Question

The magnitude of force (in newtons) acting on a body varies eith time $t$ (in micro seconds) as shown in Fig. AB, BC and CD are straight line segments. The magnitude of total impulse of the force on the body from $t=4s$ to $t=16s$ is ______ $Ns$.

Answer 1

As given in the graph,

Impulse is defined as the area under $F.t$ graph

Impulse=area of $EBCD$

$\Rightarrow AreaEBCD=areaEBCF+areaof\Delta FCD$

Impulse $I=(\frac{BE+FC}{2}\times EF)+\frac{1}{2}FC\times FD$

$=\left(\frac{200+1800}{2}\right)\times 2\times {10}^{-6}+[\frac{1}{2}\times 800\times 10\times {10}^{-6}]$

Impulse $={10}^{-6}(1000+4000)N-s$

Impulse $={10}^{-6}\left(5000\right)N-s$

Impulse $=5\times {10}^{3}N-s$