A rubber ball of mass 41 grams was moving horizontally along a smooth surface. It struck a barrier at 62 centimeters per second and rebounded in the opposite direction at 45 centimeters per second. Find the magnitude of the change in its momentum as a result of the impact.
We will begin by sketching a diagram of the situation before and after the impact. We are told in the question that the mass of the rubber ball is 41 grams, and this will not change after the impact with the barrier. We know that prior to the impact, the ball is moving at 62 centimeters per second toward the barrier. After the impact, it is moving the opposite direction with a speed of 45 centimeters per second. We are asked to calculate the change in momentum. We can do this using the formula Δ𝐻 is equal to 𝑚𝑣 minus 𝑚𝑢, where 𝑚 is the mass of the body, 𝑢 is the initial velocity, and 𝑣 is the final velocity.
In this question, we’ll take the positive direction to be toward the barrier. The change in momentum Δ𝐻 is therefore equal to 41 multiplied by negative 45 minus 41 multiplied by 62. Note that the 45 is negative as the ball is traveling away from the barrier after the impact. The right-hand side simplifies to negative 1845 minus 2542. This is equal to negative 4387. We need the magnitude of the change in momentum. Therefore, our answer must be positive. The magnitude of the change in momentum as a result of the impact is 4387 gram centimeters per second. Note that the units in this question were gram centimeters per second and not the standard units of kilogram meters per second.