An object of mass $40\ kg$ is raised to a height of $5\ m$ above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.

Given:

An object of mass $40\ kg$ is raised to a height of $5\ m$ above the ground. 

To do:

To find its potential energy and If the object is allowed to fall, we have to find its kinetic energy when it is halfway down.

Solution:

Let us know the formula used for calculating the potential energy and kinetic energy of an object:

Potential energy, $P.E.=mgh$

Kinetic energy, $K.E.=\frac{1}{2}mv^2$

Here, $m\rightarrow$ mass of the object

$g\rightarrow$ gravitational acceleration

$h\rightarrow$height

$v\rightarrow$ velocity of the object

By using the above formulas let us find out the potential energy of the object at the height of $5\ m$:

Potential energy at $5\ m$:

Here given, the mass of the object $m=40\ kg$

Height of the object to be raised $h=5\ m$

gravitational acceleration on earth $g=9.8\ m/s^2$

So, the potential energy of the object $P.E.=mgh$

$=40\times 5\times 9.8$

$=1960\ J$

Thus, the potential energy of the object at the height of $5\ m$ is $1960\ J$ and its kinetic energy will be zero. 

So, its total energy at $5\ m$ will be $1960\ J$

When the object is allowed to fall, then at halfway down:

Height $h'=\frac{5}{2}\ m=2.5\ m$

So, its potential energy $P.E.'=mgh'=40\times9.8\times2.5=980\ J$

Then, the kinetic energy of the object $K.E.=Total\ energy-potential\ enrgy$

$=1960\ J-980\ J$

$=960\ J$

So, the kinetic energy of the object halfway down is $980\ J$.

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Updated on: 10-Oct-2022

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