Pushing a crate problem

Question

Bob walks up to a crate and begins pushing with 200N force.  What is the magnitude of the frictional force?  Will the box move?  What is it's acceleration?

 

the coefficient is 0.7 and the mass is 50kg

Answer 1

There are two coefficients of friction - the static (μ_s) and the dynamic (μ_k).

You only give one.

I am going to assume you gave the static one (μ_s).

With that we can determine the frictional force and IF the box will move.

We cannot find the acceleration unless you give us the dynamic (μ_k) coefficient of friction.

 

You can find the frictional force with the fizzicks is FUN formula.

F_f = (μ_s)•F_n

 

To do this we need one other value not given but we can calculate it (the normal force) which is equal to the weight (remember weight is a Force) if the box is on a level horizontal surface.

W = mg  so  F_n = mg

F_n = mg = (50 kg)•(10 m/s²) = 500 kg•m/s² = 500 N

 (I always use 10 to practice.  It is correct within 2%.  If your teacher requires you should use 9.8 or 9.81.

 

F_n = 500 N towards the pusher and

F_p = 200 N away from the pusher so

F_net = (+200 N) + (-500 N) = -300 N

 

So the box does not move and requires the pusher to push with 500 N or 300 more Newtons to get the box to move.

btw: F_p is for F_pusher or the force the pusher applied.

You can always use whatever subscripts you want to describe things so use subscripts that make sense to you and help you keep track of things.