How Fast Must Superman Fly to Stop a Moving Train Safely?

[Smartguy94]

Homework Statement

Find the speed at which Superman (mass=89.0 kg) must fly into a train (mass = 17755 kg) traveling at 85.0 km/hr to stop it.

Running into the train at that speed would severely damage both train and passengers. Calculate the minimum time Superman must take to stop the train, if the passengers experience an average horizontal force of 0.410 their own weight

How far does the train then travel while being slowed to a stop?

Homework Equations

p=mv
F=dp/dt
F=ma
J= p2-p1
J=F(t2-t1)

The Attempt at a Solution

I found the speed at which superman should fly by

m1v1=m2v2
17755*85.0=89.0*v2
v2=1.70×10^4 km/hr

for the minimum time this is what I do, but I got it wrong

since J=F(t2-t1)
and J=p(final)-p(initial)
then J=mv-mv
J=(89)(0)-(89)(1.70×10^4)
J=1513000

J=F(t2-t1)
1513000=(.41)(t)
t=3.68x10^6hr

then for the distance I couldn't calculate it because I had no idea what the time is

 

[Simon Bridge]

Superman has to do work on the train to slow it to a stop - this work is the change in kinetic energy of the train and work is force (given) times distance.

You could treat it as a kinematics problem, assuming constant acceleration. The v-t graph is a triangle height v_train and base T (= time to stop), the slope of the graph is the acceleration: a = -F/m_train = v_train/T but conservation of energy is the way to go here.

 

[gneill]

To calculate the time required to bring the train to a halt you've chosen to use the change in momentum, Δp = F*Δt = M*Δv (You called Δp "J"). Then
$$\Delta t = \frac{M \Delta v}{F}$$The problem is, you need to know what F is. You're given the hint that the maximum horizontal force on a given passenger should be 0.410 times their weight. Well, if their weight is m*g then F = 0.410*m*g, and the maximum acceleration would be F/m = 0.410*g. Apply this acceleration to the train as a whole and you get:
$$F = 0.410 M g$$
You'll have to be careful with the units here! You've been working with km and hours, and g is usually specified in m and seconds.