Question

A cutting tool under microprocessor control has several forces acting on it. One force is $\overrightarrow{F}=-\alpha x{y}^2\hat{j}$, a force in the negative y-direction whose magnitude depend on the position of the tool. The constant is $\alpha =2.50N/m^3$. Consider the displacement of the tool from the origin to the point $x=3.00m,y=3.00m$. Calculate the work done on the tool by $\overrightarrow{F}$ if the tool is first moved out along the x-axis to the point $x=3.00m,y=0m$ and then moved parallel to the y-axis to $x=3.00m,y=3.00m$.

• A. $67.5J$
• B. $85J$
• C. $102J$
• D. $7.5J$

Answer 1

The correct option is A $67.5J$

as , $dW=f.ds$

$W=\int \overrightarrow{F}.\overrightarrow{ds}$
and force is only along y-axis ,work done along x- axis is zero
work done in moving from $(3,0)$ to $(3,3)$ is

$W={\int }_0^3-\alpha x{y}^2.dy\cos {180}^{\circ }$ and

$x=3$

$W={\int }_0^3\alpha \times 3\times y^2.dy$

$W=2.5\times 3\times {\int }_0^3{y}^{2}dy$

$W=7.5\times \{\frac{3^3}{3}-0\}$

$W=67.5J$