5.3 The Conservation of Mechanical Energy THE PRINCIPLE OF CONSERVATION OF ENERGY The term conserved means constant

5.3 The Conservation of Mechanical Energy THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY The total mechanical energy (E = KE + PE) of an object remains constant as the object moves in the absence of friction.

Conservation of Mechanical Energy The sum of KE and PE remains constant. One type of energy changes into another type. –For the falling book, the PE of the book changed into KE as it fell. –As a ball rolls up a hill, KE is changed into PE.

5.3 The Conservation of Mechanical Energy If the net work on an object by nonconservative forces is zero, then its energy does not change:

Conservation of Energy Acceleration does not have to be constant. ME is not conserved if friction is present. –If friction is negligible, conservation of ME is reasonably accurate. A pendulum as it swings back and forth a few times Consider a child going down a slide with friction. –What happens to the ME as he slides down? Answer: It is not conserved but, instead, becomes less and less. –What happens to the “lost” energy? Answer: It is converted into nonmechanical energy (thermal energy).

5.3 The Conservation of Mechanical Energy

Example 8 A Daredevil Motorcyclist A motorcyclist is trying to leap across the canyon by driving horizontally off a cliff 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.

5.3 The Conservation of Mechanical Energy

Question #23 A bird is flying with a speed of 18.0 m/s over water when it accidentally drops a 2.00 kg fish. Assuming the altitude of the bird is 5.40m, and disregarding friction, what is the speed of the fish when it hits the water? 20.7 m/s 5.3 The Conservation of Mechanical Energy

Question #24 An Olympic high jumper leaps over a horizontal bar. The jumper’s center of mass is raised 0.25m during the jump. Calculate the minimum speed with which the athlete must leave the ground to perform this feat? 2.2 m/s 5.3 The Conservation of Mechanical Energy

Question #25 A pendulum 2.0 m long is released from rest when the support string is t an angle of 25.0° with the vertical. What is the speed of the bob at the bottom of the swing? 1.9 m/s 5.3 The Conservation of Mechanical Energy

Question #26 A 755 N diver drops from a board 10.0 m above the water’s surface. Find the diver’s speed 5.00m above the water’s surface. 9.9 m/s Find the diver’s speed just before striking the water m/s 5.3 The Conservation of Mechanical Energy