Question

A green croquet ball of mass 0.50 kg is rolling at +12 m/s. It collides with a blue croquet ball that also

Answer 1

Answer:

a) 9.6 m/s

b) 11.7 m/s

c) 12 m/s

Explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum $p_{o}$ must be equal to the final momentum $p_{f}$:  

$p_{o}=p_{f}$ (1)  

Where:  

$p_{o}=m_{g} V_{o} + m_{b} U_{o}$ (2)  

$p_{f}=m_{g} V_{f} + m_{b} U_{f}$ (3)  

$m_{g}=0.5 kg$ is the mass of green ball

$m_{b}=0.5 kg$ is the mass of the blue ball

$V_{o}=12 m/s$ is the initial velocity of the green ball  

$U_{o}=0 m/s$ is the initial velocity of the blue ball  

$V_{f}$ is the final velocity of the green ball

$U_{f}$ is the final velocity of the blue ball  

Substituting (2) and (3) in (1):

$m_{g} V_{o} + m_{b} U_{o}=m_{g} V_{f} + m_{b} U_{f}$ (4)  

Isolating $U_{f}$:

$U_{f}=\frac{m_{g} V_{o} - m_{g} V_{f}}{m_{b}}$ (5)  

$U_{f}=\frac{m_{g} (V_{o} - V_{f})}{m_{b}}$ (6) This is the equation we will use for the next cases

Knowing this, let's begin with the answers:

a) In this case $V_{f}=2.4 m/s$ and we have to find $U_{f}$

$U_{f}=\frac{0.5 kg (12 m/s - 2.4 m/s)}{0.5 kg}$ (7)

$U_{f}=9.6 m/s$ (8)

b) In this case $V_{f}=0.3 m/s$ and we have to find $U_{f}$

$U_{f}=\frac{0.5 kg (12 m/s - 0.3 m/s)}{0.5 kg}$ (9)

$U_{f}=11.7 m/s$ (10)

c) In this case $V_{f}=0 m/s$ and we have to find $U_{f}$

$U_{f}=\frac{0.5 kg (12 m/s - 0 m/s)}{0.5 kg}$ (11)

$U_{f}=12 m/s$ (12)