Question

Boxcar A has a mass of 1,500 kg and a velocity of 5 m/s when it collides with a stationary 1,000 kg Boxcar B. When the boxcars collide, they couple together and move at final velocity vf. Later in a different collision, Boxcar B collides with a stationary Boxcar A, and they couple together and move at the same final velocity as during the first collision, vf. What would the initial velocity of Boxcar B have to be in the second collision to result in the coupled boxcars moving with the final velocity vf? Assume no other forces act on the boxcars.

Answer 1

Answer:

Explanation:$\begin{gathered} \text{Mass of Boxcar A, m}_A=\text{ 1500 kg} \\ \text{Initial Velocity of Boxcar A, u}_A=\text{ 5 m/s} \\ \text{Mass of Boxcar B, m}_B=\text{ 1000 kg} \\ \text{Boxcar B was stationary} \\ \text{Initial velocity of Boxcar B, u}_B=\text{ 0m/s} \\ \end{gathered}$

Final velocity of Boxcars A and B after collision, vf = ?

Using the equation for the conservation of momentum, the final velocity of both boxcars after collision will be calculated as:

$\begin{gathered} m_Au_A+m_Bu_B=(m_A+m_B)v_f \\ 1500(5)+1000(0)=(1500+1000)v_f \\ 7500=2500v_f \\ v_f=\text{ }\frac{7500}{2500} \\ v_f=\text{ }3\text{ m/s} \end{gathered}$

In a different collision:

Boxcar A is stationary before collision. That is,

$u_A=\text{ 0 m/s}$

Since Boxcar B was moving before collision, it will have a certain amount of initial velocity that we are yet to know

$u_B=\text{ ?}$

According to the question, the final velocity still remains the same. That is,

vf = 3m/s

Reapplying the equation for the conservation of momentum in order to calculate the initial velocity of Boxcar B:

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