momentum of a moving body is increased by 10%. what happens to its kinetic energy?
Answers
Answer:
If p is momentum and corresponding kinetic energy is K, we have ,for particle of mass m, the relation,
K=p^2/2m
When p is increased by 10%, the new kinetic energy will be,
K’=(1.1p)^2/2m=1.21(p^2/2m)
% increase=(change/original value)x100.=[(1.21–1)(p^2/2m/(p^2/2m)]x100=21%.
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Explanation:
║⊕ANSWER⊕║
Case1. Velocity unchanged, mass increases by 10%.
Let the original mass if the body = m,
New increased mass = 1.1 m
Let the velocity be = v
K. E with original mass = 1/2 m v²
K. E with increased mass = 1/2 × 1.1 m v²
Change in K. E= 1/2 m v² (1.1 - 1) = 0.1 of original K. E =10% change in K. E.
Case2: Mass unchanged velocity increases
Original velocity= v
Original K. E= 1/2 m v²
Changed velocity= 1.1 v
New K. E. = 1/2 m (1.1 v)² = 1.21 of original K. E.
% change in K. E= [(1.21 - 1) of original K. E/ original K. E]×100= 21%