7 Conservation of Energy. Potential Energy The Conservation of Mechanical Energy The Conservation of Energy Mass and Energy Hk: 23, 27, 39, 47, 55, 65, 69, 71. Potential Energy. Potential Energy is stored energy Potential Energy is position dependent (KE is speed dependent)
Energies and speeds are same at height y
Accelerations at y are not same
Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping.
A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie-frame type diagram of the motion is shown below.
By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J
Calculate v2: (use 1st and 2nd columns)
mg(1) = ½ m(v2)2.
g = ½ (v2)2.
v2 = 4.43m/s
Calculate PE-thermal: (use 1st and 5th columns)
mg(1) = mg(1/2) + PE-thermal
mg(1/2) = PE-thermal
PE-thermal = 9.8J
PE-elastic + PE-thermal = mg(1)
PE-elastic + 9.8 = 19.6
PE-elastic = 9.8J
Calculate v4: (use 1st and 4th columns)
½ m(v4)2 + PE-thermal = mg(1)
½ m(v4)2 + 9.8 = 19.6
½ m(v4)2 = 9.8
(v4)2 = 2(9.8)/2
v4 = 3.13m/s