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Work, Energy And Power

Question

Wired Faculty App

Show that during a free fall - total energy (Kinetic + Potential) remains constant.

Solution

Let a body of mass m be dropped from point A at a height h from the ground.

At point A:
The kinetic energy is,

K subscript A italic equals italic 1 over italic 2 m u to the power of italic 2 italic equals italic 1 over italic 2 m left parenthesis 0 right parenthesis squared italic equals 0

Potential energy is,

U subscript A equals m g h

∴ Total energy at point A,

E subscript A equals K subscript A plus U subscript A equals 0 plus m g h equals m g h

...(1)
At point B:
Let in time t, the body reach point B after falling through a distance x.
Let v be the velocity of body at B.
Now,
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rightwards double arrow

v squared equals 2 g x

Kinetic energy at B is,

K subscript B equals 1 half m v squared equals 1 half m left parenthesis 2 g x right parenthesis equals m g x

Potential energy is,

U subscript B equals m g left parenthesis h minus x right parenthesis

∴ Total energy at point B is,

space space space E subscript B equals K subscript B plus U subscript B equals m g x plus m g left parenthesis h minus x right parenthesis equals m g h

...(2)
At ground:
On reaching the ground, let velocity of the body be V.

∴

V squared equals 2 g h

Kinetic energy at ground is,

K subscript g equals 1 half m V squared equals 1 half m left parenthesis 2 g h right parenthesis equals m g h

Potential energy is,

U subscript g equals m g left parenthesis 0 right parenthesis space equals space 0

∴ Total energy at point ground is,

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Since total energy at A = total energy at B + total energy at ground.
Therefore total energy during free fall remains conserved.

Some More Questions From Work, Energy and Power Chapter

Define the unit joule.

What are different units of energy?

What is watt?

Define watt.

How many joules are there in one eV?

What is the relation between kWh and Joule?

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

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