Question

In assembling a train from several railroad cars, two of the cars, with masses 2.0 X 10^4 kg and 4.0 X 10^4 Kg are rolled toward each other. When they meet, they couple and stick together. The lighter car has an initial speed of 1.5m/s. The collision causes it to reverse direction at .25m/s.

A) Write down the statement of conservation of momentum in the case of perfectly inelastic collision/

B) What is the initial momentum of the lighter car?

C) what is the final momentum of the cars?

D) what is the initial momentum of heavier car?

E) what is the initial direction of the heavier car with respect to the final direction?

Answer 1

A) Conservation of momentum for perfectly inelastic collision:

P_{​​​​​​1}+P_{​​​​​​2}=P_{​​​​​​f}

where 1 is considered as lighter vehicle, 2 as heavier vehicle and f as both vehicles together corresponding to final momentum.

B) Initial momentum of lighter car= m×v = (2×10^4)×(1.5) kgm/s= 3×10^4 kgm/s

C) Final momentum of the cars= (m_{​​​​​​1}​​​​​+m_{​​​​2} )×v= ((2+4)×10^4)×(-0.25)=-1.5×10^4 kgm/s

D) Initial momentum of heavier car = Final momentum of both cars - Initial momentum of lighter car

= -1.5×10^4 - 3×10^4

= -4.5×10^4 kgm/s

E) Both final momentum and initial momentum of heavier car have negative sign. This implies that the initial direction of the heavier var is same as the final direction.