Two boxes sliding down a 20° ramp.

[twils_21]

°

Homework Statement

The figure shows two boxes, A and B, on a ramp. The ramp forms a 20° angle with the horizontal. Box A is in front of Box B and they are touching. Box A is 2 meters from the bottom of the ramp. The mass of A is 3 kg and the mass of B is 10.5 kg. The coefficient of kinetic friction for box A is .210 and the coefficient of kinetic friction for box B is 0.170.

How long will it take for A to reach the bottom of the ramp?

Homework Equations

F=ma
The kinematic equations
Force of Kinetic Friction=μ*n

No help needed! I solved it!

The Attempt at a Solution

I know that B is acting on A and A is acting on B. My problem is finding the net force between the two in the x direction. And then once I find that, I am having trouble finding an equation to use that will help me find how long it takes for A to reach the bottom.

I think that I might have found the correct net force but I'm not sure and I don't know what to do with that net force.

I've also drawn the two free body diagrams for the problem.

The Force that gravity exerts in the x direction on:
A=10.0554 N
B=35.1939 N
The force that the kinetic friction exerts in the x direction on:
A=-5.80166
B=-16.43804

 

[frogjg2003]

Can you show us your diagrams and work?

 

[ehild]

You can not know the force of interaction between the boxes, but you know that the force A exerts on B and the force B exerts on A are equal and opposite. Write the equation F=ma for both bodies, including the force of interaction between them (just use a symbol for it). Show the equations, please.

ehild