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## Homework Statement

A student could either pull or push, at an angle of

**30 degrees**from the horizontal, a

**50 kilo**crate on a horizontal surface, where the coeficient of kinetic friction between the crate and the surface is

**0.2**. The crate is to be moved a horizontal distance of

**15m**. (a) Compared with pushing, pulling requires the student to do (1) less, (2) the same, or (3) more work. (b) Calculate the minimum work required for both pulling and pushing.

## Homework Equations

W=Fd

F=mgcos30

f_k=u_k(F_n)

## The Attempt at a Solution

For (a), unless somebody can correct me and/or lead me in the right direction, I believe that the amount of work that is done to either push or pull the crate the required distance would be same. Conceptually, if you are wanting to move the crate in a certain direction, regardless of whether you decide to push or pull, assuming that the force to move the object is being applied from the same angle, the frictional force acting on the crate would still be resisting the force in the opposite direction of the movement of the crate. The work required to move the crate would be same, just that when you actually do it, you end up utilizing different muscle(s) when trying to move it either by push or pull, which can sometimes lead one to think that doing one method means exerting more work than the other.

**Please correct/advise me if this is the wrong mode of thinking.**

For (b):

F=mgcos30

F=(50kg)(9.81m/s/s)cos30

F=424.79N

f_k=u_k(F_n)

f_k=(0.2)(50kg)(9.81m/s/s)

f_k=98.1N

F is being applied in the (+) direction, with the appropriate f_k resisting it in the (-) direction, therefore F-f_k=F_net

F_net=424.79N-98.1N

F_net=326.69N

W=F_net(d)

W=326.69N(15m.)

**W=4900.35J**

Thank you in advance for any help.