Question

A 50-kg toboggan is coasting on level snow. As it passes beneath a bridge, a 20-kg parcel is dropped straight down and lands in the toboggan. If KE1 is the original kinetic energy of the toboggan and KE2 is the kinetic energy after the parcel has been added, what is the ratio KE2/KE1

Answer 1

Answer:

$KE2/KE1=0.71$

Explanation:

By conservation of the linear momentum:

m1*V1 = (m1+m2)*V2

Solving for V2:

$V2 = \frac{m1}{m1+m2}*V1$

The kinetic energies are:

$KE1=1/2*m1*V1^2$

$KE2 = 1/2*(m1+m2)*V2^2$

$KE2 = 1/2*(m1+m2)*(\frac{m1}{m1+m2}*V1)^2$

Simplifying:

$KE2 = 1/2*\frac{m1^2}{m1+m2}*V1^2$

The ratio will be:

$KE2/KE1=\frac{1/2*\frac{m1^2}{m1+m2}*V1^2}{1/2*m1*V1^2} =\frac{m1}{m1+m2}$

$KE2/KE1=0.71$