p = mv
Scenario #4
At a station ,a train weighs approximately 1000kg and is moving at 50m/s on a railway and collides with an incoming train weighing 1000kg and moving at -20m/s.
1)If these two trains stick together and begin to move after having being collided with one another , at what velocity will they move at?
2)The collision that occurred was an inelastic one , Suppose if the collision that occurred was a elastic one , at what rate of speed will the trains move at on the railway?
3)If the trains weighed 2000kg what will be the momentum of the trains?
1. M1*V1 + M2*V2 = M1*V + M2*V.
1000*50 - 1000*20 = 1000V + 1000V,
30,000 = 2000V,
V = 15 m/s.
3. Momentum = 2000*50 - 2000*20 = 60,000 kg*m/s.
To answer these questions, we can use the principle of conservation of momentum. This principle states that the total momentum of a closed system remains constant before and after a collision.
1) If the trains stick together and move after colliding, we can calculate the final velocity using the conservation of momentum equation:
Initial momentum = Final momentum
The initial momentum of Train 1 is given by:
p1 = m1 * v1 = 1000 kg * 50 m/s = 50,000 kg·m/s (since it is moving in the positive direction)
The initial momentum of Train 2 is given by:
p2 = m2 * v2 = 1000 kg * (-20 m/s) = -20,000 kg·m/s (since it is moving in the negative direction)
The final momentum of the system (trains sticking together) is given by:
pf = (m1 + m2) * vf
Using the conservation of momentum equation, we can equate the initial and final momentum:
p1 + p2 = pf
Substituting the values we have:
50,000 kg·m/s + (-20,000 kg·m/s) = (1000 kg + 1000 kg) * vf
30,000 kg·m/s = 2000 kg * vf
Solving for vf:
vf = 30,000 kg·m/s / 2000 kg = 15 m/s
Therefore, the trains will move at a velocity of 15 m/s after the collision.
2) If the collision was elastic, the total kinetic energy of the system would be conserved. However, in an inelastic collision like the one mentioned, some kinetic energy is lost due to deformation and other factors.
To calculate the velocity after an elastic collision, we can use the conservation of both momentum and kinetic energy equations.
Using the same initial momentum values as before (p1 and p2), the kinetic energy before the collision (KEi) is given by:
KEi = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
Substituting the values:
KEi = (1/2) * 1000 kg * (50 m/s)^2 + (1/2) * 1000 kg * (-20 m/s)^2
Calculating KEi:
KEi = 625,000 J
In an elastic collision, the final kinetic energy (KEf) would be equal to the initial kinetic energy. However, since this is an inelastic collision, some kinetic energy is lost. So we cannot directly determine the final velocity without knowing the specific energy loss or deformation.
3) If the trains weighed 2000 kg in total, we can calculate the momentum of the trains by using the formula p = mv.
The total momentum (p) is given by:
p = (m1 + m2) * v
Substituting the values:
p = 2000 kg * vf (where vf is the final velocity calculated in question 1)
Therefore, the momentum of the trains with a total weight of 2000 kg would be 30,000 kg·m/s.