Chapter 6 Work and Energy

6.1 Work Done by a Constant Force

6.1 Work Done by a Constant Force

6.2 The Work-Energy Theorem and Kinetic Energy DEFINITION OF KINETIC ENERGY The kinetic energy KE of an object with mass m and speed v is given by

6.2 The Work-Energy Theorem and Kinetic Energy When a net external force does work on an object, the kinetic energy of the object changes from its initial value of KE0 to a final value of KEf , the difference between the two values being equal to the work:

6.3 Gravitational Potential Energy DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY The gravitational potential energy PE is the energy that an object of mass m has by virtue of its position relative to the surface of the earth. That position is measured by the height h of the object relative to an arbitrary zero level:

6.4 Conservative Versus Nonconservative Forces A force is conservative when the work it does on a moving object is independent of the path between the object’s initial and final positions.

6.4 Conservative Versus Nonconservative Forces Non-conservative force – a force is non-conservative if the work it does on an object moving between two points depends on the path of motion between the points. The work done by the kinetic frictional force is always negative.

6.4 Conservative Versus Nonconservative Forces In normal situations both conservative and nonconservative forces act simultaneously on an object, so the work done by the net external force can be written as

6.4 Conservative Versus Nonconservative Forces THE WORK-ENERGY THEOREM

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

6.5 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, provided that the net work done by external nononservative forces is zero.

6.5 The Conservation of Mechanical Energy

6.5 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.

6.5 The Conservation of Mechanical Energy

6.5 The Conservation of Mechanical Energy

DEFINITION OF AVERAGE POWER Average power is the rate at which work is done, and it is obtained by dividing the work by the time required to perform the work.

6.7 Power

6.8 Other Forms of Energy and the Conservation of Energy THE PRINCIPLE OF CONSERVATION OF ENERGY Energy can neither be created nor destroyed, but can only be converted from one form to another.

Problems To Be Solved 6.12, 6.23, 6.39, 6.60, 6.63, 6.65 B6.1 The heart may be regarded as an intermittent pump that forces about 70cm3 of blood into the 1.0cm radius aorta about 75 times a minute. Measurements show that the average force with which the blood is pushed into the aorta is about 5.0N. What is the approximate power used in moving the blood to the aorta? Ans: 1.39W

B6. 2 A dieter lifts a 10kg mass a distance of 0. 5m 1000 times B6.2 A dieter lifts a 10kg mass a distance of 0.5m 1000 times. (a) How much work does he do against gravitational force? (b) Fat supplies 3.8×107J of energy per kilogram, which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up? Ans: (a) 49000J; (b) 6.4×10-3kg

B6. 3 A beer can is dropped from a window 30m above the ground B6.3 A beer can is dropped from a window 30m above the ground. How fast will it be moving just before it lands?(Neglect air resistance) Ans: 24.25m/s

B6. 4 A 55kg carton of bananas with an initial speed of 0 B6.4 A 55kg carton of bananas with an initial speed of 0.45m/s slides down a ramp inclined at an angle of 23⁰ with the horizontal. If the coefficient of friction between the carton and the ramp is 0.24, how fast will the carton be moving after it has travelled a distance of 2.1m down the ramp? Ans: 2.68m/s