Solve for Crate Mass: Torque and Static Friction Problem | 40 kg Answer

[Aoiumi]

I have a problem that I can't figure out. I hope someone can help.

Homework Statement

A crate that is 1.0 m tall and 0.5 m in depth is pushed at its top with a horizontal force. The minimum force required to tip the crate is 100 N--what is the mass of the crate? The center of mass is in the center of the crate. Static frictional force prevents slipping. g = 10 m/s^2.

Homework Equations

τ=FRsinθ

The Attempt at a Solution

I know the answer is 40 kg's but I can't figure this out. Force is applied horizontally to the upper right hand corner of the box, and I assume the pivot point is in the lower left hand corner so torque = 100N(1.0m), or 10 N m. I'm not quite sure where to go from here. My guess was that you have to set up an equation and set this value equal to something else, but I'm not sure what. Should angles come into play at all?

 

[SteamKing]

What other force acting on the crate will tend to keep it on the ground? Hint: If you tried to lift the crate, you would have to overcome this force.

 

[Aoiumi]

There is a weight force too, the unknown mass of the object times gravity.

 

[SteamKing]

Correct. Draw a free body diagram of the box and write equations of equilibrium.