Two boxes sliding down a 20° ramp.

In summary, 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. It will take A 2 meters to reach the bottom of the ramp.
  • #1
twils_21
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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
 
Last edited:
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  • #2
Can you show us your diagrams and work?
 
  • #3
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
 

FAQ: Two boxes sliding down a 20° ramp.

What is the acceleration of the two boxes sliding down a 20° ramp?

The acceleration of the two boxes sliding down a 20° ramp is determined by the angle of the ramp and the mass of the boxes. The acceleration is equal to the force of gravity acting on the boxes, which is 9.8 m/s^2, multiplied by the sine of the angle of the ramp.

How does the mass of the boxes affect their speed while sliding down the ramp?

The mass of the boxes does not affect their speed while sliding down the ramp. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net external force acting on it and inversely proportional to its mass. Therefore, the mass of the boxes does not play a role in determining their speed down the ramp.

Why does the angle of the ramp affect the speed of the boxes?

The angle of the ramp affects the speed of the boxes because it determines the acceleration of the boxes. As the angle of the ramp increases, the acceleration of the boxes increases, resulting in a higher speed. This is due to the fact that the component of the force of gravity acting down the ramp increases as the angle increases.

What is the relationship between the length of the ramp and the time it takes for the boxes to reach the bottom?

The relationship between the length of the ramp and the time it takes for the boxes to reach the bottom is directly proportional. This means that as the length of the ramp increases, the time it takes for the boxes to reach the bottom also increases. This is because a longer ramp allows the boxes to travel a greater distance, resulting in a longer time to reach the bottom.

How does friction affect the motion of the boxes down the ramp?

Friction can slow down the motion of the boxes down the ramp. As the boxes slide down the ramp, they experience friction from the surface of the ramp, which opposes their motion. This frictional force reduces the acceleration of the boxes and therefore, their speed down the ramp. However, if the ramp is frictionless, the boxes will continue to accelerate down the ramp until they reach the bottom.

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