Kinetic energy of an object is given as the energy possessed by an object due to its motion or its particle movement. Whereas potential energy possessed by an object is due to the position. The main difference of these two energies are kinetic energy depend upon the surroundings but potential energy is completely independent of the surroundings. Kinetic energy is given as the half of the product of the mass and the square of the velocity. And potential energy is the product of the mass, acceleration due to gravity and height. The problems related to these two energy are given below.

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The practice problems regarding the potential energy and kinetic energy are given below.

### Solved Examples

**Question 1: **A ball hits on a floor from a height of 19.6 m. Determine the velocity with which the ball strikes the ground?

** Solution: **

The given parameters are h=19.6 m, v=?

On hitting to the ground, kinetic energy = potential energy

So, $\frac{1}{2}$m$v^{2}$=mgh

$v^{2}$=2gh

v=$\sqrt{2gh}$

v=$\sqrt{2\times 9.8\times 19.6}$=19.6 m/s

**Question 2: **An object of mass 10 kg is initially at rest, which is subjected to a force of 20N. Calculate the kinetic energy of the body after 10s?

** Solution: **

It is given that m=10kg, u=0, t=10s, F=20N

We know that F=ma

a=$\frac{F}{m}$=$\frac{20}{10}$=2 m/$s^{2}$

v=u+at

v=0+2×10=20m/s

Kinetic energy= $\frac{1}{2}$m$v^{2}$

$\frac{1}{2}$$\times 10\times 20^{2}$=2000 J

**Question 3: **A meter scale of mass 100g is pivoted at one end. If it is held at 30º with a horizontal, what is the potential energy associated with it?

** Solution: **

Weight acts at the midpoint of the scale, which is the center of gravity of the scale. When the scale is held at an angle 30º with the horizontal,

h=lsinθ=0.5sin30º=0.25m

Hence center of gravity rises by 0.25 m and potential energy is given by,

P.E=mgh=0.1×9.8×0.25=0.245 J

The given parameters are h=19.6 m, v=?

On hitting to the ground, kinetic energy = potential energy

So, $\frac{1}{2}$m$v^{2}$=mgh

$v^{2}$=2gh

v=$\sqrt{2gh}$

v=$\sqrt{2\times 9.8\times 19.6}$=19.6 m/s

It is given that m=10kg, u=0, t=10s, F=20N

We know that F=ma

a=$\frac{F}{m}$=$\frac{20}{10}$=2 m/$s^{2}$

v=u+at

v=0+2×10=20m/s

Kinetic energy= $\frac{1}{2}$m$v^{2}$

$\frac{1}{2}$$\times 10\times 20^{2}$=2000 J

Weight acts at the midpoint of the scale, which is the center of gravity of the scale. When the scale is held at an angle 30º with the horizontal,

h=lsinθ=0.5sin30º=0.25m

Hence center of gravity rises by 0.25 m and potential energy is given by,

P.E=mgh=0.1×9.8×0.25=0.245 J