Question

A piece of taffy slams into and sticks to another identical piece of taffy that is at rest. The momentum of the two pieces stuck together after the collision is the same as it was before the collision, but this is not true of the kinetic energy, which is partly turned into heat. What percentage of the kinetic energy is turned into heat?

A. 0%
B. 25%
C. 50%
D. 75%

Answer 1

C. 50%

Step-by-step explanation:

Lets consider that the mass of taffy is m and its initial velocity is u and final velocity is v. Momentum is conserved so we can write it as,

`mu = 2mv\\v = (u)/(2) \\`

The initial kinetic energy =
`(mu^(2) )/(2)`

As the Kinetic energy partly converted into heat.

The final kinetic energy =
`(m((u)/(2))^(2) )/(2)` =
`(mu^(2) )/(4)`

Change in the kinetic energy =
`(mu^(2) )/(2) - (mu^(2) )/(4) = (mu^(2) )/(4)`

now we can determine the fraction of kinetic energy that has turned into heat

=
`(Heat energy)/(initial K.E)` =
`((mu^(2) )/(4) )/((mu^(2) )/(2) ) = 1/2`

= 50%