A 9600 kg boxcar traveling at 17 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 9.0 m/s. What is the mass of the second car?
I know that this is an inelastic collision because the 2 stick together but I need help PLEASE!!
conservation of momentum:
9600*17+m*0=(m+9600)9
solve for m.
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass with its velocity:
Momentum (p) = mass (m) × velocity (v)
Given information:
Mass of the first boxcar, m1 = 9600 kg
Initial velocity of the first boxcar, v1 = 17 m/s
Final velocity of the combined boxcars, vf = 9.0 m/s
Let's assume the mass of the second boxcar is m2.
Before the collision, the momentum is given by the sum of the individual momenta:
Initial momentum = (mass of the first boxcar × velocity of the first boxcar) + (mass of the second boxcar × velocity of the second boxcar, which is 0 as the second boxcar is at rest)
After the collision, the total momentum is equal to the momentum of the combined boxcars:
Final momentum = (mass of the combined boxcars × final velocity)
According to the law of conservation of momentum:
Initial momentum = Final momentum
Therefore,
(mass of the first boxcar × velocity of the first boxcar) = (mass of the combined boxcars × final velocity)
(9600 kg × 17 m/s) = (m1 + m2) × 9.0 m/s
Now we can solve for the mass of the second boxcar, m2:
9600 kg × 17 m/s = (9600 kg + m2) × 9.0 m/s
163,200 kg·m/s = (9600 kg + m2) × 9.0 m/s
Dividing both sides of the equation by 9.0 m/s:
18,133.333 kg = 9600 kg + m2
Subtracting 9600 kg from both sides of the equation:
m2 = 18,133.333 kg - 9600 kg
m2 = 9533.333 kg
Therefore, the mass of the second boxcar is approximately 9533.33 kg.
To solve this problem, we can apply the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the mass of the first boxcar as m1, the initial velocity as v1, the mass of the second boxcar as m2, and the final velocity as vf.
Before the collision:
Total momentum before = momentum of the first boxcar + momentum of the second boxcar
Total momentum before = m1 * v1 + m2 * 0 (since the second boxcar is at rest)
After the collision:
Total momentum after = momentum of the two boxcars together
Total momentum after = (m1 + m2) * vf
According to the conservation of momentum principle:
Total momentum before = Total momentum after
m1 * v1 + m2 * 0 = (m1 + m2) * vf
Plugging in the values from the problem:
9600 kg * 17 m/s + m2 * 0 = (9600 kg + m2) * 9 m/s
Now we can solve for m2, the mass of the second car.
9600 kg * 17 m/s + 0 = (9600 kg + m2) * 9 m/s
163,200 kg m/s = 9,600 kg * 9 m/s + m2 * 9 m/s
163,200 kg m/s = 86,400 kg m/s + 9 m/s * m2
163,200 kg m/s - 86,400 kg m/s = 9 m/s * m2
76,800 kg m/s = 9 m/s * m2
To get the mass of the second car (m2), divide both sides of the equation by 9 m/s:
(76,800 kg m/s) / (9 m/s) = m2
8,533.33 kg = m2
Hence, the mass of the second boxcar is approximately 8,533.33 kg.