At the end of the semester, I usually toss graded final exams in the air as a tw

Question

At the end of the semester, I usually toss graded final exams in the air as a twisted form of celebration. These papers together usually have an average mass of 7.4 kg. I am able to throw these papers in the air until they reach a maximum height of 1.32 m in 0.85s. Considering the conservation of mechanical energy, determine the initial velocity of the papers when it left my hands to reach this maximum height, the amount of energy that what lost during their flight, the average power required to toss the papers to this height.

Explanation / Answer

i)

since the mechanical energy is conservaed

energy at the leaving hands = energy at the maximum height

K1+U1 = K2+U2

(0.5*m*u^2) + 0 = 0 + (m*g*h)

m = 7.4 kg

u is the initial speed = ?

g = 9.8 m/s^2

h = 1.32 m

then

0.5*m*u^2 = m*g*h

u = sqrt(gh/0.5) = sqrt(9.81*1.32/0.5) = 5.08 m/s

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ii) since energy is conserved there is no loss in the amount of energy

iii) average power p = m*g*h/t = (7.4*9.81*1.32)/0.85 = 112.73 W

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