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?
vf^2=vi^2+2ad
but a= F/mass
solve for F
be certain to change velocity initial to m/s
To calculate the force Superman must exert to stop the train, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, we want to find the force required to bring the train to a stop, which means the acceleration will be negative since it is opposite to the direction of motion.
First, let's calculate the acceleration:
- We need to convert the speed of the train from km/h to m/s. To do this, divide the speed by 3.6: 120 km/h รท 3.6 = 33.33 m/s.
- Next, we can use the displacement (distance) and speed to calculate the acceleration. The formula to find acceleration is: a = (vf^2 - vi^2) / (2 * d), where vf is the final velocity (0 m/s since the train is stopping), vi is the initial velocity (33.33 m/s), and d is the displacement (150 m). Plugging in the values, we get: a = (0^2 - 33.33^2) / (2 * 150) = -111.108 m/s^2 (negative sign indicates deceleration).
Now that we have the acceleration, we can calculate the force Superman must exert:
- Use the formula F = m * a, where m is the mass of the train (3.6x10^5 kg) and a is the acceleration (-111.108 m/s^2): F = (3.6x10^5 kg) * (-111.108 m/s^2) = -3.996x10^7 N (negative sign indicates opposite direction to acceleration).
To compare this force to the weight of the train, we can calculate the weight:
- The weight is equal to the mass multiplied by the acceleration due to gravity (approximately 9.8 m/s^2): weight = (3.6x10^5 kg) * (9.8 m/s^2) = 3.528x10^6 N.
To express the force as a percentage of the weight:
- Divide the force by the weight and multiply by 100: percentage = (|-3.996x10^7| / 3.528x10^6) * 100 = 1132.55%.
Finally, to find 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 is equal in magnitude but opposite in direction to the force Superman exerts on the train: -3.996x10^7 N.