Kinetic & Potential Energy / Momentum Problem

Doc Al discuss finding the velocity of a small cube as it slides down a circular path cut into a larger block. The blocks are initially at rest and there is no friction. Doc Al mentions using the equations for conservation of momentum and kinetic energy, but there seems to be a mistake in the algebra. They both agree that the kinetic energy of the larger block should not be ignored. In summary, the conversation discusses finding the velocity of a cube sliding down a circular path cut into a larger block, using equations for conservation of momentum and kinetic energy, and acknowledging the kinetic energy of the larger block.
  • #1
x93
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Homework Statement


From Kleppner and Kolenkow:
A small cube of mass m slides down a circular path of radius R cut into a large block of mass M, as shown. M rests on a table, and both blocks move without friction. The blocks are initially at rest, and m starts from the top of the path.
Find the velocity v of the cube as it leaves the block.

Ans. clue. If m=M, v=√(gR)

http://img390.imageshack.us/img390/5575/blocksbi2.jpg [Broken]

Homework Equations


KE=(1/2)mv2
PE=mgh
mivi=mfvf
KEi=KEf


The Attempt at a Solution


For m, initial energy PEm=mgR
Just before m leaves block M, KEm=(1/2)mv2=mgR
Thus, v=√(2gR).
From here, I set up equations for conservation of momentum as well as kinetic energy.
I then used substitution and tried to solve for the velocity of m as it leaves the block, M, but the algebra just isn't working out. Did I make a mistake?
 
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  • #2
Do not ignore the KE of the large block. ehild
 

1. What is the difference between kinetic and potential energy?

Kinetic energy is the energy of motion, while potential energy is the energy an object has due to its position or condition. Kinetic energy is dependent on an object's mass and velocity, while potential energy is dependent on an object's height and its interaction with other objects.

2. How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the object's mass and v is its velocity. This formula can be used to calculate the kinetic energy of any moving object.

3. What factors affect an object's potential energy?

The factors that affect an object's potential energy include its mass, height, and the acceleration due to gravity. Additionally, the potential energy can also be affected by external forces, such as friction or air resistance.

4. What is the relationship between kinetic energy and momentum?

Kinetic energy and momentum are directly related to each other. Momentum is defined as the product of an object's mass and velocity, while kinetic energy is directly proportional to an object's mass and the square of its velocity. This means that an increase in an object's momentum will result in an increase in its kinetic energy.

5. How do you solve a momentum problem?

To solve a momentum problem, you need to use the formula P = m * v, where P is the object's momentum, m is its mass, and v is its velocity. You can use this formula to find the momentum of an object before and after a collision or interaction with another object. Remember to use the correct units and consider the direction of the momentum in your calculations.

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