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November √36th 2009 Objectives SWBAT identify situations when they should use the conservation of mechanical energy SWBAT Solve problems using mechanical energy SWBAT recognize the different forms that energy takes Catalyst If you start with a $5 bill and you split it into 4 $1 bills and 4 quarters was your money conserved? Why? You have 10min to finish the problems from the HW Agenda HW Review Work-KE Potential For Energy? Practice! HW Answers 1. 2. 3. 4. Pg 176 7.8m 21m 5.1m 300N Conservation of Mechanical Energy 5-3 Problem A 70.0kg stuntman is attached to a bungee cord with an unstretched length of 15m. He jumps off a bridge spanning a river from a height of 50.0m. When he finally stops, the cord has a stretched length of 44.0m. Disregard the weight of the bungee cord. Assuming the spirng constant of the bungee cord is 71.8 N/m, what is the total potantial energy relative to the water when the man stops falling? Problem 2 When a 2kg mass is attached to a verticali spring, the spring is stretched 10cm such that the mass is 50cm above the table. a. b. c. What is the gravitational potential energy associated with this mass relative to the table? What is the spring’s elasticf potential energy is the spring constant is 400 N/m? What is the total energy of this system? Pendulum Demo Take a looksee…. Where is the PE of the pendulum the highest? Why the top of course, Mr. McKnight! Exactly! So, where is the KE of the pendulum the highest? Why the bottom of course, Mr. McKnight! It is moving the fastest at the bottom!! What kinds of Energy do we know about? Kinetic Energy Gravitational Potential Energy Elastic Potential Energy There are also nuclear, chemical, internal and electrical energy These are all classified as Mechanical Energy. The energies involved in motion These are classified as non-mechanical Energy Tell me something I don’t know Mechanical Energy is conserved… Your initial ME equals your final ME Conservation of mechanical Energy: MEi=MEf *****This is ONLY when we neglect friction (which we often do) Misconception Alert!!! While ME is conserved, TOTAL Energy is also conserved (all the different kinds of Energy…we just won’t analyze it here) Let’s see if it works… I’m going to drop this 1kg object to the floor from a height of 1.5m… What At the top when KE = 0 What is the maximum PE? is the maximum KE? (hint ME is conserved) At the bottom when PE = 0 Let’s prove it…with our handy dandy kinematic equations! So…sum it up We can use the distance the egg has fallen and a kinematic equation to find the speed at any time (KE) Or…We can use the height of the egg to find the PEg at any time. The great part… KE+ΣPE = 14.7J EVERY TIME in this case Data Table… Height above ground (m) Displacement (m) ie. How far the object has dropped 1.5 0 0 0 14.715 14.715 1.2 0.3 2.426108 2.943 11.772 14.715 0.9 0.6 3.431035 5.886 8.829 14.715 0.6 0.9 4.202142 8.829 5.886 14.715 0.3 1.2 4.852216 11.772 2.943 14.715 0 1.5 5.424942 14.715 0 14.715 Vf KE PE ME = KE + PE Problem… Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00m. What is her speed at the bottom of the slide? Assume she has a mass of 25kg. 7.67m/s Last thing Energy is conserved even if acceleration varies. So if the slide in the last problem had varying angles on the way down, we wouldn’t be able to calculate the acceleration easily, meaning no Kinematic formulas BUT, b/c we know the ME we can skip acceleration and find the final speed without all the extra work! Group Whiteboard it!!!!! A small 10.0g ball is held to a slingshot that is stretched 6cm. The spring constant is 2.0x102 N/m. a. b. c. d. What is the elastic potential energy of the slingshot before it is released? What is the KE of the ball just after the slingshot is released? What is the ball’s speed at that instant? How high does the ball rise if it is shot directly upward? Questions… Pg185; 1, 2, 4, 5 Pg186; 1, 2, 3,