1. Part 2: Solving Energy Problems

2. Kinetic Energy Recall that Ek is the energy of motion.
The amount of kinetic energy is dependent upon mass and velocity.
Ek = ½mv2
Ek = kinetic energy
m = mass
v = velocity

3. Ek=1/2mv2 Ek=1/2mv2 Ek=1/2(7)(3)2 √2Ek/m=v Ek=1/2(7)(9)
A 7.00 kg bowling ball moves at 3.00 m/s. How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball?
Ek1 = ?
m1 = 7 kg
v1 = 3m/s
Ek2 = Ek1
m2 = kg
V2 = ?
Ek=1/2mv2
Ek=1/2mv2
Ek=1/2(7)(3)2
√2Ek/m=v
Ek=1/2(7)(9)
√2(31.5)/.00245=v
Ek=1/2(63)
√63/.00245=v
Ek=31.5 J
√ =v
160.4 m/s=v

4. Gravitational Potential Energy
Recall that this is the energy due to height.
The higher above the “zero-point” an object is, the more Eg it has.
Eg = mgh
Eg = gravitational potential energy
m = mass
g = acceleration due to gravity
h = height above “zero”.

5. A 65kg hiker reaches the peak of Mt
A 65kg hiker reaches the peak of Mt. Everest, which is 8800m above sea level. What is the hiker’s gravitational potential energy?
Eg = ?
m = 65kg
g = 9.8m/s2
h = 8800m
Eg=mgh
Eg=(65)(9.8)(8800)
Eg=5,605,600 J

6. Elastic Potential Energy
Recall that this is the energy that exists when elastic objects are stretched or compressed.
The “zero-point” for Es is when the object is in a relaxed state.
Es = ½k(Δx)2
Es = elastic potential energy
k = spring constant (varies by object)
Δx = distance “spring” is stretched/compressed

7. Es=1/2k(Δx)2 Es=(1/2)(13.8)(.05)2 Es=(1/2)(13.8)(.0025) Es=.01725 J
A spring that has a spring constant of 13.8 is compressed .05m. How much elastic potential energy is in the system?
Es = ?
k = 13.8 N/m
Δx = .05m
Es=1/2k(Δx)2
Es=(1/2)(13.8)(.05)2
Es=(1/2)(13.8)(.0025)
Es= J