A ball of mass 1.84 kg is dropped from a height y, = 1.49 m and then bounces back up to a height of y, = 0.87 m.
How much mechanical energy is lost in the bounce?

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11.408 joules

Explanation:

soln

From the question above

Mass of ball = m = 1.84kg

Height of ball when dropped = 1.49m

Height of ball when it bounces back up = 0.87m

Recall

Potential energy (P.E) = mass × height × g

Kinetic energy(K.E) = 1/2 × mass × (velocity)²

Mechanical energy = K.E + P.E

M.E lost = M.E when ball dropped – M.E when ball bounces back up

Recall that g = acceleration due to gravity = 10ms²

P.E/K.E when ball dropped = 1.84 × 1.49 × 10

P.E/K.E when ball dropped = 27.416J

P.E/K.E when ball bounces back = 1.84 × 0.87 × 10

P.E /K.Ewhen ball bounces back = 16.008J

Since P.E = K.E

M.E when ball dropped = 27.416J

M.E when ball bounces back = 16.008J

Therefore,

M.E lost = 27.416 - 16.008

M.E lost = 11.408Joules