Two identical smooth steel spheres, Sphere A and Sphere B
PHYSICS · Multi-part · ISC · Physics · Laws of Motion · Laws of Motion
Problem
Two identical smooth steel spheres, Sphere A and Sphere B, each of mass m, are initially at rest on a horizontal, friction-free surface.
A horizontal force is applied to each sphere for precisely 0.60s. The time dependence of the force for each sphere is described verbally below.
• Force for Sphere A (Graph A): The force instantly rises to 8.0N at t=0 and remains constant at that value until t=0.60s, after which it is zero.
• Force for Sphere B (Graph B): The force increases linearly from 0N at t=0 to 12.0N at t=0.30s, then decreases linearly back to 0N at t=0.60s.
Answer the questions that follow, using clear reasoning based on the information provided.
(a) Describe, without carrying out a detailed numerical calculation, which sphere experiences the greater magnitude of change in momentum during the 0.60s interval. Explain your reasoning using features of the two force–time functions.
(b) The speeds of the spheres at t=0.60s are to be compared. Explain how the graphs of force versus time for the two spheres allow you to determine which sphere attains the greater speed, and justify your conclusion qualitatively.
(c) Suppose a third sphere of the same mass is acted on by a force that has the same shape as Graph B but with its peak value doubled. Predict qualitatively how the final speed of the third sphere would compare with those of Spheres A and B, and justify your answer.