Answer to Question #162086 in Mechanics | Relativity for Bholu

Question

Consider a particle of mass m on x-y plane.The particle is moved by a force F~ =xy ˆi + y jˆ fromthe origin (0, 0) to a point (1, 1) along a straight

Line joining the two pints. Find the workdone

By the force.

Answer 1

$F=xy\hat{i}+y\hat{j}$

$W=\int_0^1dw=\int_0^1Fds$

$W=\int_0^1dw=\int_0^1Fdx\hat{i}+\int_0^1Fdy\hat{j}$

$\text{moving from (0, 0) to point (1, 1) in a straight line}$

$\text{is described by the equation } y=x$

$dy=dx$

$W=\int_0^1xydx\hat{i}+\int_0^1ydy\hat{j}=$

$\int_0^1x^2dx\hat{i}+\int_0^1xdx\hat{j}=(\frac{x^3}{3}+\frac{x^2}{2})|_0^1=\frac{5}{6}$

Answer:$\frac{5}{6}N$