Conservation of Energy Total Energy before Total Energy

Conservation of Energy Total Energy before = Total Energy After Comes from = Goes to Assets = Expenditures Fs + mgh + 1/2 mv 2 + 1/2 kx 2 = Fs + mgh + 1/2 mv 2 + 1/2 kx 2

v = 4. 5 m/s A 250 kg cart going 4. 5 m/s rolls down a 1. 75 m tall hill. What is the velocity of the cart at the bottom? 250 kg 1. 75 m Fs + mgh + 1/2 mv 2 + 1/2 kx 2 = Fs + mgh + 1/2 mv 2 + 1/2 kx 2 7. 4 m/s

Example 1 v = 6. 2 m/s 890 kg An 890 kg cart rolling 6. 2 m/s along a level surface hits a 3. 6 m long puddle that exerts 3200 N of average retarding force. What is the cart’s velocity after this? 3. 6 m (Puddle - Exerts 3200 N of retarding force) 3. 5 m/s

Example 2 u = 4. 6 m/s 350 kg 66 m A 350 kg cart is going 4. 6 m/s. For what distance must a person exert a forward force of 53 N so that when the cart gets to the top of a 1. 8 m tall hill it is going 2. 4 m/s? 1. 8 m

Example 3 0. 550 N A 0. 124 kg pine cone falls 45. 0 m from a tree. It is going 22. 0 m/s when it strikes the ground. What is the average force of air friction that acts on the pine cone as it falls?

15 kg What speed at the bottom? u=0 h = 2. 15 m (15 kg)(9. 81 N/kg)(2. 15 m) = 1/2(15 kg)v 2 v = 6. 4948… 6. 5 m/s

15 kg u = 5. 8 m/s What speed at the bottom? h = 2. 15 m (15 kg)(9. 81 N/kg)(2. 15 m) + 1/2(15 kg)(5. 8 m/s)2= 1/2(15 kg)v 2 v = 8. 7076… 8. 7 m/s

What speed at the top? u = 8. 6 m/s 15 kg h = 2. 15 m h = 4. 25 m (15 kg)(9. 81 N/kg)(2. 15 m) + 1/2(15 kg)(8. 6 m/s)2 =(15 kg)(9. 81 N/kg)(4. 25 m) 1/2(15 kg)v v = 5. 723… 5. 7 m/s

v = 3. 68 m/s 2. 34 kg The hammer pushes in the nail 3. 50 mm. (. 00350 m). What force did it exert on the nail 1/ 4530 N 2(2. 34 kg)(3. 68 m/s)2 = F(. 0035 m)

18 m A 125 kg experiment falls 18. 0 m and has its velocity arrested in 1. 50 m by an air bag. What force does the air bag exert on the experiment in stopping the experiment? (125 kg)(9. 81 N/kg)(18. 0 m + 1. 50 m) = F(1. 50 m) F = 15, 941. 25 15, 900 N

450 kg h = 1. 75 m u = 5. 8 m/s What distance will it compress the 15000 N/m spring in stopping the cart? (450 kg)(9. 81 N/kg)(1. 75 m) + 1/2(450 kg)(5. 8 m/s)2 = 1/2(15000 N/m)x 2 x = 1. 428… 1. 4 m

What must be the spring constant to give the 115 g marble a velocity of 2. 13 m/s on top of the hill if the spring is compressed 3. 15 cm? h =. 452 m 1/ 1550 N/m 2 k(. 0315 m)2 = 1/2(. 115 kg)(2. 13 m/s)2 + (. 115 kg)(9. 81 N/kg)(. 452 m) k = 1553. 63…