Question -
Answer -
A ball rebounding between two walls locatedbetween at┬аx┬а= 0 and┬аx┬а= 2 cm; after every 2s, the ball receives an impulse of magnitude 0.08 ├Ч 10тАУ2┬аkg m/sfrom the walls
The given graph shows that a body changesits direction of motion after every 2 s. Physically, this situation can bevisualized as a ball rebounding to and fro between two stationary wallssituated between positions┬аx┬а= 0 and┬аx┬а= 2cm. Since the slope of the┬аxтАУt┬аgraph reverses afterevery 2 s, the ball collides with a wall after every 2 s. Therefore, ballreceives an impulse after every 2 s.
Mass of the ball,┬аm┬а= 0.04kg
The slope of the graph gives the velocity ofthe ball. Using the graph, we can calculate initial velocity (u) as:
.
Velocity of the ball before collision,┬аu┬а=10тАУ2┬аm/s
Velocity of the ball after collision,┬аv┬а=тАУ10тАУ2┬аm/s
(Here,the negative sign arises as the ball reverses its direction of motion.)
Magnitudeof impulse = Change in momentum
=0.08 ├Ч 10тАУ2┬аkg m/s