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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 $980\ J$.