**Sliding in Socks**

Part A = 1.84 m

Part B = 1.55 m

**Solution Below:**

Part A

Express your answer in meters.

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

Express your answer in meters.

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

could you please explain problem 8.36 part A and B

thank you

What is problem 8.36?

Can you please help me with this question?

Two point charges, Q1=−31μC and Q2=49μC, are separated by a distance of 12 cm. The electric field at the point P is zero. How far from Q1 is P?

Thank you!

Sure! For your numbers, the answer should be 0.466 m. We posted a detailed solution here.