## Related questions with answers

A $0.75\text{~ kg}$ book travels vertically $16$ meters up and then $16$ meters down before returning to its starting point. a) How much of the book's upward movement is caused by gravity? b) How much of the book's downward motion is caused by gravity? c) How much work did gravity complete on the book over the course of the round trip competition? d) On the basis of \syour answer to section (c), would you argue that the gravitational force \sis conservative or non conservative? Why not?

Solution

VerifiedThe task is to calculate the work of gravitational force when we raise a book to a certain height and when we lower a book. Work is defined as the scalar product of force and displacement vector.

$\begin{align*} W&=\int \vec{F}\cdot \vec{ds} \end{align*}$

If the force and path are constant and have the same direction, the above equation is simplified.

$\begin{align*} W&=F\cdot s \end{align*}$

If the force and path are constant and have the different direction, the above equation is.

$\begin{align*} W&=-F\cdot s \end{align*}$

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