Truck with attached inclined plane and a block on the incline

In summary, the block stays on the incline because the weight of the block provides a horizontal force that opposes the force of the incline.
  • #1
rakailee
6
0
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.
Screen Shot 2020-05-11 at 12.01.26 PM.png
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?
 
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  • #2
Do you know trig? Can you draw a force diagram?
 
  • #3
phinds said:
Do you know trig? Can you draw a force diagram?
this?
Screen Shot 2020-05-11 at 12.49.06 PM.png
 
  • #4
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.
 
  • #5
phinds said:
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.
 
  • #6
rakailee said:
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.
 
  • #7
rakailee said:
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?
 
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  • #8
kuruman said:
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.
 

Related to Truck with attached inclined plane and a block on the incline

1. What is the purpose of the inclined plane on the truck?

The inclined plane on the truck is used to make it easier to move heavy objects, such as the block on the incline. By decreasing the angle of the incline, the force required to move the block is also decreased.

2. How does the angle of the incline affect the movement of the block?

The steeper the angle of the incline, the more force is required to move the block. This is because the steeper angle increases the component of the block's weight that is acting against the direction of movement.

3. What is the relationship between the weight of the block and the force required to move it up the incline?

The weight of the block is directly proportional to the force required to move it up the incline. This means that as the weight of the block increases, so does the force required to move it. This relationship is described by Newton's Second Law of Motion.

4. How does friction affect the movement of the block on the incline?

Friction acts in the opposite direction of movement and can make it more difficult to move the block up the incline. The amount of friction depends on the surface of the incline and the block, as well as the force applied to the block.

5. Can the truck with the inclined plane and block be used to demonstrate other scientific principles?

Yes, this setup can also be used to demonstrate the concept of work and energy. As the block is moved up the incline, work is done against the force of gravity. This work is converted into potential energy as the block gains height on the incline.

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