Question

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.30 m before stopping. How far does the lighter fragment slide

Answer 1

Answer:

the distance d traveled by the lighter fragment is 58.1 m.

Explanation:

mass of the lighter fragment = m

the lighter fragment traveled a distance = ?

mass of the heavier fragment = 7m

the distance covered by the heavier fragment = 8.30 m

The two particles will be given the same amount of energy from the explosion. This energy is used to do work by the two fragments.

work done by heavier fragment w = mgd

where m is the mass

g is acceleration due to gravity

d is the distance traveled.

substituting, the work done by the heavier fragment is

w = 7m x g x 8.3 = 58.1mg

The same way, the lighter fragment does work of

w = mgd

equating the two work done since they are given the same amount of energy from the explosion, we have

58.1mg = mgd

mg cancels out, we have

the distance d traveled by the lighter fragment d = 58.1 m