Superman must stop a 190-km/h train in 180m to keep it from hitting a stalled car on the tracks.
part a)If the train's mass is 3.8×10^5kg , how much force must he exert (find the magnitude)?
part b)Compare to the weight of the train (give as %).
partc) How much force(in magnitude) does the train exert on Superman?
(a) v=190 km/h =52.8 m/s,
a =v^2/2•s =(52.8)^2/2•180 = 7.74 m/s^2,
F = m•a = 3.8•10^5•7.74 = 2.94•10^6 N.
(b) Weight = mg = 3.8•10^5•9.8= 3.76•10^6 N.
(c) F12 = -F21 = >
F = 2.94•10^6 N.
for part b, what would be the percentage. i got 10% but it isnt right
John: show your work, you wouldn't want anyone to think you are answer grazing.
percent= force/mass*g * 100
i got it its 79% i was label some of the numbers with the wrong variables. tahnks and will keep that in mind
Part a) Well, I must say Superman has a real "loco" situation on his hands here! To calculate the force needed, we can use Newton's second law, F=ma. The mass of the train is 3.8×10^5 kg, and to stop it in 180 m, we need to bring it to rest. Since the final velocity is 0, we can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. Rearranging the equation, we get a = (v^2 - u^2) / (2s). Plugging in the values, we have a = (0 - (190)^2) / (2 * 180). Let me just calculate that for you... The force Superman must exert is approximately 79,688 N.
Part b) Now let's compare that to the weight of the train. The weight of an object is given by the equation W = mg, where m is the mass and g is the acceleration due to gravity. The weight of the train is therefore W = (3.8×10^5 kg) * (9.8 m/s^2). Let me do some quick math here... The weight of the train is approximately 3.724×10^6 N. So, when we compare the force Superman must exert to the weight of the train, we can say it's around 2.14% of the weight. Looks like Superman has to put some "super" strength into this one!
Part c) Now, let's turn the tables, or in this case, the tracks. To determine the force the train exerts on Superman, we can use Newton's third law. According to Newton, for every action, there's an equal and opposite reaction. So, the magnitude of the force the train exerts on Superman would be the same as the force Superman exerts on the train, which we calculated earlier to be approximately 79,688 N. It's a "forceful" situation indeed!
To solve this problem, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the product of its mass (m) and acceleration (a), or F = ma.
part a) To find the force Superman must exert to stop the train, we need to calculate the acceleration of the train. We can use the equation v^2 = u^2 + 2as, where v is the final velocity (0 in this case as the train is brought to a stop), u is the initial velocity (190 km/h or 52.78 m/s), a is the acceleration, and s is the distance (180 m).
Rearranging the equation to solve for acceleration (a), we get a = (v^2 - u^2) / (2s).
Plugging in the values, a = (0 - (52.78 m/s)^2) / (2 * 180 m) = -69.55 m/s^2 (Note: we have a negative value to indicate that the acceleration is opposite to the direction of motion).
Now, we can find the force using Newton's second law. F = ma, where m is the mass of the train (3.8×10^5 kg) and a is the acceleration (-69.55 m/s^2).
F = (3.8×10^5 kg) * (-69.55 m/s^2) = -2.65×10^7 N (Note: we have a negative value to indicate that the force should be exerted in the opposite direction to the train's motion).
Therefore, the magnitude of the force Superman must exert to stop the train is 2.65×10^7 N.
part b) To compare the force required to the weight of the train, we need to calculate the weight of the train. Weight can be calculated using the formula W = mg, where W is the weight, m is the mass (3.8×10^5 kg), and g is the acceleration due to gravity (approximately 9.8 m/s^2).
W = (3.8×10^5 kg) * (9.8 m/s^2) = 3.724×10^6 N.
To express the force required as a percentage of the weight, we can divide the force by the weight and multiply by 100.
Percentage = (Force / Weight) * 100 = (-2.65×10^7 N / 3.724×10^6 N) * 100 ≈ -712.07%
Therefore, the force Superman needs to exert is approximately 712.07% of the weight of the train.
part c) The force exerted on Superman by the train can be found using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
Since Superman exerts a force on the train to stop it, the train exerts the same magnitude of force on Superman in the opposite direction. Therefore, the force exerted on Superman by the train is also 2.65×10^7 N.