Question

A 4700 kg (magnetic train no friction) open train car is moving on a straight track at 24 m/s when suddenly it begins to pour rain. After a few minutes the train is measured to be moving at 18 m/s A. what is the mass of the rain that has collected in the open train car? B. is this an elastic or inelastic collision?

Answer 1

ANSWERS

A. 1566.67 kg

B. Inelastic collision

Step-by-step explanation

A. The mass of the train car without water is m₁ = 4700 kg. The initial velocity is u₁ = 24 m/s. The mass of water collected by the train car will be m₂, and the velocity of both the train car and the mass of rain collected after a few minutes is v = 18 m/s.

By conservation of linear momentum,

`m_1u_1=(m_1+m_2)v`

Replace with the known values,

`4700kg\cdot24m/s=(4700kg+m_2)\cdot18m/s`

Solving for m₂,

`m_2=(4700kg\cdot24m/s)/(18m/s)-4700kg\approx1566.67kg`

Hence, the mass of rain that has collected in the open train car is 1566.67 kg.

B. If the collision is elastic, the kinetic energy before and after the collision must be conserved. If the following equality is true, then the collision is elastic:

`(1)/(2)m_1u^2_1=(1)/(2)(m_1+m_2)v^2`

Replace the known values and solve each side,

`\begin{gathered} (1)/(2)\cdot4700kg\cdot24^2m^2/s^2=(1)/(2)(4700kg+1566.67kg)\cdot18^2m^2/s^2 \\ solving \\ 1,353,600J=1,015,200.54J \end{gathered}`

As we can see in the results, kinetic energy is partially lost, and therefore, this is an inelastic collision.