Superman must stop a 110-km/h train in 100m to keep it from hitting a stalled car on the tracks. The train's mass is 3.6 × 105 kg.
Vo = 110km/h = 110000m/3600s = 30.56 m/s
V^2 = Vo^2 + 2a*d = 0
a = -(Vo^2)/2d = -(30.56^2)/200 = -4.67
m/s^2.
F = m*a = 3.6*10^5 * (-4.67) = -1.68*10^6 N.
Note: The negative sign means that the force opposes the motion.
To determine if Superman can stop the train, we need to calculate the force required to bring it to a stop.
The force needed to stop an object can be calculated using Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
In this case, the acceleration required to bring the train to a stop is the change in speed divided by the time taken:
a = Δv / Δt
We are given the initial speed of the train (110 km/h), but we need to convert it to m/s to use it in the calculations:
110 km/h = (110 * 1000) / (60 * 60) m/s = 30.56 m/s
Now we can calculate the acceleration:
a = (0 - 30.56 m/s) / (0.100s)
Since the train needs to be brought to a complete stop, the final velocity is considered to be zero. The time taken (Δt) is given as 0.100s, as mentioned in the problem.
Now, we can calculate the force:
F = (3.6 × 10^5 kg) * (0 - 30.56 m/s) / (0.100s)
F = - (3.6 × 10^5 kg) * (30.56 m/s) / (0.100s)
F = - 1.1024 × 10^8 N
The negative sign indicates that the force required to stop the train is in the opposite direction to its initial motion. This means Superman needs to exert a force of approximately 1.1024 × 10^8 Newtons in order to stop the train and prevent it from hitting the stalled car.