Question

Two hard, steel carts collide head-on and then ricochet off each other in opposite directions on a frictionless surface. Cart 1 has a mass of 0.350 kg and an initial velocity of 2 m/s. Cart 2 has a mass of 0.500 kg and an initial velocity of -0.500 m/s. After the collision, cart 1 recoils with a velocity of -4 m/s.

a. 1 m/s
b. -1 m/s
c. -3 m/s
d. -5 m/s

Answer 1

The final velocity of Cart 2 after the collision is 1 m/s, determined by using the conservation of momentum for an elastic collision on a frictionless surface.

Step-by-step explanation:

The question asks for the final velocity of Cart 2 after a head-on elastic collision with Cart 1 on a frictionless surface. We will use the conservation of momentum because no external forces are acting on the system (net F = 0). The equation for conservation of momentum is:

m1v1 + m2v2 = m1v'1 + m2v'2

Substituting the given values and solving for v'2, we find:

(0.350 kg * 2 m/s + 0.500 kg * (-0.500 m/s) = 0.350 kg * (-4 m/s) + 0.500 kg * v'2)

Solving the equation for v'2 yields:

v'2 = (0.350 kg * 2 m/s - 0.350 kg * (-4 m/s) - 0.500 kg * (-0.500 m/s)) / 0.500 kg

Resulting in v'2 = 1 m/s. Therefore, the final velocity of Cart 2 is 1 m/s, which corresponds to option (a).