Question

Superman must stop a 190 km/h train in 190 m to keep it from hitting a stalled car on the tracks.

a) If the train's mass is 4.0x10⁵ kg, how much force does he exerts?
b) How much force (in magnitude) does the train exert on superman?

Answer 1

a) Superman exerts a force of -5.791 x 10^6N to stop the train. b) The magnitude of the force the train exerts on Superman is also 5.791 x 10^6 N.

Step-by-step explanation:

a) To calculate the force Superman exerts, we can use the equation:

Force = Mass x Acceleration

First, let's convert the train's speed from km/h to m/s:

190 km/h = (190 x 1000) m/3600 s = 52.7778 m/s

Next, we can use the formula:

Acceleration = Change in Velocity/Time

We know the final velocity of the train is 0 m/s, the initial velocity is 52.7778 m/s, and the distance is 190 m. Plugging these values into the formula:

Acceleration = (0 - 52.7778)/t

The time it takes to stop the train will be the same as the time it takes to apply the necessary force. Solving for t:

t = 190/52.7778 = 3.6 s

Now, we can substitute the values into the first formula:

Force = Mass x Acceleration = 4.0 x 10^5 kg x (0 - 52.7778)/3.6 s = -5.791 x 10^6 N

Since the force is negative, it means Superman exerts a force in the opposite direction of the train's motion, slowing it down.

b) To calculate the force the train exerts on Superman, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Therefore, the force exerted on Superman by the train will be equal in magnitude, but opposite in direction, to the force Superman exerts on the train. So, the magnitude of the force the train exerts on Superman is also 5.791 x 10^6 N.