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.

 

[Nickie]

It seems like you are on the right track. To solve this problem, you will need to use the equation for torque, τ=FRsinθ, where F is the applied force, R is the distance from the pivot point to the point where the force is applied, and θ is the angle between the force and the lever arm (in this case, the height of the crate). Since the crate is not tipping, the torque from the applied force must be equal to the torque from the static frictional force. So, you can set up an equation like this: τ from applied force = τ from static frictional force. Then, substitute in the values you know (100 N for the applied force, 1.0 m for the distance from the pivot point to the point where the force is applied, and the unknown mass for the static frictional force). From there, you can solve for the mass of the crate. Remember to pay attention to units and make sure they are consistent throughout your calculations. Good luck!