A block of mass $50 \mathrm{~kg}$ is pulled with a constant speed of $4 \mathrm{~ms}^{-1}$ across a…
A block of mass $50 \mathrm{~kg}$ is pulled with a constant speed of $4 \mathrm{~ms}^{-1}$ across a horizontal floor by an applied force of $500 \mathrm{~N}$ directed $30^{\circ}$ above the horizontal. The rate at which the force does work on the block in watt is
$\frac{2000}{\sqrt{3}}$
$500 \sqrt{3}$
$1732$
$1864$
Solution
Mass of block, $m=50 \mathrm{~kg}$,
speed of block, $v=4 \mathrm{~ms}^{-1}$,
$F=500 \mathrm{~N}$ and $\theta=30^{\circ}$,
The rate at which the force does work on the block is equal to power which is given as
$P=$ Force in the horizontal direction $\times$ velocity
$\begin{aligned} & =500 \times \cos 30^{\circ} \times v \\ & =500 \times \frac{\sqrt{3}}{2} \times 4=100 \sqrt{3} \\ & =100 \times 1.732=1732 \mathrm{~W}\end{aligned}$