Below figure 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 ?
Below figure 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 ?
A ball rebounding between two walls located between at $x=0$ and $x=2 \,cm ;$ after every
$2$ $s$, the ball receives an impulse of magnitude $0.08 \times 10^{-2} \,kg\, m / s$ from the walls
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 twe stationary walls situated between positions $x=0$ and $x=2 \,cm .$ since the slope of the $x-$ graph reverses after every $2$ $s$, the ball collides with a wall after every $2$ $s$. Therefore, bal receives an impulse after every $2$ $s$. Mass of the ball, $m=0.04 \,kg$
The slope of the graph gives the velocity of the ball. Using the graph, we can calculate initial velocity $(u)$ as:
$u=\frac{(2-0) \times 10^{-2}}{(2-0)}=10^{-2}\, m / s$
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 $=|m v-m u|$
$=|0.04(v-u)|$
$=\left|0.04\left(-10^{-2}-10^{-2}\right)\right|$
$=0.08 \times 10^{-2} \,kg\, m / s$
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