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Energy Kinetic and potential
Energy can be classified as potential or kinetic • Potential energy: energy of position The boulder has more gravitational potential energy when measured from point A compared to B. PE = mgh
PE = mgh • m = mass in kilograms • g = acceleration due to gravity (9.8 m/s2) • h = height in meters • Potential Energy is measured in kg • m/s2• m = newton meter = Joules
Example 1: • If the boulder has a mass of 8kg, and distance B is 10m, what is the potential energy of the boulder relative to the plateau? 8kg 10m
Answer: • PE = mgh • = 8kg • 9.8m/s2 • 10m • =784 J 8kg 10m
Example 2: • If distance A is 20m, what is the potential energy of the boulder relative to the bottom? 8kg 20m
Answer: • PE = mgh • = 8kg • 9.8m/s2 • 20m • = 1568 J 8kg 20m
Example 3 • When work is done to stretch something, it is called elastic potential energy. Find the elastic potential energy stored in a drawn bow if it takes an average force of 100N to pull the arrow back a distance of 0.5 meters.
Answer: • PE = mgh = Fd Fxd = 100N x 0.5m = 50J
Kinetic energy • Energy of motion • KE = ½ mv2
KE = 1/2mv2 • m = mass in kilograms • v = velocity in meters/sec • Kinetic energy is measured in • kg • m/s • m/s = • kg m/s2 • m = • newton meter = • Joules
Example 4 • The bird has a mass of 2 kg. It is flying at a speed of 5 m/s. Find its kinetic energy. • KE = ½ mv2 • = ½ • 2kg • (5m/s)2 • = ½ • 2kg • 25 m2/s2 • = 25 joules
Kinetic and potential energy conversions • Describe the energy conversions in this picture: • At the top: • ¼ of the way down: • ½ way down: • ¾ down • At the bottom: • Is the sum of KE + PE a constant? All PE, no KE 3/4 PE, 1/4 KE 1/2 PE, 1/2 KE 1/4 PE, 3/4 KE No PE, All KE Yes! It’s always 10,000 J in this case.
Where are PE and KE maximums in this picture? PE and KE Max PE no KE Max KE No PE Max PE No KE
What happens when the cord is cut? Potential energy is converted to kinetic energy!
Kinetic and potential energy convert to one another PE max PE max no KE no KE KE max KE max no PE no PE
How is mass related to energy? • Albert gave us the answer! E=mc2
E=mc2 • E = energy in joules • m = mass in kilograms • c = speed of light • (3 x 108 m/s)
Example: • How much energy can be given off by 5 grams of mass? ( 10 paper clips = 5 g) • 5g = 0.005 kg • E=mc2 • = 0.005kg x (3 x 108 m/s)2 • = 0.005 kg x 9 x 1016 m2/s2 • = 0.045 x 1016 • = 450,000,000,000,000 J
WOW!!! • 450,000,000,000,000 J is the amount of energy in 3 million gallons of gasoline!
Einstein's theories of relativity have been proved during solar eclipses. Light is bent by gravity
See ya! The End