Question

1. If an object of mass m collides and velocity v collides inelastically with an object of mass 3m that is initially at rest, then the amount of total system mass in motion will increase by a factor of ___ and the velocity of the system will decrease by a factor of ___. The new velocity will be ___v.

2. If an object of mass m collides and velocity v collides inelastically with an object of mass 4m that is initially at rest, then the amount of total system mass in motion will increase by a factor of ___ and the velocity of the system will decrease by a factor of ___. The new velocity will be ___v.

3. If an object of mass 3m collides and velocity v collides inelastically with an object of mass 4m that is initially at rest, then the amount of total system mass in motion will increase by a factor of ___ and the velocity of the system will decrease by a factor if ___. The new velocity will be ___v.

4.  If an object of mass 5m collides and velocity v collides inelastically with an object of mass 3m that is initially at rest, then the amount of total system mass in motion will increase by a factor of ___ and the velocity of the system will decrease by a factor if ___. The new velocity will be ___v.

Answer 1

1) After collsion the total moving mass is 4m (m + 3m), thus mass in motion will increase by a factor of 4.

velocity after collsion is given by

$v=\frac{mv}{4m}=\frac{v}{4}$

Thus, it decreases by a factor of 4.

The new velocity is

$\frac{1}{4}*v$

2) Applying similar procedure here also, we obtain

mass in motion will increase by a factor of 5.

velocity of the system will decrease by a factor of 5.

The new velocity is

$\frac{1}{5}*v$

3) mass in motion will increase by a factor of 7/3 = 2.33

velocity of the system will decrease by a factor of 1-3/7 = 0.57

The new velocity is

$\frac{3}{7}*v$

4) mass in motion will increase by a factor of 8/5 = 1.6

velocity of the system will decrease by a factor of 1-5/8 = 0.375

The new velocity is

$\frac{5}{8}*v$