A 9500 kg boxcar traveling at 19 m/s strikes a stationary second car. The two stick together and move off with a speed of 10 m/s. What is the mass of the second car?
Apply the law of conservation of linear momentum. Let the second (struck) car's mass be M2, and the first car's mass be M1.
M1*19 = (M1 + M2)*10
Solve for M2
9 M1 = 10 M2
You finish it.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the momentum before the collision is equal to the momentum after the collision.
The momentum before the collision can be calculated by multiplying the mass (m) of the boxcar by its velocity (v):
Momentum before collision = mass of boxcar × velocity of boxcar
momentum_before = m1 × v1
= 9500 kg × 19 m/s
= 180,500 kg·m/s
After the collision, the two cars stick together and move with a common velocity. This final momentum can be calculated by multiplying the combined mass (M) of the boxcar and the second car by the final velocity (V) after the collision:
Momentum after collision = (mass of boxcar + mass of second car) × velocity after collision
momentum_after = (m1 + m2) × V
= (9500 kg + m2) × 10 m/s
= 9500 kg × 10 m/s + m2 × 10 m/s
= 95,000 kg·m/s + 10 m/s × m2
Since the momentum before the collision is equal to the momentum after the collision, we can equate the two equations:
momentum_before = momentum_after
180,500 kg·m/s = 95,000 kg·m/s + 10 m/s × m2
Subtracting 95,000 kg·m/s from both sides gives:
180,500 kg·m/s - 95,000 kg·m/s = 10 m/s × m2
85,500 kg·m/s = 10 m/s × m2
To find the mass of the second car (m2), we divide through by 10 m/s:
85,500 kg·m/s ÷ 10 m/s = m2
m2 = 8,550 kg
Therefore, the mass of the second car is 8,550 kg.