Question

A piece of taffy slams into and sticks to an identical piece of taffy at rest. The momentum of the combined pieces after the collision is the same as before the collision, but this is not true of the kinetic energy, which partly degrades into heat. What percentage of the kinetic energy becomes heat?
A) 25%
B) 0%
C) 75%
D) 50%
E) need more information.

Answer 1

Answer:

D) 50%

Explanation:

According to conservation of momentum:

$m_{1} v_{1i} + m_{2} v_{2i} = m_{1} v_{1f} + m_{2} v_{2f}$

Assuming that the second taffy started at rest, both pieces have the same mass and that they combined after the collision, their final velocity is:

$m v_{1i} = (m+m) v_{f}\\v_{f} = 0.5 v_{1i}$

The initial kinetic energy of the system is:

$E_{ki} = \frac{m*v_{1i}^2}{2}$

Since the second taffy was not moving, it had no kinetic energy at first.

The initial kinetic energy of the system is:

$E_{kf} = \frac{2m*v_{f}^2}{2}\\E_{kf} = \frac{2m*(0.5v_{1i})^2}{2}\\E_{kf} = \frac{0.5m*v_{1i}^2}{2}$

The percentage of kinetic energy that becomes heat is given by:

$H=1 - \frac{E_{kf}}{E_{ki}}\\H=1 - \frac{\frac{0.5m*v_{1i}^2}{2}}{\frac{m*v_{1i}^2}{2}}\\\\H=1- 0.5 = 0.5$

THerefore, 50% of the kinetic energy becomes heat