Conservation of Momentum and Energy in Elastic Collisions

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In summary, a package of mass m is released from rest at a warehouse loading dock and slides down a 2.44 m high frictionless chute to a waiting truck. The truck driver went on a break without removing the previous package, causing the two packages to stick together. Using kinematics and conservation of momentum, the common speed of the two packages after the collision is 0.865 m/s. However, if the collision is elastic, the rebound height for the package of mass m is still 2.44m. It is important to use both conservation of energy and momentum in this problem to accurately solve for the rebound height.
  • #1
mathewings
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A package of mass m is released from rest at a warehouse loading dock and slides down a 2.44 m high frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 7.00m, from the bottom of the chute. Suppose the packages stick together. What is their common speed after the collision?

Answer: 0.865 m/s

I solved this easily using kinematics to determine the small mass's velocity upon hitting the large mass. Then using conservation of momentum to isoalte the combined velocity. However, this secodn question confuses me:

Suppose the collision between the packages is elastic. To what height does the package of mass m rebound?

I've tried conservation of energy equations and always end up with a rebound to the original height of 2.44m. Can anyone offer suggestions?
 
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  • #2
mathewings said:
I've tried conservation of energy equations and always end up with a rebound to the original height of 2.44m. Can anyone offer suggestions?
What makes you think your answer is incorrect?
 
  • #3
How did you set up your conservation of energy equation for the collision? (You still need conservation of momentum as well.)
 

FAQ: Conservation of Momentum and Energy in Elastic Collisions

What is momentum and energy?

Momentum is a measure of an object's motion and is calculated by multiplying its mass by its velocity. Energy, on the other hand, is the ability to do work and is measured in joules.

What is the difference between momentum and energy?

Momentum is a vector quantity that takes into account an object's mass and velocity, while energy is a scalar quantity that only considers the object's ability to do work. Additionally, momentum is conserved in a closed system, while energy can be transformed from one form to another.

How are momentum and energy related?

Momentum and energy are related through the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. This means that in a closed system, the total energy (including both kinetic and potential energy) will remain constant.

What are some real-life examples of momentum and energy?

Some real-life examples of momentum include a train moving at high speed, a car crashing into a wall, and a baseball being thrown. Examples of energy include a light bulb producing light, a battery powering a phone, and a roller coaster moving due to gravitational potential energy.

How can momentum and energy be calculated and measured?

Momentum can be calculated by multiplying an object's mass by its velocity, while energy can be calculated using equations such as the work-energy theorem or the conservation of energy principle. These quantities can be measured using instruments such as a stopwatch, scale, or force sensor.

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