Relantioship between kneitic aur work
Answers
The relationship between work done on a body and its kinetic energy is very nicely captured by Work-Kinetic Energy Theorem.
This theorem essentially says that if a force is exerted on a body, the force does work on the body (often described as a dot product of Force and displacement). Then this work done is equal to the difference between Final KE and initial KE.
or Work Done by a Force, W = KE (final) - KE (initial)
To give an example say a foot ball of mass 2 Kg is kicked by a force of 10 N and its velocity changes from 0 m/s to 8 m/s and cause a displacement of 6.4 m then the following equation will connect the numbers -
KE initial = zero
KE final - 1/2 X 2 X 8 (sq.) = 64 J
W = Work done = F.d = 10 X 6.4 = 64 J
If the equation W = KE (f) - KE (i) is correct, the numbers should fit in well. Let us see by putting the values we have calculated above-
W = KE (f) - KE (i)
64 = 64 - 0 which is true.
In fact you can use this equation to find an unknown variable. So if displacement d was not known, we could have used this equation to find it
You may watch this video from he Science Cube to understand this better-
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Originally Answered: What is the relation between kinetic energy and work done?
Oh yes there is a relation named as work energy theorem which gives relation between kinetic energy and work done.
For work done=W
Force=f
Displacement=d
Acceleration=a
And mass=m
We know that,
W=fd
From Newton's third law,
F=ma
So, W=mad. Eqn1
Now from eqn1 of motion
V(f)^2-V(i)^2=2ad
Ad={V(f)^2-V(i)^2}÷2
Substitute above in eqn1
W=[m{V(f)^2-V(i)^2}]÷2
W=mV(f)^2÷2 - mV(i)^2÷2
W=ke(f) - ke(i)
W=∆ke
Above equation is the required relation
Stating that the change in kinetic energy is equal to the work done.
Thanks for reading and comment if have some suggestions…
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First off, a few basic equations:
Kinetic energy = 0.5 * Mass * Velocity^2
Work = Force * Distance
Force = Mass * Acceleration
Add the equation of constant acceleration:
Final velocity^2 = Initial velocity^2 + 2 * Acceleration * Distance
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From these, they can be rewritten as:
Acceleration = Force / Mass
Distance = (Final velocity^2 - Initial velocity^2) / (2 * Force / Mass)
Work = (Final velocity^2 - Initial velocity ^2) * 0.5 * Mass
Change in Kinetic energy = (0.5 * Mass * Final velocity^2) - (0.5 Mass * Initial velocity)
The 0.5 * Mass can then be taken outside the brackets to give:
Change in Kinetic energy = 0.5 * Mass * (Final velocity^2 - Initial velocity^2)
Therefore: Work = Change in Kinetic energy.
While it may seem strange to some that it takes more energy to increase the speed by the same amount of a faster moving object than of a slower moving object, here is the proof:
Work = Force * Distance
Force = Mass * Acceleration
Distance = Average velocity / Time
Work = Mass * Acceleration * Average velocity / Time
Therefore Work done increases when the Average velocity is greater, even though the same acceleration is applied to the same mass for the same amount of time.