Question

Four railroad cars, each of mass 2.50x10^4 kg, are coupled together and coasting along
horizontal tracks at speed vi toward the south. A very strong but foolish actor, riding on
the second car, uncouples the front car and gives it a big push, increasing its speed to 4
m/s southward. The remaining three cars continue moving south, now at 2 m/s.
a) find the initial speed of the four cars.
b) by how much did the potential energy within the body of the actor change ?

Answer 1

Answer on Question #75243-Physics-Other

Four railroad cars, each of mass $2.50 \times 10^{4} \mathrm{~kg}$, are coupled together and coasting along horizontal tracks at speed vi toward the south. A very strong but foolish actor, riding on the second car, uncouples the front car and gives it a big push, increasing its speed to $4 \mathrm{~m} / \mathrm{s}$ southward. The remaining three cars continue moving south, now at $2 \mathrm{~m} / \mathrm{s}$.

a) find the initial speed of the four cars.

b) by how much did the potential energy within the body of the actor change?

Solution

a) From the conservation of momentum:

$$4 m v _ {i} = 4 m + 3 m (2)$$ $$4 v _ {i} = 4 + 6$$ $$v _ {i} = \frac {10}{4} = 2.5 \frac {m}{s}.$$

b) From the conservation of energy:

$$\Delta E _ {p} = - \Delta E _ {k} = \frac {4 m}{2} 2.5 ^ {2} - \frac {4 ^ {2}}{2} m - \frac {3 m (2) ^ {2}}{2} = - 1.5 m = - 3.75 \cdot 10 ^ {4} J.$$

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