fuller discussion.

Will be sure to tell my teacher. :P I guess this should suffice though. Thanks.
 

1. What is work done by friction (rolling resistance)?

Work done by friction, also known as rolling resistance, is the force that opposes the motion of an object as it rolls along a surface. It is caused by the interaction between the surface of the object and the surface it is rolling on, and it results in the conversion of kinetic energy into heat.

2. How is work done by friction (rolling resistance) calculated?

The amount of work done by friction is calculated by multiplying the coefficient of rolling resistance by the normal force and the distance traveled. The coefficient of rolling resistance is a constant that depends on the materials in contact, and the normal force is the perpendicular force exerted by the surface on the object.

3. What factors affect the amount of work done by friction (rolling resistance)?

The amount of work done by friction is affected by several factors, including the type of surface the object is rolling on, the weight of the object, and the speed at which it is rolling. Additionally, the material and condition of the object's wheels or tires can also impact the amount of rolling resistance.

4. How does work done by friction (rolling resistance) impact the efficiency of machines?

In machines that involve rolling motion, such as cars or bicycles, work done by friction can significantly reduce their efficiency. This is because some of the energy that is supposed to be used for motion is instead converted into heat through friction. To improve efficiency, engineers often try to minimize rolling resistance by using smoother or harder materials for surfaces in contact.

5. Can work done by friction (rolling resistance) ever be beneficial?

While work done by friction is usually seen as a source of energy loss, it can also be beneficial in some situations. For example, in car brakes, friction is used to slow down or stop the vehicle. In addition, some machines, such as roller coasters, use friction to control the speed and motion of the ride, making it both safe and enjoyable.

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