How Does Momentum Change Affect Force on a Wall with Rebounding Ice Cubes?

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In summary, small ice cubes with a mass of 5.00 g slide down a frictionless ski-jump track and leave the track at an angle of 40.0° above the horizontal. After bouncing off a vertical wall at the highest point of their trajectory with half their original speed, 10.0 cubes strike the wall per second. To determine the average force exerted on the wall, the velocity at the highest point of the trajectory and the change in momentum of each cube when it bounces must be calculated. The resulting momentum change will be used to find the average force exerted on the wall.
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Touchme
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Small ice cubes, each of mass 5.00 g, slide down a frictionless ski-jump track in a steady stream, as shown in Figure P6.71. Starting from rest, each cube moves down through a net vertical distance of y = 1.75 m and leaves the bottom end of the track at an angle of 40.0° above the horizontal. At the highest point of its subsequent trajectory, the cube stikes a vertical wall and rebounds with half the speed it had upon impact. If 10.0 cubes strike the wall per second, what average force is exerted on the wall?

I have no idea how to solve this question. I know how to get the final velocity when the ice is lauched. mgh = 0.5mv^2 and the answer is 5.857 m/s. Can someone guide me in doing this? Hints or suggestion will help too.
 

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  • #2
Touchme said:
Small ice cubes, each of mass 5.00 g, slide down a frictionless ski-jump track in a steady stream, as shown in Figure P6.71. Starting from rest, each cube moves down through a net vertical distance of y = 1.75 m and leaves the bottom end of the track at an angle of 40.0° above the horizontal. At the highest point of its subsequent trajectory, the cube stikes a vertical wall and rebounds with half the speed it had upon impact. If 10.0 cubes strike the wall per second, what average force is exerted on the wall?

I have no idea how to solve this question. I know how to get the final velocity when the ice is lauched. mgh = 0.5mv^2 and the answer is 5.857 m/s. Can someone guide me in doing this? Hints or suggestion will help too.
This question was posted elsewhere, but the thread died out I believe. First step after finding the velocity at the end of the ramp is to find the velocity at the highest point of the trajectory, and then the change in momentum of each cube when it bounces. The average force is related to the momentum changes of the cubes and the time interval between the bounces.
 
  • #3
At the highest point of the trajectory the y-velocity component will be zero. This means that only the horizontal velocity component remains. This means that the force that the ice blocks will exert on the wall will be horizontal. The wall will respond with a reaction force of similar magnitude in the opposite direction sending it back horizontally in the opposite direction. What will the resulting momentum change be for a single ice cube?
 

Related to How Does Momentum Change Affect Force on a Wall with Rebounding Ice Cubes?

1. What is momentum and how is it calculated?

Momentum is a measure of an object's motion, and it is calculated by multiplying its mass by its velocity.

2. How does an object's momentum change when a force is applied to it?

When a force is applied to an object, its momentum changes by the amount of force applied multiplied by the time it was applied for. This is described by Newton's Second Law of Motion, which states that force is equal to mass times acceleration.

3. How does the direction of a force affect an object's momentum?

The direction of a force affects an object's momentum by changing its velocity in that direction. If the force is applied in the same direction as the object's motion, it will increase its momentum. If the force is applied in the opposite direction, it will decrease its momentum.

4. What is the relationship between momentum and mass?

The relationship between momentum and mass is direct. The greater the mass of an object, the greater its momentum will be, given the same velocity. This is because momentum is directly proportional to mass.

5. Can momentum be conserved in a closed system?

Yes, momentum is conserved in a closed system, meaning that the total momentum of all the objects in the system will remain constant, even if they collide or interact with each other. This is described by Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

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