Energy Kinetic and potential
Energy can be classified as potential or kinetic Potential energy: energy of position 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 m = mass in kilograms g = acceleration due to gravity g = acceleration due to gravity (9.8 m/s 2 ) (9.8 m/s 2 ) h = height in meters h = height in meters Potential Energy is measured in Potential Energy is measured in kg m/s 2 m = kg m/s 2 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? 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 PE = mgh = 8kg 9.8m/s 2 10m = 8kg 9.8m/s 2 10m =784 J =784 J 8kg 10m
Example 2: If distance A is 20m, what is the potential energy of the boulder relative to the bottom? If distance A is 20m, what is the potential energy of the boulder relative to the bottom? 8kg 20m
Answer: PE = mgh PE = mgh = 8kg 9.8m/s 2 20m = 8kg 9.8m/s 2 20m = 1568 J = 1568 J 8kg 20m
Example 3 When work is done to stretch something, it is called elastic potential energy. 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 PE = mgh = Fd Fxd = 100N x 0.5m = 50J
Kinetic energy Energy of motion Energy of motion KE = ½ mv 2 KE = ½ mv 2
KE = 1/2mv 2 m = mass in kilograms m = mass in kilograms v = velocity in meters/sec v = velocity in meters/sec Kinetic energy is measured in Kinetic energy is measured in kg m/s m/s = kg m/s m/s = kg m/s 2 m = kg m/s 2 m = newton meter = newton meter = Joules 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. K 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: Describe the energy conversions in this picture: At the top: At the top: ¼ of the way down: ¼ of the way down: ½ way down: ½ way down: ¾ down ¾ down At the bottom: At the bottom: Is the sum of KE + PE a constant? 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?
What happens when the cord is cut? Potential energy is converted to kinetic energy!
Kinetic and potential energy convert to one another KE max no PE PE max no KE PE max no KE
How is mass related to energy? Albert gave us the answer! Albert gave us the answer! E=mc 2
E=mc 2 E = energy in joules E = energy in joules m = mass in kilograms m = mass in kilograms c = speed of light c = speed of light (3 x 10 8 m/s) (3 x 10 8 m/s)
A small mass gives a great amount of energy
Nuclear energy- clean power for the world?
Example: How much energy can be given off by 5 grams of mass? ( 10 paper clips = 5 g) How much energy can be given off by 5 grams of mass? ( 10 paper clips = 5 g) 5g = kg 5g = kg E=mc 2 E=mc 2 = 0.005kg x (3 x 10 8 m/s) 2 = 0.005kg x (3 x 10 8 m/s) 2 = kg x 9 x m 2 /s 2 = kg x 9 x m 2 /s 2 = x = x = 450,000,000,000,000 J = 450,000,000,000,000 J
WOW!!! 450,000,000,000,000 J is the amount of energy in 3 million gallons of gasoline! 450,000,000,000,000 J is the amount of energy in 3 million gallons of gasoline!