Suppose a 52 n sled runs on packed snow. the coefficient of friction is only 0.11. if a person weighing 700 n sits on the sled, what force is needed to pull the sled across the snow at constant speed?

A force of 83 N is needed to pull the sled with constant speed.

Explanation:

Hi there!

Please, see the attached figure for a graphical description of the problem.

We have the following horizontal forces applied on the sled:

F = applied force.

Fr = friction force.

And the following vertical forces:

N = normal force.

W = weight of the sled + weight of the person

According to the Newton´s second law:

∑F = m · a

Where "m" is the mass of the object and "a" is its acceleration

So, in the horizontal direction:

F - Fr = m · a

We have to find what force, F, is needed so that the sled moves with constant speed (acceleration = 0). Then:

F - Fr = 0

F = Fr

The applied force has to be equal in magnitude to the friction force.

The friction force is calculated as follows:

Fr = μ · N

Where μ is the coefficient of friction and N is the normal force.

To find the normal force, let´s apply Newton´s second law in the vertical direction:

∑F = N - W = m · a

Notice that the sled is not accelerated in the vertical direction so that a = 0:

N - W = 0

N = W

The normal force is equal to the weight and the weight is the sum of the weight of the sled plus the weight of the person:

W = 52 N + 700 N = 752 N

Then:

N = 752 N

Fr = 0.11 · 752 N

Fr = 83 N

Then

F = 83 N

A force of 83 N is needed to pull the sled with constant speed.