Kinetic Energy/Linear Momentum

In summary, the problem involves three air carts with masses of m, 2m, and 4m, all equipped with putty bumpers. The cart with mass 4m is initially at rest, while the other two carts are moving towards it with a speed of v0. Using the equations vf= (m1v1,i + m2v2,i) / m1+m2 and KE=0.5(m)v^2, the final speed of the carts can be calculated to be 3v0/7. The second part of the problem involves finding the ratio of the final kinetic energy to the initial energy. The final kinetic energy is found to be 1.5mV0, but the
  • #1
shaggyace
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0

Homework Statement


Three air carts have masses denoted as m, 2m, and 4m, all lined up one after another ron an air track. Initially, the cart denoted as 4m is at rest, whereas the other two carts are moving toward the cart at rest with a speed, v0 . All carts are equipped with putty bumpers that give completely inelastic collisions.

a. Find the final speed of the carts expressed through the given variables.

b. Calculate the ratio of the final kinetic energy of the system to the initial energy


Homework Equations



vf= (m1v1,i + m2v2,i) / m1+m2

KE=0.5(m)v^2

The Attempt at a Solution



I already got the first part. I worked it out to 3v0/7.
Im having trouble deriving the second part. I think I found the final kinetic energy as 1.5mV0
But I can't find the initial kinetic energy. What would be included in terms of mass? Is it the first two carts that are initially moving? or all the masses? and if so, how would you combine the zero velocity of the larger cart with the initial nonzero velocities of the other two carts. I am really confused with this part.
 
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  • #2
shaggyace said:
I think I found the final kinetic energy as 1.5mV0
But I can't find the initial kinetic energy.
That looks like the initial KE to me. How did you arrive at it?

(To find the total KE at any point, just find the KE of each mass and add them up. If something's not moving, what would be its KE?)
 

1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is a scalar quantity and is dependent on the mass and velocity of the object.

2. How is kinetic energy different from potential energy?

Kinetic energy is the energy of motion, while potential energy is the energy that an object has due to its position or state. Kinetic energy is dependent on an object's velocity, while potential energy is dependent on its position or configuration.

3. How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

4. What is linear momentum?

Linear momentum is a vector quantity that describes the motion of an object. It is the product of an object's mass and velocity and is conserved in a closed system.

5. What is the relationship between kinetic energy and linear momentum?

There is a direct relationship between kinetic energy and linear momentum. As an object's kinetic energy increases, its linear momentum also increases. This is because both quantities are dependent on an object's mass and velocity.

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