Question

How many joules of potential energy does a $1\;kg$ book gain when it is elevated $4\;m$? What about when it is elevated $8\;m$?

Answer 1

We know that potential energy is the energy posed by an object due to its change in position. Thus clearly, the potential energy depends only on the starting and end position but not its rejection of motion. Since it is also an energy it is measured in terms of joules.
Formula used:
$U=mgh$

Complete answer:
Potential energy is also defined as the work done in moving the given object from one position to another, against any forces acting on that body at the given time period. And thus has the SI units joules . Also , potential energy is a conservative force which means to say that it depends only on the initial and final position of the object and not on the path taken by it to reach the final position. Then it is expressed mathematically as
$W=-\Delta U$
Then, we also know that work done is the force required to move or displace the given object, and is mathematically given as $W=F.s$
Then, comparing the two we have
$\implies -\Delta U=F.s$
$\implies U=mgh$; where $m$ is the mass of the object raised to a height $h$ against the force of gravity with an acceleration $g$.
Now substituting the value, we have
$U_4=1\times 10\times 4=40J$ and $U_8=1\times 10\times 8=80J$
Thus the potential energy due to height $4\;m$ and $8\;m$ are $40\;J$ and $80\;J$ respectively.

Note:
Unlike potential energy, kinetic energy is a non-conservative force which depends on the path or the trajectory of the object. Also, the negative sign in the above equation denotes that work done by the system decreases the potential energy of the system, whereas work done on the system will increase potential energy of the system.