A(n) 13,300 lb railroad car traveling at 7.4 ft/s couples with a stationary car of 6790 lb. The acceleration of gravity is 32 ft/s^2. What is their velocity after the collision (ft/s)?
And what impulse did the first car receive? Answer in units of lbs.
Any help would be grateful, THANKS
Use conservation of momentum. When the cars are coupled, they have the same velocity
13,300lb*7.4 ft/s = (13,300+6790)lb*Vfinal
It is not necessary to convert the weight unit to mass in this case. g would appear on both sides and cancel out.
Vfinal = 7.4 ft/s*(0.662) = 4.9 ft/s
The impulse received by the first car equals its loss of momentum:
(13,300/32.2)slug *(4.9 - 7.6)ft/s
= -1115 slug ft/s (or lbf-seconds)
Mass units of slugs are needed when calculating momentum.
To find the velocity after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Let's assume that the velocity of the railroad car after the collision is v1 (ft/s) and the velocity of the stationary car after the collision is v2 (ft/s).
The momentum of the railroad car before the collision is given by:
momentum1 = mass1 * velocity1
The momentum of the stationary car before the collision is given by:
momentum2 = mass2 * velocity2
The total momentum before the collision is equal to the total momentum after the collision:
momentum1 + momentum2 = (mass1 + mass2) * velocity_after
Now, let's substitute the given values:
mass1 = 13,300 lb, velocity1 = 7.4 ft/s
mass2 = 6,790 lb, velocity2 = 0 ft/s
momentum1 = 13,300 lb * 7.4 ft/s
momentum2 = 6,790 lb * 0 ft/s
The total momentum before the collision is:
momentum1 + momentum2 = (13,300 lb * 7.4 ft/s) + (6,790 lb * 0 ft/s)
Simplifying the equation:
momentum1 + momentum2 = (13,300 lb * 7.4 ft/s)
Now, we divide both sides of the equation by (mass1 + mass2) to solve for velocity_after:
momentum1 + momentum2 = (mass1 + mass2) * velocity_after
((13,300 lb * 7.4 ft/s) / (mass1 + mass2)) = velocity_after
After calculating the right-hand side of the equation, we will get the velocity after the collision in ft/s.
To find the impulse received by the first car, we can use the formula:
Impulse = change in momentum
The change in momentum is equal to the final momentum minus the initial momentum of the car. Since the car was initially at rest, the initial momentum is zero.
Therefore, the impulse received by the first car is equal to its final momentum. We can find the final momentum by multiplying the mass of the first car with its final velocity.
Impulse = mass1 * velocity_after
After calculating, we will get the impulse received by the first car in units of lbs.
To solve this problem, we can use the principle of conservation of momentum.
1. Calculate the momentum of the first car before the collision:
Momentum = mass × velocity
Momentum = 13,300 lb × 7.4 ft/s
2. Calculate the momentum of the second car before the collision:
Momentum = mass × velocity
Momentum = 6790 lb × 0 ft/s (the second car is stationary)
3. Calculate the total momentum before the collision:
Total momentum before collision = Momentum of first car + Momentum of second car
4. Calculate the total mass before the collision:
Total mass before collision = mass of first car + mass of second car
5. Calculate the velocity after the collision using the principle of conservation of momentum:
Total momentum before collision = Total momentum after collision
Total mass before collision × Velocity after collision = Total momentum before collision
6. Solve for Velocity after collision:
Velocity after collision = Total momentum before collision / Total mass before collision
Let's plug in the values and calculate:
1. Momentum of the first car before the collision:
Momentum = 13,300 lb × 7.4 ft/s = 98,420 lb·ft/s
2. Momentum of the second car before the collision:
Momentum = 6790 lb × 0 ft/s = 0 lb·ft/s
3. Total momentum before the collision:
Total momentum before collision = 98,420 lb·ft/s + 0 lb·ft/s = 98,420 lb·ft/s
4. Total mass before the collision:
Total mass before collision = 13,300 lb + 6790 lb = 20,090 lb
5. Velocity after the collision:
Velocity after collision = 98,420 lb·ft/s / 20,090 lb
Velocity after collision ≈ 4.899 ft/s
Therefore, the velocity of the two cars after the collision is approximately 4.899 ft/s.
To calculate the impulse received by the first car, we can use the formula:
Impulse = Change in momentum
Since the second car is stationary, the change in momentum of the first car is equal to its initial momentum:
Impulse = Momentum of the first car before the collision
Impulse = 98,420 lb·ft/s
Thus, the impulse received by the first car is 98,420 lb·ft/s.