8.34 An 18-kg weight is lifted to a height of 12 m and then realeased to fall fr

Question

8.34 An 18-kg weight is lifted to a height of 12 m and then realeased to fall freely. What is the potential energy, kinetic energy, and the total energy at (a) the highest point, (b) 3 m above the ground, and (c) at the ground?
*I am having problems solving for kinetic energy.
Answers given: a) Ep=2100 J, Ek=0, Et=2100 J b) Ep=530 J, Ek=1570 J, Et=2100 J c) Ep=0, Ek=2100 J, Et=2100 J

8.43 An 80-lb girl sits in a swing of negliable weight. If she is given an initial velocity of 20 ft/s, to what height will she rise?
Answer given: 6.25 ft

Explanation / Answer

1.
mass m= 18 kg
height = h = 12m

a. Highest point :
Potential Energy Ep= mgh = 18 x 9.8 x 12 = 2116.8 joules
Kinetic energy Ek = 0 ( velocity is zero )
Total Energy Et = 2116.8 Joules

b. At 3m above ground:
Distance fallen h= (12- 3) = 9 meter
From conservation of energy:
0.5 mv^2 = mgh
0.5 v^2 = 9.8 x 9
v = 13.282 m/s
Potential Energy Ep= mgh = 18 x 9.8 x 9 = 529.2 Joules
Kinetic Energy = 0.5 mv^2 = Ek = 1587.6 Joules
Total Energy Et = 2116.8 Joules

c. At ground :
Potential Energy Ep= 0 ( no height)
Kinetic Energy Ek= 2116.8 joules
Total Energy Et = 2116.8 Joules

We can clearly see that our answers are correct as the total energy is conserved and add up to 2116.8 Joules in each of the three cases .

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