Two railroad freight cars with masses 110 Mg and 150 Mg approach with equal speeds of 0.310 m/s . They collide, the lighter car rebounding opposite its original direction at 0.270 m/s.
Find the velocity of the heavier car after the collision. Assume the original direction of the lighter car is positive. Express your answer to two significant figures and include the appropriate units.
What fraction of the original kinetic energy was lost in this inelastic collision?Express your answer using two significant figures.
I am calculating -.28 m/s for the 1st part but it is not correct.
Lets pick the original direction of the light car as positive. Before
110*.31 - 150*.31 = -12.4
That momentum must be conserved
After
110(-.27) + 150vf = -12.4
To find the velocity of the heavier car after the collision, 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 momentum of an object is given by the product of its mass and velocity:
Momentum = mass * velocity
Let's assume the positive direction as the initial direction of the lighter car. Therefore, the momentum before the collision can be calculated as:
Initial Momentum = (mass of lighter car) * (velocity of lighter car) + (mass of heavier car) * (velocity of heavier car)
= (110 Mg) * (0.310 m/s) + (150 Mg) * (0)
Since the heavier car is initially at rest, its velocity before the collision is 0.
Now, let's consider the momentum after the collision. The lighter car rebounds opposite to its original direction, which means its velocity after the collision will be negative. The heavier car will have some velocity after the collision.
Final Momentum = (mass of lighter car) * (velocity of lighter car) + (mass of heavier car) * (velocity of heavier car)
= (110 Mg) * (-0.270 m/s) + (150 Mg) * (velocity of heavier car)
According to the conservation of momentum principle, the initial momentum is equal to the final momentum. Therefore, we can set up an equation:
(110 Mg) * (0.310 m/s) + (150 Mg) * (0) = (110 Mg) * (-0.270 m/s) + (150 Mg) * (velocity of heavier car)
Simplifying the equation, we get:
34.1 Mg*m/s = -29.7 Mg*m/s + (150 Mg) * (velocity of heavier car)
Now, let's solve for the velocity of the heavier car after the collision:
34.1 Mg*m/s + 29.7 Mg*m/s = (150 Mg) * (velocity of heavier car)
63.8 Mg*m/s = (150 Mg) * (velocity of heavier car)
Dividing both sides of the equation by 150 Mg, we get:
velocity of heavier car = (63.8 Mg*m/s) / (150 Mg)
velocity of heavier car = 0.425 m/s
So, the velocity of the heavier car after the collision is 0.425 m/s (rounded to two significant figures).
To find the fraction of the original kinetic energy lost in this inelastic collision, we need to compare the initial kinetic energy to the final kinetic energy. The kinetic energy is given by the formula:
Kinetic Energy = (1/2) * (mass) * (velocity)^2
The initial kinetic energy can be calculated using the mass and velocity of both cars before the collision. The final kinetic energy can be calculated using the mass and velocity of both cars after the collision.
Let's calculate the initial kinetic energy:
Initial Kinetic Energy = (1/2) * (mass of lighter car) * (velocity of lighter car)^2 + (1/2) * (mass of heavier car) * (velocity of heavier car)^2
= (1/2) * (110 Mg) * (0.310 m/s)^2 + (1/2) * (150 Mg) * (0)^2
= 5.3895 Mg * m^2/s^2 + 0
= 5.3895 Mg * m^2/s^2
Now, let's calculate the final kinetic energy:
Final Kinetic Energy = (1/2) * (mass of lighter car) * (velocity of lighter car)^2 + (1/2) * (mass of heavier car) * (velocity of heavier car)^2
= (1/2) * (110 Mg) * (-0.270 m/s)^2 + (1/2) * (150 Mg) * (0.425 m/s)^2
= 0.48645 Mg * m^2/s^2 + 12.765625 Mg * m^2/s^2
= 13.252075 Mg * m^2/s^2
The fraction of the original kinetic energy lost in the collision can be calculated by taking the ratio of the difference in kinetic energy to the initial kinetic energy:
Fraction of Energy Lost = (Initial Kinetic Energy - Final Kinetic Energy) / Initial Kinetic Energy
= (5.3895 Mg * m^2/s^2 - 13.252075 Mg * m^2/s^2) / 5.3895 Mg * m^2/s^2
= -7.862575 Mg * m^2/s^2 / 5.3895 Mg * m^2/s^2
= -1.455 (rounded to two significant figures)
Note that the negative sign indicates that the kinetic energy was lost in the collision.
So, the fraction of the original kinetic energy lost in this inelastic collision is approximately -1.455 (rounded to two significant figures).