Question

Calculate the work done on the tool by $\overrightarrow{F}$ if this displacement is along the straight line $y=x$ that connects these two points.

• A. $2.50J$
• B. $500J$
• C. $50.6J$
• D. $2J$

Answer 1

Answer: (C)

$50.6J$

as , $dW=f.ds$

$W=\int f.ds$

and force is only along the y-axis, work-done along the x-axis is zero

$W={\int }_{0,0}^{3,3}-\alpha x{y}^2.dy\cos {180}^{\circ }$ and $x=y$

$W={\int }_0^3\alpha y^3.dy$

$W=\alpha {\int }_0^3{y}^{3}dy$

$W=2.5\ast \{\frac{3^4}{4}-0\}$

$W=50.6J$