a 25,ooo 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 train 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.
To determine whether the conductor will have enough stopping distance to avoid striking the cow, we need to calculate the stopping distance of the train.
We can start by calculating the initial kinetic energy of the train using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the train (m) = 25,000 kg
Velocity of the train (v) = 20 m/s
Plugging in the values:
Kinetic Energy = (1/2) * 25,000 kg * (20 m/s)^2
= 10,000 kg * (400 m^2/s^2)
= 4,000,000 kg*m^2/s^2
Now, we know that the work done by the brakes in stopping the train is equal to the change in kinetic energy. Since the train comes to a complete stop, the work done by the brakes cancels out the initial kinetic energy.
Work done by the brakes = Change in kinetic energy
Since work is given by the formula:
Work = Force * Distance
We can rearrange the formula to:
Force = Work / Distance
Given:
Work done by the brakes = 62,500 N
Force = 62,500 N
Distance = ?
Plugging in the values:
62,500 N = (4,000,000 kg*m^2/s^2) / Distance
Now, we can solve for the distance by rearranging the formula:
Distance = (4,000,000 kg*m^2/s^2) / 62,500 N
Distance = 64 meters
Therefore, the stopping distance of the train is 64 meters, which is greater than the distance between the cow and the train (75 meters). Hence, the conductor will not have enough stopping distance to avoid striking the cow.