A 500-g cart moving at 2. 0 m/s on an air track elastically strikes a 1,000-g cart at rest.
What are the resulting velocities of the two carts?
The resulting velocity of the 500-g cart is 0 m/s. The resulting velocity of the 1000-g cart is 1 m/s.
To solve this problem, we need to apply the law of conservation of momentum.
According to the law of conservation of momentum, 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. Thus, we can write the equation for the conservation of momentum as:
(mass1 * velocity1) + (mass2 * velocity2) = (mass1 * final_velocity1) + (mass2 * final_velocity2)
Given:
Mass1 = 500 g = 0.5 kg
Velocity1 = 2.0 m/s
Mass2 = 1,000 g = 1 kg
Velocity2 = 0 m/s (since the second cart is at rest)
Let's solve for the final velocities:
(0.5 kg * 2.0 m/s) + (1 kg * 0 m/s) = (0.5 kg * final_velocity1) + (1 kg * final_velocity2)
1.0 kg m/s = 0.5 kg * final_velocity1 + 1 kg * final_velocity2
Now, we can rearrange the equation to solve for the final velocities:
final_velocity1 = (1.0 kg m/s - 1 kg * final_velocity2) / 0.5 kg
Substituting the given values, we get:
final_velocity1 = (1.0 kg m/s - 1 kg * 0 m/s) / 0.5 kg
final_velocity1 = 1.0 m/s
Finally, since the momentum is conserved, we can find the final_velocity2 by rearranging the equation:
final_velocity2 = (1.0 kg m/s - 0.5 kg * final_velocity1) / 1 kg
Substituting the given values, we get:
final_velocity2 = (1.0 kg m/s - 0.5 kg * 1.0 m/s) / 1 kg
final_velocity2 = 0.5 m/s
Therefore, the resulting velocities of the two carts are:
- The first cart has a final velocity of 1.0 m/s.
- The second cart has a final velocity of 0.5 m/s.