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Laws Of Motion

Question
CBSEENPH11020080

Figure 5.17 shows the position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the body? What is the magnitude of each impulse?


Solution
Between x = 0 and x = 2 cm, ball will be rebounding between two walls.
After every 2 s,
Magnitude of the impulse received by the ball = 0.08 × 10–2 kg m/s
The given graph shows that a body changes its direction of motion after every 2 s.
Physically, this situation can be visualized as a ball rebounding to and fro between two stationary walls situated between positions x = 0 and x = 2 cm.
The slope of the position-time graph reverses after every 2 s, the ball collides with a wall after every 2 s.
Therefore, ball receives an impulse after every 2 s.
Given, 
Mass of the ball, m = 0.04 kg
The slope of the graph gives the velocity of the ball.
Using the graph,
Initial velocity, (u) = fraction numerator left parenthesis 2 space minus space 0 right parenthesis space straight x space 10 to the power of negative 2 end exponent over denominator left parenthesis 2 minus 0 right parenthesis end fraction space equals space 10 to the power of negative 2 end exponent space m divided by s
Velocity of the ball before collision, u = 10–2 m/s
Velocity of the ball after collision, v = –10–2 m/s 
Here, the negative sign arises as the ball reverses its direction of motion.
Magnitude of impulse = Change in momentum 
                                 = | mv - mu |
                                 = | 0.04 (v - u) |
                                 = | 0.04 (-10-2 - 10-2) |
                                 = 0.08 × 10-2 kg m/s