A 25,000 kilogram train is traveling down a track at 20 meters per second. A cow wanders onto the tracks 75 meters ahead of the train, causing the conductor to slam on the brakes. The rain skids to a stop. If the brakes can provide 62,500 Newtons of friction, will the conductor have enough stopping distance to avoid striking the cow?

Question

A 25,000 kilogram train is traveling down a track at 20 meters per second. A cow wanders onto the tracks 75 meters ahead of the train, causing the conductor to slam on the brakes. The rain skids to a stop. If the brakes can provide 62,500 Newtons of friction, will the conductor have enough stopping distance to avoid striking the cow?

Answer 1

To determine if the conductor will have enough stopping distance to avoid striking the cow, we need to calculate the stopping distance of the train.

First, let's calculate the initial momentum of the train. Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v).
- Mass of the train (m): 25,000 kilograms
- Velocity of the train (v): 20 meters per second

Momentum (p) = mass (m) × velocity (v)
p = 25,000 kg × 20 m/s
p = 500,000 kg·m/s

Next, we can use the principle of conservation of momentum to calculate the stopping distance. The momentum before the brakes are applied should equal the momentum after the train comes to a stop.

When the train stops, its final velocity (vf) will be zero. So, using the principle of conservation of momentum:

Initial momentum (before brakes) = Final momentum (after brakes)

Momentum before brakes (p) = momentum after brakes (0)
p = m × vf

Now, let's rearrange the equation to solve for the final velocity (vf):
vf = p / m
vf = 0 / 25,000 kg
vf = 0 m/s

Hence, the final velocity of the train after applying the brakes is 0 m/s.

Now, we can calculate the stopping distance using the formula:

Stopping distance = (initial velocity^2) / (2 × deceleration)

The deceleration can be found using Newton's second law of motion. The force of friction (F) can be related to deceleration (a) by the equation:

F = m × a

Rearranging the equation:
a = F / m
a = 62,500 N / 25,000 kg
a = 2.5 m/s^2

Now, we can calculate the stopping distance:

Stopping distance = (initial velocity^2) / (2 × deceleration)
Stopping distance = (20 m/s)^2 / (2 × 2.5 m/s^2)
Stopping distance = 400 m^2/s^2 / 5 m/s^2
Stopping distance = 80 m

Since the stopping distance of the train is 80 meters and the cow is 75 meters ahead of the train, the conductor will have enough stopping distance to avoid striking the cow.