# Stopping distance of a car rolling down a hill

• Barnt
In summary, the Homework Statement asks if the mass of a car affects the distance it travels before stopping. The result shows that the mass does not affect the distance traveled before stopping, however the rolling resistance does.

#### Barnt

Hello,

This is an investigation I have been studying recently, can someone help with the following...

1. Homework Statement

Method:

1. Place a toy car at the top of a ramp.
2. Let it go.
3. Measure the distance it travels from the bottom of the ramp.
4. Add a 100 g mass to the car and repeat.
5. Repeat with additional masses attached.

I expect the car with more mass to travel further. However, the results show very little variation

## Homework Equations

This is what I have been thinking...

GPE = KE

Therefore, the masses cancel, therefore each of the cars have the same velocity at the end of the ramp.

The car with the most mass has the most KE. Therefore , more Work is needed to change the cars velocity to zero. Therefore, the car with the most mass should travel the furthest before stopping.

## The Attempt at a Solution

[/B]
I was thinking, the normal force is equal to the car's weight. When the car's weight increases, the normal force increases. The normal force is the force that is doing the work to stop the car. Since the normal force increases when the weight increases, enough work is done to slow the car down.

Equation:

ma = µR
ma = µmg

However, I understand this would only apply to a block sliding down a ramp, not a car with rotating wheels.

Do my results make sense? Should the mass cause the distance traveled by the car to increase?

Barnt said:
Therefore, the masses cancel, therefore each of the cars have the same velocity at the end of the ramp.
That needs an additional assumption about the motion (but the result is right).
Barnt said:
Therefore, the car with the most mass should travel the furthest before stopping.
Where does the work to stop the car come from? Is that the same for both cars?
Barnt said:
The normal force is the force that is doing the work to stop the car.
It is not. It is normal to the motion of the car (on the horizontal part), it cannot do work. It leads to something else that does work, however.

A car with wheels has rolling resistance, within the scope of this question it is very similar to sliding friction.

So, friction is doing the work to stop the car. Friction force = µR. So, ma = µmg. Meaning if the weight increases the friction force increases too, so the mass will not affect the distance traveled by the car before stopping. So, the KE increases with mass but so does the friction force.

Right.
This true while on the ramp already.

If drag becomes important then the situation gets more complicated.

Barnt said:
friction is doing the work to stop the car. Friction force = µR.
To clarify, as mfb indicated, it is a matter of rolling resistance, not friction.
The wheels rotate, so the friction between the wheels and ground is static friction. Static friction does not do work because the points in contact do not move relative to each other.
Rolling resistance is a bit more complicated. In general, it is made up of three different things:
- imperfectly elastic deformation of the wheels
- imperfectlly elastic deformation of the ground
- axial friction
Axial friction is proportional to load, just like regular planar kinetic friction, so leads to the same result. Losses from deformation can rise faster than linearly, though, so a greater mass could lead to less distance.