Superman must stop a 120km/h train in 150m to keep it from hitting a stalled car on the tracks.If the train's mass is 3.6x10^5kg,how much force must he exert?Compare to the weight of the train (give as%).How much force does the train exerts on Superman?
Vo=120,000m/h * (1/3600)h/s = 33.33m/s.
Vf^2 = Vo^2 + 2ad,
a = (Vf^2 - Vo^2) / 2d,
a = (0 - (33.33)^2) / 300,
a = - 3.7m/s.
F = ma = 3.6*10^5 * (-3.7) = -13.3*10^5 = -1.3*10^6N = Force applied
in opposite direction of train's force.
To find out how much force Superman must exert to stop the train, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration is the change in velocity (v) divided by the distance it takes to stop (d).
First, we need to find the change in velocity. Since Superman wants to stop a moving train, the change in velocity would be from 120 km/h to 0 km/h, which is a decrease of 120 km/h.
To convert this change in velocity from km/h to m/s, we need to multiply it by 1000/3600, since 1 km/h is equal to 1000 m/3600 s. So, the change in velocity is:
120 km/h * (1000 m/3600 s) = 33.33 m/s
Next, we can calculate the acceleration using the formula:
a = Δv / Δt
where Δv is the change in velocity and Δt is the time it takes to change the velocity. In this case, the time is not given, but we can assume that Superman stops the train in a very short amount of time, so we'll approximate it to 0. Therefore,
a = 33.33 m/s / 0 s (approximated to 0) = ∞ (infinity)
Since the acceleration is extremely high and the time taken to stop the train is considered negligible, Superman must exert an infinitely high force to stop the train. In practical terms, this means that Superman's force would be strong enough to stop the train.
Comparing the force exerted by Superman to the weight of the train, we need to calculate the weight of the train first.
Weight (W) is equal to mass (m) multiplied by the acceleration due to gravity (g). Here, g is approximately 9.8 m/s².
W = m * g
W = (3.6 x 10^5 kg) * (9.8 m/s²) = 3.528 x 10^6 N
Now, we can compare Superman's force to the weight of the train:
Superman's force = weight of the train = 3.528 x 10^6 N
Therefore, the force exerted by Superman to stop the train is 100% of the train's weight.
Lastly, the force the train exerts on Superman can be calculated using Newton's third law of motion, which states that every action has an equal and opposite reaction. Thus, the train exerts an equal force on Superman, which would be 3.528 x 10^6 N.