Question

A 3-car train is being pulled on frictionless tracks. The lead car has a mass of 2000 kg, while the
2nd two cars each have masses of 1500 kg. How much force is required to accelerate the train at
3 m/s2? If the train is being pulled by this force and the last car suddenly detaches, what will its new
acceleration be?

Answer 1

To determine the force required to accelerate the entire train at \(3 \, \text{m/s}^2\), we first need to calculate the total mass of the train.

The lead car has a mass of \(2000 \, \text{kg}\) and the other two cars each have a mass of \(1500 \, \text{kg}\).

Calculating the total mass:

\[
\text{Total Mass} = \text{Mass of Lead Car} + \text{Mass of 2nd Car} + \text{Mass of 3rd Car}
\]

\[
\text{Total Mass} = 2000 \, \text{kg} + 1500 \, \text{kg} + 1500 \, \text{kg} = 5000 \, \text{kg}
\]

Now, using Newton's second law \(F = ma\) to find the force required:

\[
F = \text{Total Mass} \times \text{Acceleration}
\]

\[
F = 5000 \, \text{kg} \times 3 \, \text{m/s}^2 = 15000 \, \text{N}
\]

Therefore, the force required to accelerate the train at \(3 \, \text{m/s}^2\) is \(15000 \, \text{N}\).

Next, if the last car (which has a mass of \(1500 \, \text{kg}\)) suddenly detaches, we need to calculate the new total mass of the train:

\[
\text{New Total Mass} = \text{Mass of Lead Car} + \text{Mass of 2nd Car}
\]

\[
\text{New Total Mass} = 2000 \, \text{kg} + 1500 \, \text{kg} = 3500 \, \text{kg}
\]

Since the force applied to the train remains \(15000 \, \text{N}\), we can now calculate the new acceleration of the remaining train using \(F = ma\):

\[
a = \frac{F}{m}
\]

\[
a = \frac{15000 \, \text{N}}{3500 \, \text{kg}} \approx 4.29 \, \text{m/s}^2
\]

Therefore, after the last car detaches, the new acceleration of the remaining train will be approximately \(4.29 \, \text{m/s}^2\).