Question

Suppose that the coefficient of friction between your feet and the floor, while wearing socks, is 0.250. Knowing this, you decide to get a running start and then slide across the floor.

Part A

If your speed is 3.00 m/s when you start to slide, what distance will you slide before stopping?
Express your answer in meters.

Part B

Now, suppose that your young cousin sees you sliding and takes off her shoes so that she can slide as well (assume her socks have the same coefficient of friction as yours). Instead of getting a running start, she asks you to give her a push. So, you push her with aforce of 125 N over a distance of 1.00 m. If her mass is 20.0 kg, what distance d does she slide (i.e., how far does she move after the push ends)? Remember that the friction force is acting anytime that she is moving.
Express your answer in meters.

Answer 1

Part A Answer

The way to solve this is to understand that friction will create a force, and this force will account for a change in energy from start to finish. This change in energy is called work. To start with, recognize that there is a certain kinetic energy when you first start to slide:

KE_i = 1/2 * m * v^2

When you stop sliding, the kinetic energy will be zero. The change is due to the frictional force, and is called work:

W = KE_i – KE_f

And remember that the force due to friction is:

F_fr = μ * m * g

Work is force times distance, so:

W = F_fr * d
W = μ * m * g * d

Therefore:

W = KE_i – KE_f
μ * m * g * d = (1/2 * m * v_i^2) – (1/2 * m * v_f^2)

As you can see, the mass (“m”) cancels out:

μ * g * d = (1/2 * v_i^2) – (1/2 * v_f^2)

Now solve:

μ * g * d = (1/2 * v_i^2) – (1/2 * v_f^2)
0.250 * 9.8 * d = (1/2 * 3.00^2) – (1/2 * 0.00^2)
2.45 * d = 4.5
d = 1.84 m

1.84 m

Part B Answer

The work done pushing is 125 N * 1.00 m = 125 J. So this is the work that friction will do to stop her. The frictional force is equal to μ * m * g, so start by solving for that:

F_fr = μ * m * g
F_fr = 0.250 * 20 * 9.8
F_fr = 49 N

Since you did 125 J of work pushing, friction must do the same amount of work to stop your sister. Work is equal to force times distance, so:

125 = 49 * d
d = 2.55 m

But this is not the answer – remember that you pushed your sister over a distance of 1.00 m. You need to subtract this from the above, in order to find out how far she continues to slide once you stop pushing (because friction is still acting on your sister as you are pushing). So the answer is 2.55 m – 1.00m, which equals 1.55m.

1.55 m