Kinetic energy formula
Question: Why
is the mass halved in the formula for Kinetic Energy (KE = ½ mv
2)?
Answer:
Lets imagine an object (mass m) moving with
velocity u and being brought to rest by a steady retarding force F in a distance
s.
Work done by the retarding force = Fs = kinetic energy lost (converted to
heat)
But using v
2 = u
2 + 2as with v = 0 and a = -F/m (- sign
denotes deceleration) we have:
u
2 = 2as = 2F/m so F =
[mu
2]/2s
Therefore: Kinetic energy = Fs = [mu
2]/2s =
[mu
2]/2
So that is why the half appears in the formula.
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