Finding box weight from sliding force and friction coefficient

[Migi Alarcon]

Homework Statement

A force of 180 N is required to slide a loaded box along a horizontal floor. If the coefficient of friction is 0.32, what is the weight of the box?

The Attempt at a Solution

I'm not knowledgeable about any solutions able to retrieve the correct answer since the mass of the box is absent. I have tried

180 = 0.32 (9.8)
180 = 3.13
and M = 57.50 kg

but I'm just not certain about it. I'm really stuck on this one but there must be a solution.

 

[Grinkle]

Find and write the equation that relates the co-efficient of friction to the force of friction and the normal force. That will help you understand if your approach is correct or not.

 

[stevendaryl]

My suggestion is always write down equations in terms of variables, first, and only plug in actual numbers at the end.

So pick some variable names. Maybe Ff for the force of friction, cf for the coefficient of friction and Fg for the force of gravity. Write down an equation relating these variables, and then solve for Fg. Note: the problem is asking about the weight of the box, rather than the mass of the box. The weight is just the force of gravity. You could then solve for the mass of the box from the force of friction, but the problem doesn't ask you to.

 

[haruspex]

180 = 0.32 (9.8)
180 = 3.13
and M = 57.50 kg

As they stand, the first two lines make no sense. Presumably you meant
180 = 0.32 (9.8)M
180 = 3.13M

You correctly found the mass, but as stevendaryl points out, you are asked for the weight, not the mass.

There is another possible snag. You have assumed the force is to be applied horizontally. It asks for the force "required", which suggests the minimum magnitude of force over all possible directions.