3.5 The Law of Conservation of Mechanical Energy p. 106 Conservation of Mechanical Energy EpEp EkEk A frictionless pendulum would swing from its high point to its lowest point. The potential energy at the top of its position would be converted to kinetic energy at the bottom of its swing. E k = E p The total work done remains constant through out the pendulums motion. Total mechanical energy = E k = E p = constant ½ mv mgh 1 = ½ mv mgh 2 Of course in the real world there is always friction and some energy lost as heat would have to be included in the formula stated above. Energy can be transformed from one form to another, but it is never created and it is never destroyed. Total energy remains constant.

3.5 The Law of Conservation of Mechanical Energy p. 108 Categorizing Force in a System A force is conservative if the work done by it in moving the object is independent of the object’s path. In this case only the initial and final position of the object are used the determine the amount of work done on the object. A force is non-conservative if the work done by it in moving an object depends on the objects path. Friction is an example of a non- conservative force. The longer the path the more force of friction is used and the more heat energy is generated.

3.5 The Law of Conservation of Mechanical Energy p. 108 Types of Collisions in a system Elastic Collisions In this type of collisions the total kinetic energy of the system is conserved. Energy can be transferred from one object to another, but no energy is transferred to the surrounding. In this type of collisions the total kinetic energy of the system is not conserved. Some (or all) of the kinetic energy is transferred to other forms (such as sound, elastic, deformation, and heat energy). Eventually all forms of energy become low grade heat energy. Inelastic Collisions Regardless of the type of collision momentum is always conserved which is due to the vector nature of momentum.

3.5 The Law of Conservation of Mechanical Energy p. 109 Applying the Law of Conservation of Energy: A ballistic Pendulum mbmb M vbvb m + M h A ballistic pendulum is used to measure the speed of bullet and uses both the law conservation of momentum and law of conservation of mechanical energy in its solution. The bullet is shot into a block of wood or clay causing the bullet-block to swing up to some height, h. From this height, mass of both block and bullet, the initial speed of the bullet can be determined.

3.5 The Law of Conservation of Mechanical Energy p. 109 The bullet entering the block transfers its momentum to the block: m b v b = (m + M)v(Law of Conservation of momentum) The impact cause the bullet and block combination to move. The combination bullet and block gains kinetic energy: E k = ½ (m b + M)v 2 Since the block is connected to a string, it will swing upwards reaching a maximum height, h. The kinetic energy is converted to potential energy. E k = ½ (m b + M)v 2 = (m b + M)gh = E p (Law of Conservation of Mechanical Energy.)

3.5 The Law of Conservation of Mechanical Energy p. 109 If there is very little energy lost as heat due to friction then: ½ (m b + M)v 2 = (m b + M)gh v 2 = 2gh Going back to the through the original momentum equation: m b v b = (m + M)v v = 2gh √ 2gh = v = v b = mbvbmbvb (m + M) √ mbmb √ x By placing in this equation all the know values, the speed of the bullet just before it hit the block can be determined (Where v is the initial speed of the block and bullet after impact.)

3.5 The Law of Conservation of Mechanical Energy In this section, you should understand how to solve the following key questions. Page #107 - Practice Problems Conservation Of Mechanical Energy #1– 3 Page#110Quick Check #1 – 3 Page #111 – Review Questions #1 – 7 To be sure you understand the concepts presented in the entire chapter on Energy: Page #113 – 116 Chapter 3 Review Questions #1 – 21