Question

A sled of mass m is coasting on the icy surface of a frozen river. While it is passing under a bridge, a package of equal mass m is dropped straight down and lands on the sled (without causing any damage). The sled plus the added load then continue along the original line of motion. How does the kinetic energy of the (sled load) compare with the original kinetic energy of the sled

Answer 1

The final kinetic energy is half of the sled's original kinetic energy.

Step-by-step explanation:

The law of conservation of momentum is:

initial momentum = final momentum

`mv_(1) =(m+m)v_(2) \\v_(2) =(v_(1) )/(2)`

The initial kinetic energy is equal to:

`E_(ki) =(1)/(2) mv_(1) ^(2)`

The final kinetic energy is:

`E_(kf) =(1)/(2) (m+m)v_(2) ^(2) \\E_(kf) =mv_(2) ^(2) \\E_(kf) =m((v_(1) )/(2) )^(2) \\E_(kf) =(1)/(2) E_(ki)`

As you can see from the result, the final kinetic energy is half of the sled's original kinetic energy.