2.Boxcar A, with a mass of 1500 kg, is travelling at 25 m/s to the east. Boxcar B has a mass of 2000 kg and is initially at rest. The boxcars collide inelastically and move together after they get stuck. What is their combined velocity?
Ma*V = 1500*25 = 37,500 = Momentum
of Boxcar A.
(Ma+Mb)*V = 37,500
(1500+2000)V = 37,500
3500V = 37,500
V = 10.71 m/s.
To find the combined velocity of the two boxcars after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass with its velocity. So, we can calculate the momentum of each boxcar before the collision, and then use that information to find their combined velocity after the collision.
Let's assign variables to the quantities involved:
- Mass of Boxcar A (m1) = 1500 kg
- Initial velocity of Boxcar A (v1) = 25 m/s
- Mass of Boxcar B (m2) = 2000 kg
- Initial velocity of Boxcar B (v2) = 0 m/s (initially at rest)
- Combined velocity after collision (vf)
The momentum of each boxcar before the collision can be calculated as follows:
Momentum of Boxcar A before collision (p1) = m1 * v1 = 1500 kg * 25 m/s = 37500 kg·m/s
Momentum of Boxcar B before collision (p2) = m2 * v2 = 2000 kg * 0 m/s = 0 kg·m/s
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
p1 + p2 = final momentum
Since the boxcars get stuck together and move with a common velocity vf after the collision, their final momentum can be calculated as the product of their combined mass (m1 + m2) and the final velocity (vf):
final momentum = (m1 + m2) * vf
As per the conservation of momentum law, we can equate the two expressions for momentum:
p1 + p2 = (m1 + m2) * vf
Substituting the known values:
37500 kg·m/s + 0 kg·m/s = (1500 kg + 2000 kg) * vf
Simplifying further:
37500 kg·m/s = 3500 kg * vf
Now, we can solve for vf:
vf = 37500 kg·m/s / 3500 kg = 10.71 m/s (rounded to two decimal places)
Therefore, the combined velocity of the two boxcars after the inelastic collision is approximately 10.71 m/s.