A railway track travelling along a level at 9 m/s collides with, and becoms coupled to a stationary truck. Find the velocity of the coupled trucks immediately after the collision if the stationary truck has a mass which is :
A ) equal to the mass of the moving truck
B) twice the mass of the moving truck
I assume that your 9 m/s speed refers to a "truck" (railcar) on the track. You wrote that the track is moving.
In both cases, apply the law of conservation of momentum. Let M be the mass of the initially moving truck
In the first case,
M*V1 = (2M)*Vfinal
Vfinal = (V1)/2 = 4.5 m/s
In the second case,
M*V1 = (M + 2M)*Vfinal = 3M*Vfinal
Vfinal = ___
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the mass of the moving truck as m1, the velocity of the moving truck as v1, the mass of the stationary truck as m2, and the velocity of the coupled trucks after the collision as v'.
1) When the stationary truck has a mass equal to the mass of the moving truck (A), the momentum before the collision is given by:
Momentum before collision = (mass of moving truck) x (velocity of moving truck)
= m1 x v1
After the collision, the two trucks are attached and moving together. The total mass of the coupled trucks is m1 + m2, and since the velocities are the same for both trucks (they are coupled), we can calculate the velocity (v') using the conservation of momentum:
Momentum after collision = (total mass) x (velocity after collision)
(m1 + m2) x v' = m1 x v1
v' = (m1 x v1) / (m1 + m2)
2) When the stationary truck has a mass twice that of the moving truck (B), the momentum before the collision is given by:
Momentum before collision = (mass of moving truck) x (velocity of moving truck)
= m1 x v1
Using the same logic as before, the total mass of the coupled trucks is now m1 + 2m1 = 3m1. So, applying the conservation of momentum:
Momentum after collision = (total mass) x (velocity after collision)
(3m1) x v' = m1 x v1
v' = (m1 x v1) / (3m1)
Simplifying these equations, we find:
A) v' = (m1 x v1) / (m1 + m2)
B) v' = (m1 x v1) / (3m1)
So, the velocity of the coupled trucks immediately after the collision depends on the masses of the trucks.