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:

$K_{B} = 0.5\cdot K_{A}$

Explanation:

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

Cart A:

$K_{A} = \frac{1}{2} \cdot m \cdot v_{A}^{2}$

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

$v_{A} = \frac{5\cdot F}{m}$

Then,

$K_{A} = 12.5\cdot \frac{F^{2}}{m}$

Cart B:

$K_{B} = m \cdot v_{B}^{2}$

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

$v_{B} = \frac{5\cdot F}{2\cdot m}$

$K_{B} = 6.25\cdot \frac{F^{2}}{m}$

The kinetic energy of cart B is 0.5K.

Answer 2

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

Explanation: Please see the attachments below