Problem 5 - University Physics with Modern Physics

Question

Consider these three situations: (i) A ball moving to the right at speed \(v\) is brought to rest. (ii) The same ball at rest is projected at speed \(v\) toward the left. (iii) The same ball moving to the left at speed \(v\) speeds up to \(2 v\). In which situation(s) does the ball undergo the largest change in momentum? a) situation (i) d) situations (i) and (ii) b) situation (ii) e) all three situations c) situation (iii)

Step-by-Step Solution

Answer

a) A ball is moving to the right at speed 'v,' and is brought to rest. b) A ball is initially at rest, and is projected at a speed of 'v' towards the left. c) A ball is moving to the left at speed 'v,' and speeds up to 2v. d) none of the above e) all three situations Answer: e) all three situations

Step 1: Situation (i)

In this situation, the ball moves to the right at speed 'v' and is brought to rest. Initial momentum = mv Final momentum = 0 (as the ball comes to rest) Change in momentum = 0 - mv = -mv

Step 2: Situation (ii)

In this situation, the ball is initially at rest and is projected at a speed of 'v' towards the left. Initial momentum = 0 Final momentum = -mv (as the ball moves to the left) Change in momentum = -mv - 0 = -mv

Step 3: Situation (iii)

In this situation, the ball is moving to the left at speed 'v' and speeds up to 2v. Initial momentum = -mv Final momentum = -2mv (as the ball speeds up to 2v) Change in momentum = -2mv - (-mv) = -mv By comparing the change of momentum in each situation, we see that the ball experiences the largest change in momentum in all three situations. The change in each situation is -mv. Hence, the correct answer is: e) all three situations