Question

A student does an experiment to check the mass of a cart. The student sends a 1 kg cart with a spring attached at the front end into a collision with a cart of unknown mass. After the collision, the student notes that the 1 kg cart moves forward with reduced speed, and the unknown cart moves forward at a faster speed than the 1 kg cart. What does this experiment show about the mass of the unknown cart?

1) the unknown cart is more than 1 kg
2) the unknown cart is 1 kg
3) the unknown cart is less than 1 kg
4) no information about the mass of the unknown cart can be obtained from this experiment.

Answer 1

The experiment shows that the unknown cart is less than 1 kg because the conservation of momentum requires that the lighter cart would need to move quicker to compensate for its smaller mass in order to conserve the total momentum of the system. Therefore, the correct option is 3.

Step-by-step explanation:

During the collision between the two carts, the principle of conservation of momentum must be considered. If the 1 kg cart moves forward with reduced speed and the unknown cart moves forward at a faster speed than the 1 kg cart, it implies that the unknown cart has less mass than the 1 kg cart. This is because, in the absence of external forces, the momentum of the system consisting of both carts before and after the collision must be the same. If the lighter cart moves faster after the collision, it compensates for its smaller mass, conserving the overall momentum.

Thus, given that momentum equals mass times velocity (p = m * v), and knowing that momentum is conserved in a collision (p₁ + p₂ = constant), we can conclude that the unknown cart must be lighter to have acquired a higher speed after the collision.