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  4. The only force acting on a 2 kg body that is moving in xy- plane has a magnitude of 5 N . The body initially has a velocity of 4 m/s in the positive x -direction. Some time later, the body has a velocity of 6 m/s in the positive y- direction. The work done on the body by the 5 N force during this time is

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Q. The only force acting on a $ 2 \,kg $ body that is moving in $ xy- $ plane has a magnitude of $ 5\, N $ . The body initially has a velocity of $ 4 \,m/s $ in the positive $ x $ -direction. Some time later, the body has a velocity of $ 6 \,m/s $ in the positive $ y- $ direction. The work done on the body by the $ 5 \,N $ force during this time is

AMUAMU 2018Work, Energy and Power

Solution:

Given, $m = 22\, kg$ ,
$V_{1}=4\, m /s $ and $V_{2}=6\, m /s$ $F=5\, N$
According to work-energy theorem,
$\int F_{net} dx=\Delta zkE=\left(KE\right)_{2}-\left(KE\right)_{1}$
$=\frac{1}{2}mv_{2}^{2}-\frac{1}{2}mv_{1}^{2}$
$=\left[\left(6\right)^{2}-\left(4\right)^{2}\right]\frac{2}{2}$ [putting values]
$=\left[36-16\right]=20 \,J$