Truck with attached inclined plane and a block on the incline

[rakailee]

Homework Statement

100 kg block on a frictionless incline, 60 degrees above, attached to a truck. Truck is moving along the ground, it's 1500 kg (including incline). What's the static friction force on the truck if the block doesn't move relative to incline.

Relevant Equations

Newton's 2nd law, friction.

I tried solving this by assuming the acceleration of the truck and block to be the same so the block would stay on the incline. Also, I would assume truck ma = static friction, block ma = mgsintheta... then I solved for a to plug into 1st equation to get 12990 N. Is this correct? I wasn't sure whether this would work because I used the rotated axes for the block so the acceleration is tilted and I don't know whether I can still assume the acceleration of block and truck to be the same. How would I solve it otherwise?

 

[phinds]

Do you know trig? Can you draw a force diagram?

 

[rakailee]

Do you know trig? Can you draw a force diagram?

this?

 

[phinds]

I'm sure that all means something to you but it just looks like scribbles to me and I don't see the relationship to the problem.

 

[rakailee]

I'm sure that all means something to you but it just looks like scribbles to me and I don't see the relationship to the problem.

I was attempting to draw free body diagrams in response to your question about whether I could draw a force diagram.

 

[haruspex]

I was attempting to draw free body diagrams in response to your question about whether I could draw a force diagram.

The FBD for the truck is missing the normal force from the ground and it should not show the weight of the block. The weight of the block is a force on the block; the force that acts on the truck's incline is the normal force.

 

[kuruman]

Homework Statement:: 100 kg block on a frictionless incline, 60 degrees above, attached to a truck. Truck is moving along the ground, it's 1500 kg (including incline). What's the static friction force on the truck if the block doesn't move relative to incline.
Relevant Equations:: Newton's 2nd law, friction.

block ma = mgsintheta

There is a problem here. You are correct in saying that the acceleration of the truck and the block are the same. Therefore, the acceleration of the block is in the horizontal direction. The weight cannot provide a horizontal acceleration. What force can and what is its horizontal component?

 

[rakailee]

There is a problem here. You are correct in saying that the acceleration of the truck and the block are the same. Therefore, the acceleration of the block is in the horizontal direction. The weight cannot provide a horizontal acceleration. What force can and what is its horizontal component?

I understand how to solve it from there, thanks! I should've realized that acc of block must be horizontal as well.