Question

You are pulling your little sister on a sled (combined mass M). The sled slides on top of snowy ground (coefficients Ms, Mk). Starting from rest, you pull on the tow rope with a horizontal force magnitude T. After pulling a distance d, you stop pulling and jump on the sled, raising the total mass to 2M. You slide an additional distance 2d. Determine the force T, with which you were pulling.

Note: Do not use the 2nd law directly. Instead, use work and energy.

Answer 1

The mass is being pulled with a force T

It moves a distance d

So, the work done is

Work = Force*displacement = T*d

The mass on the sled is M

The normal reaction force is then

N = Mg

The frictional force is

F = Mk*Mg

The energy used used by friction is (Mk*Mg)*d

The remaining energy is

E = T*d - (Mk*Mg)*d

Now, there is no applied force.

The new mass of the sled is 2M

the distance it moved is 2d

So, the energy used in this stage is

E' = (Mk*2Mg)*2d = 4*(Mk*Mg)*d

This energy is what is remaining from earlier.

So,

E' = E

T*d - (Mk*Mg)*d = 4*(Mk*Mg)*d

T*d = 5*(Mk*Mg)*d

T = 5(Mk*Mg)