show the total energy of a particle performing vertical circular motion is
conserved or constant ??
Answers
Answer:
conserved
Explanation:
the answer is that is is conserved.
The total energy of a particle performing vertical circular motion is conserved or constant.
Proof : Let us take lowest point as frame of reference.
Given : V(lowest point) = √5gr, V(top point) = √gr and when string is horizontal V= √3gr
1. For lowest point, h=0
K.E = 1/2×mv^2 = 1/2×m×(√5gr)^2
= 1/2×m×5gr = 5/2×mgr
P.E = mg(0) = 0
T.E = K.E + P.E = 5/2×mgr + 0
= 5/2×mgr
2. For top point, h=2r
K.E = 1/2×m×(√gr)^2 = 1/2×mgr
P.E = mg(2r)
T.E = K.E + P.E = 1/2×mgr + mg(2r)
= 5/2×mgr
3. When string is horizontal, h=r
K.E = 1/2×m×(√3gr)^2 = 1/2×3mgr
= 3/2×mgr
P.E = mgr
T.E = K.E + P.E = 3/2×mgr + mgr
= 5/2×mgr
Hence proved that the total energy of a particle performing vertical circular motion is conserved or constant.