Question

Two carts, one twice as heavy as the other, are at rest of a horizontal, frictionless track. A person pushes each cart with the same force for 5 seconds. If the kinetic energy of the lighter cart after the push is K , the kinetic energy of the heavier cart is: (10 points)

Answer 1

Answer: The kinetic energy of the heavier cart is 1/2K

Explanation: Please see the attachments below

Answer 2

`K_(B) = 0.5\cdot K_(A)`

Step-by-step explanation:

Both carts are modelled by using the Principle of Energy Conservation and Work-Energy Theorem:

Cart A:

`K_(A) = (1)/(2) \cdot m \cdot v_(A)^(2)`

By assuming a constant acceleration, final velocity is equal to:

`v_(A) = (5\cdot F)/(m)`

Then,

`K_(A) = 12.5\cdot (F^(2))/(m)`

Cart B:

`K_(B) = m \cdot v_(B)^(2)`

By assuming a constant acceleration, final velocity is equal to:

`v_(B) = (5\cdot F)/(2\cdot m)`

`K_(B) = 6.25\cdot (F^(2))/(m)`

The kinetic energy of cart B is 0.5K.