Answered: A 29,000 kg freight car is coasting at…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 42P: A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain...

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Question

A 29,000 kg freight car is coasting at 0.700 m/s with negligible friction under a hopper that dumps 150,000 kg of scrap metal into it.

(a)

What is the final velocity (in m/s) of the loaded freight car? (Enter the magnitude.)

(b)

How much kinetic energy (in J) is lost?

Expert Solution

Step 1

(a)

According to the conservation of momentum, the momentum of the system in the direction of coasting must be conserved. The momentum conservation gives,

$m v = (m + M) v'$

Here, m is the mass of the freight car, v is the initial velocity of the freight car, M is the mass of the scrap metal and $v'$ is the final velocity of the loaded freight car.

Rearranging the equation,

$\begin{array}{rcl} v' & = & \frac{m v}{m + M} \\ = & \frac{(29000 kg) (0.700 m/s)}{29000 kg + 150000 kg} \\ = & 0.113 m/s \end{array}$

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