Physics Energy
Energy in its Many Forms • Energy is defined as the ability to change an object or its environment. • Energy is stored in many forms; energy can be stored as chemical bonds or an object on a high shelf has the potential to change anything it falls on.
Forms of Energy • Kinetic and potential energy are 2 forms of energy. • Moving objects have a form of energy called Kinetic Energy. • Potential energy is energy stored in an object because of its state or position. • Work is the transfer of energy by mechanical means. This energy may come from stored (potential) energy and is transferred by kinetic energy.
Doing Work to Change Kinetic Energy • The kinetic energy of an object is given by the equation: • The kinetic energy is proportional to the mass of the object. • Kinetic energy is also proportional to the square of the velocity. • Kinetic energy is measured in Joules.
Work-Energy Theorem • According to Newton’s Third Law, F = ma, and the Work equation, W = Fd, Work can be redefined as W = mad. • Displacement can be defined as • Therefore, W = = KE • The change in KE of an object is equal to the net work done on it. • The work-energy theorem states: The net work done on an object is equal to its change in kinetic energy.
Work-Energy Theorem • The work-energy theorem indicates that if the net work is positive, the kinetic energy increases. • Likewise, if the net work is negative, the kinetic energy decreases. • Examples: A pitcher throws a baseball—the net force and the motion are in the same direction and KE is positive. When the catcher stops the ball, the net force is in the negative direction and the KE goes to zero.
Example Problem • A shotputter heaves a 7.26-kg shot with a final velocity of 7.5 m/s. • A. What is the kinetic energy of the shot? • B. The shot was initially at rest, How much work was done on it to give it this kinetic energy?
Solution • Known: Unknown: • M = 7.26 kg KE = ? • = 0 m/s W = ? • = 7.50 m/s • A. • B. Work done = change in KE • W =
Potential Energy • Potential energy is the energy of position. • The equation for potential energy is: PE = mgh (mass x gravity x height) h is the reference level for the problem. It can be set at any level but cannot be changed during the problem. Energy can also be stored in the bending or stretching of an object.
KE and PE • Kinetic energy and potential energy are related. • If you throw a ball into the air, it has kinetic energy. However, at the top of the trip, the ball stops and kinetic energy is transferred to potential energy. As soon as the ball starts falling again, the PE is transferred back to KE.
Practice Problem • A 2.00 kg textbook is lifted from the floor to a shelf 2.10 m above the floor. • A. What is its gravitational potential energy relative to the floor? • B. What is its gravitational potential energy relative to the head of a 1.65 m tall person?
Solution • Known: Unknown: • M = 2.00 kg PE • H1 = 2.10 m • H2 = 2.10 m - 1.65 m = 0.45 m • A. PE = 2.00 kg x 9.8 m/s2 x 2.10 m • PE = 41.2 J • B. PE = 2.00 kg x 9.8 m/s2 x 0.45 m • PE = 8.8 J
The Law of Conservation of Energy • The law of conservation of energy states: within a closed, isolated system, energy can change form, but the total amount of energy is constant. • That is, energy can be neither created nor destroyed. Energy can only be transformed into another form.
Mechanical Energy • The sum of potential and kinetic energy is often called mechanical energy. • The total energy of a closed system does not change. Therefore, KEi + PEi = KEf + PEf
Practice Problem • A large chunk of ice with mass 15.0 kg falls from a roof 8.00 m above the ground. • A. Find the kinetic energy of the ice when it reaches the ground. • B. What is the speed of the ice when it reaches the ground?
Solution Known: M = 15.0 kg g = 9.8 m/s2 h = 8.00 m KEi = 0 PEf = 0 A. KEi + PEi = KEf + PEf 0 + 15 x 9.8 x 8.00 = KEf + 0 KEf = 1.18 x 103 J Unknown: Kef Vf B. KEf = ½ mv2 1.18 x 103J = ½ 15v2 V2 = 2(1.18 x 103)/15 Vf = 12.5 m/s
Application of KE and PE • A roller coaster constantly changed the KE and PE by its changing position.
