A 12100kg railroad car travels alone on a level frictionless track with a constant speed of 15.0m/s . A 6100kg load, initially at rest, is dropped onto the car.
What is the car's new speed?
To determine the car's new speed after the load is dropped onto it, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the load is dropped is equal to the total momentum after the load is dropped.
Let's calculate the initial momentum of the car before the load is dropped:
Momentum of the car before = mass of the car × velocity of the car
Mass of the car = 12100 kg
Velocity of the car = 15.0 m/s
Initial momentum of the car before the load is dropped = 12100 kg × 15.0 m/s
Now, let's calculate the momentum of the load after it is dropped:
Momentum of the load after = mass of the load × velocity of the load
Mass of the load = 6100 kg
Velocity of the load = ?
Since the load was initially at rest, its initial velocity is 0 m/s.
Now, the total momentum after the load is dropped can be calculated by adding the momentum of the car after the load is dropped and the momentum of the load after it is dropped.
Total momentum after = Momentum of the car after + Momentum of the load after
According to the conservation of momentum principle, the total momentum before the load is dropped should be equal to the total momentum after the load is dropped.
Therefore,
Momentum before = Momentum after
12100 kg × 15.0 m/s = Momentum of the car after + (6100 kg × velocity of the load)
Now, we can solve for the velocity of the load:
15.0 × 12100 = (6100 × velocity of the load)
By rearranging the equation, we find:
Velocity of the load = (15.0 × 12100) / 6100
Plugging in the given values:
Velocity of the load = 30.0 m/s
Therefore, the car's new speed after the load is dropped onto it is 30.0 m/s.
To find the new speed of the car after the load is dropped, we can apply the principle of conservation of momentum.
The initial momentum of the car is given by:
Initial momentum of car = mass of car * initial velocity of car
P1 = m1 * v1
P1 = 12100 kg * 15.0 m/s
The final momentum of the car and the load combined is given by:
Final momentum of car + load = (mass of car + mass of load) * final velocity
P2 = (m1 + m2) * v2
P2 = (12100 kg + 6100 kg) * v2
According to the principle of conservation of momentum, the initial and final momentum should be equal:
P1 = P2
12100 kg * 15.0 m/s = (12100 kg + 6100 kg) * v2
181500 kg*m/s = 18200 kg * v2
Now, we can solve for the final velocity (v2):
v2 = 181500 kg*m/s / 18200 kg
v2 ≈ 9.99 m/s
Therefore, the car's new speed after the load is dropped is approximately 9.99 m/s.