Calculating Velocity in a Collision Scenario
What was the velocity of the first cart when the second cart was still at rest?
A 2.00 kg cart is rolling across a frictionless, horizontal track toward a 1.20 kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. At a certain instant after the carts collide, the first cart’s velocity is 5.10 m/s, and the second cart’s velocity is 2.20 m/s.
Answer:
To find the velocity of the first cart when the second cart was still at rest, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Let's denote the initial velocity of the first cart as v1 and the initial velocity of the second cart as v2 (which is 0 since it is at rest). The mass of the first cart is 2.00 kg and the mass of the second cart is 1.20 kg. After the collision, the velocity of the first cart is 5.10 m/s and the velocity of the second cart is 2.20 m/s.
Using the conservation of momentum, we can write:
(mass of first cart) * (initial velocity of first cart) + (mass of second cart) * (initial velocity of second cart) = (mass of first cart) * (final velocity of first cart) + (mass of second cart) * (final velocity of second cart)
Substituting the given values:
(2.00 kg) * (v1) + (1.20 kg) * (0 m/s) = (2.00 kg) * (5.10 m/s) + (1.20 kg) * (2.20 m/s)
Simplifying the equation:
2.00 kg * v1 = 10.20 kgm/s + 2.64 kgm/s
2.00 kg * v1 = 12.84 kgm/s
Finally, we can solve for v1:
v1 = 12.84 kgm/s / 2.00 kg
v1 = 6.42 m/s
Therefore, the velocity of the first cart when the second cart was still at rest was 6.42 m/s.