A rock is thrown into a railroad car standing on a level frictionless track. If the rock has a mass of ms = 1.100 kg and is tossed with a velocity v = 6.3 m/s, how far up will the car go (mc = 5.400 kg) before stopping?
Please explain
the words "into" and "up" , the velocity (with out direction) make this very ill defined.
By up, the railroad car is going up a hill. Sorry if that was unclear
To solve this problem, we need to use the principle of conservation of momentum.
Conservation of momentum states that the total momentum of a system before an event is equal to the total momentum of the system after the event, provided that no external forces act on the system.
In this case, the system consists of the rock and the railroad car. Before the rock is thrown, the system is at rest, so the total momentum is zero.
After the rock is thrown, the momentum of the rock is given by the equation:
momentum of the rock = mass of the rock * velocity of the rock
Mrock = ms * vs
And the momentum of the car is given by the equation:
momentum of the car = mass of the car * velocity of the car
Mcar = mc * vc
Since the system is isolated, the total momentum of the system before the rock is thrown is equal to the total momentum of the system after the rock is thrown.
Msystem_before = Msystem_after
0 = Mrock + Mcar
ms * vs + mc * vc = 0
Now we can solve for vc, the velocity of the car after the rock is thrown.
vc = (-ms * vs) / mc
Now that we have the velocity of the car after the rock is thrown, we can use the principle of conservation of mechanical energy to determine how far up the car will go before stopping.
The principle of conservation of mechanical energy states that the total mechanical energy of a system is conserved, provided that no external forces do work on the system. In this case, the only force acting on the system is gravity, which is a conservative force and does not perform work.
The total mechanical energy of the system is given by the sum of the kinetic energy of the rock-car system and the gravitational potential energy of the car.
Total mechanical energy before = Total mechanical energy after
0 + mcar * g * h = (1/2) * (ms + mc) * vc^2 + 0
Solving for h, the height the car will go up, we have:
h = [(1/2) * (ms + mc) * vc^2] / (mcar * g)
Now we can substitute the given values into the equation and solve for h.