Prove that the total mechanical energy of a freely falling body is conserved.
Answers
Answer:
Let us understand this principle more clearly with the following example. Let us say, a ball of mass m is dropped from a cliff of height H, as shown above.
At height H:
Potential energy (PE) = m×g×H
Kinetic energy (K.E.) = 0
Total mechanical energy = mgH
At height h:
Potential energy(PE) = m×g×h
Kinetic energy (K.E.) =1/2(mv^2)
Using the equations of motion, the velocity v1 at a height h for an object of mass m falling from a height H can be written as Conservation Of Mechanical Energy
Hence, the kinetic energy can be given as,
Conservation Of Mechanical Energy
Total mechanical energy = (mgH – mgh) – mgh = mgH
At height zero:
Potential energy: 0
Kinetic energy: 1/2(mv^2)
Using the equations of motion we can see that velocity v at the bottom of the cliff, just before touching the ground is Conservation Of Mechanical Energy
Hence, the kinetic energy can be given as,
Conservation Of Mechanical Energy
Total mechanical energy: mgH
We saw the total mechanical energy of the system is constant throughout.
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Answer:
Explanation:
if a ball of mass m is dropped from a cliff of height H.
At height H:
Potential energy (PE) = m×g×H
Kinetic energy (K.E.) = 0
Total mechanical energy = mgH
At height h:
Potential energy(PE) = m×g×h
Kinetic energy (K.E.) =1/2(mv^2)
Using the equations of motion, the velocity v1 at a height h for an object of mass m falling from a height H can be written as Conservation Of Mechanical Energy
Hence, the kinetic energy can be given as,
Conservation Of Mechanical Energy
Total mechanical energy = (mgH – mgh) – mgh = mgH
At height zero:
Potential energy: 0
Kinetic energy: 1/2(mv^2)
Using the equations of motion we can see that velocity v at the bottom of the cliff, just before touching the ground is Conservation Of Mechanical Energy
Hence, the kinetic energy can be given as,
Conservation Of Mechanical Energy
Total mechanical energy: mgH
hence the total mechanical energy of the system is constant throughout.
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