Question
Figure $5.17$ shows the position-time graph of a body of mass $0.04kg$. 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?
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Answer
A ball rebounding between two walls located between at x = 0 and x = 2cm; after every 2s, the ball receives an impulse of magnitude $0.08 \times 10^{-2}kgm/s$ from the walls The given graph shows that a body changes its direction of motion after every 2s. Physically, this situation can be visualized as a ball rebounding to and fro between two stationary walls situated between positions x = 0 and x = 2cm. Since the slope of the x - t graph reverses after every 2s, the ball collides with a wall after every 2s. Therefore, ball receives an impulse after every 2s. Mass of the ball, m = 0.04kg The slope of the graph gives the velocity of the ball. Using the graph, we can calculate initial velocity (u) as: $\text{u}=\frac{(2-0)\times10^{-2}}{(2-0)}=10^{-2}\text{m/s}$ 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 $= |mv - mu| = |0.04 (v - u)| = |0.04(-10^{-2} - 10^{-2})| = 0.08 \times 10^{-2}kgm/s$
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