Law of the Conservation of Mechanical Energy. When gravity is the only external influence on an object, its mechanical energy remains constant. FORMULA: (PE + KE) = C where C is some constant value. Law of the Conservation of Mechanical Energy.
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When gravity is the only external influence on an object, its mechanical energy remains constant.
EXAMPLE: When a ball is thrown upward it slows down, losing kinetic energy. However, as height increases the value of potential energy also increases. As it begins to fall back down its velocity increases, increasing its kinetic energy while its potential energy is reduced as it moves to a lower height.
In other word, as kinetic energy decreases, potential energy increases and vice-versa, keeping the sum of the energies constant.
Total mechanical energy possessed by the ball:
PE + KE = C
(wt * h) + ½(mv2) = C
wt = (2 kg)(9.81 m/s2) = 19.62 N
At the start of this event, the ball is held so that 100% of the energy is potential energy and KE = 0
(19.62 N)(1.5 m) + 0 = C
29.43 J = C
Immediately before impact the height is 0 so therefore PE = 0
(Remember, the sum of PE + KE stays the same)
PE + KE = C = 29.43 J
0 + ½(mv2) = 29.43 J
½(2 kg)(v2) = 29.43 J
v2 = 29.43 J/kg
1 J = 1 Nm, 29.43 N = (1 kg)(29.43 m/s2), 29.43 N/kg = 29.43 m/s2
Therefore 29.43 J/kg = (29.43 Nm)/(1 kg) = (29.43 N/kg)(1m) = 29.43 m2/s2
v2 = 29.43 m2/s2
v = 5.42 m/s
pp 411- 412
Introductory Problems 9 and 10
Additional Problems 7, 8, and 9