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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