Answer:
a) ΔE = 25 %
b) v = 8,85 m/s
c) The energy was used against air resistance
Explanation:
In any situation total energy of a body is equal to potential energy plus
kinetic energy, then, just at the moment when Isaac dop the ball the situation is:
Ei = Ep + Ek where Ep = m*g*h and Ek = 1/2*m*v²
As v = 0 (Isaac drops the ball)
Ei = Ep = m*g*h = 2*m*g
At the end (when the ball bounced to 1,5 m
E₂ = Ep₂ + Ek₂ again at that point v =0 and
E₂ = 1,5*m*g*
Ei = E₂ + E(lost)
E(lost) = Ei - E₂
E(lost) = 2*m*g* - 1,5*m*g and the fraction of energy lost is
E(lost)/Ei
ΔE = (2*m*g* - 1,5*m*g )/ 2*m*g
ΔE = 0,5*m*g / 2*m*g
ΔE = 0,5/2
ΔE = 0,25 or ΔE = 25 %
b) The speed of the ball is
Potential energy is converted in kinetic energy just when the ball is touching the ground, then
m*g*h = 1/2*m*v²
2*h*g = 1/2 *v²
v² = 4*g*h
v² = 4*2*9,8
v² = 78,4
v = 8,85 m/s
If the impact is an elastic collision, then Ek before and after the impact is the same.
