train car with mass m1 = 521 kg is moving to the right with a speed of v1 = 7.9 m/s and collides with a second train car. The two cars latch together during the collision and then move off to the right at vf = 5.1 m/s.
1)What is the initial momentum of the first train car? I got 4115.9 kg m/s as the correct answer.
2)What is the mass of the second train car?
I don't know how to do the second question please help.
1) 521*79 = 4115.9 kg*m/s
2) 4115.9 = (M1 + M2)*5.1
M1 + M2 = 807.0 kg
M2 = 807 - 521 = 286 kg
..not very heavy for a railroad car.
To solve the second question, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
1) The initial momentum of the first train car can be calculated using the formula: P = m1 * v1
P = 521 kg * 7.9 m/s
P = 4115.9 kg m/s
2) Let's assume the mass of the second train car is m2, and its velocity before the collision is v2. After the collision, both trains latch together and move with a final velocity vf. Since they latch together and move as one object, their momentum after the collision is calculated using the formula: P = (m1 + m2) * vf
Using the principle of conservation of momentum, we can equate the two momentum values before and after the collision:
m1 * v1 = (m1 + m2) * vf
Now, we can substitute the given values and solve the equation for m2:
521 kg * 7.9 m/s = (521 kg + m2) * 5.1 m/s
4142.9 kg m/s = (521 kg + m2) * 5.1 m/s
Dividing both sides of the equation by 5.1 m/s:
4142.9 kg m/s / 5.1 m/s = 521 kg + m2
811.9 kg = 521 kg + m2
Subtracting 521 kg from both sides of the equation:
811.9 kg - 521 kg = m2
291.9 kg = m2
Therefore, the mass of the second train car is 291.9 kg.
To find the mass of the second train car, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The initial momentum of the first train car is given as 4115.9 kg m/s. This value represents the total momentum before the collision.
After the collision, the two cars latch together, so their masses must be combined. Let's denote the mass of the second train car as m2.
The final momentum after the collision is given as vf = 5.1 m/s.
Using the principle of conservation of momentum, we can write the equation:
Total initial momentum = Total final momentum
(mass of first train car * velocity of first train car) = (combined mass * velocity of latched cars)
(521 kg * 7.9 m/s) = ((521 kg + m2) * 5.1 m/s)
Now we can solve this equation to find the mass of the second train car. Rearranging the equation, we have:
(521 kg * 7.9 m/s) = ((521 kg + m2) * 5.1 m/s)
Multiply both sides of the equation by 5.1 m/s:
(521 kg * 7.9 m/s * 5.1 m/s) = (521 kg + m2) * 5.1 m/s
Now, solve for m2:
m2 = (521 kg * 7.9 m/s * 5.1 m/s) / 5.1 m/s
m2 = (521 kg * 7.9 m/s)
m2 = 4103.9 kg
Therefore, the mass of the second train car is 4103.9 kg.