Work and Energy Sections Work Done by a

Work and Energy

Sections Work Done by a Constant Force Work Done by a Variable Force The Work–Energy Theorem: Kinetic Energy Potential Energy Conservation of Energy Power

Work The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement: Unit of work is Joules (J)

Work In (a), there is a force but no displacement: no work is done. In (b), the force is parallel to the displacement, and in (c) the force is at an angle to the displacement.

Work What is the correct unit of work expressed in SI units? (A) kg m 2/s 2 (B) kg m 2/s (C) kg m/s 2 (D) kg 2 m/s 2

Work A delivery clerk carries a 3. 4 kg package from the ground to the fifth floor of an office building, a total height of 15 m. How much work is done by the clerk? 510 J

Work How much work does the force of gravity do when a 2. 5 kg object falls a distance of 3. 5 m? 88 J

Work A rope is used to pull a metal box 15. 0 m across the floor. The rope is held at an angle of 46 o with the floor and a force of 628 N is used. How much work does the force on the rope do? 6. 54 x 103 J

Work How much work did the movers do (horizontally) pushing a 160 kg crate 10. 3 m across a rough floor without acceleration, if the effective coefficient of friction was 0. 50?

Work Can work be done on a system if there is no motion? (A) Yes, if an outside force is provided. (B) Yes, since motion is only relative. (C) No, since a system which is not moving has no energy. (D) No, because of the way work is defined.

Work Object falls in a gravitational field m mg h m Wg = mgh Energy

Work A 50 N object was lifted 2. 0 m vertically and is being held there. How much work is being done in holding the box in this position? (A) more than 100 J (B) 100 J (C) less than 100 J, but more than 0 J (D) 0 J

Kinetic Energy and the Work Energy Theorem The quantity is (A) the kinetic energy of the object. (B) the potential energy of the object. (C) the work done on the object by the force. (D) the power supplied to the object by the force.

Kinetic Energy and the Work Energy Theorem (Problem) If the speed of an arrow is doubled, by what factor does its KE increase?

Kinetic Energy and the Work Energy Theorem Work done is equal to the change in the kinetic energy: • If the net work is positive, the kinetic energy increases. • If the net work is negative, the kinetic energy decreases.

Kinetic Energy and the Work Energy Theorem How much work is required to accelerate an 1125 kg car from 10 m/s to 25 m/s? (work on board) Wnet = 2. 95 x 105 J

Gravitational Potential Energy When an object is thrown upward. Positive work done by the gravitational force Negative work done by the gravitational force Earth

Gravitational Potential Energy An object can have potential energy by virtue of its position. Familiar examples of potential energy: • A wound-up spring • A stretched elastic band • An object at some height above the ground

Gravitational Potential Energy In raising a mass m to a height h, the work done by the external force is y 2 Fext h m mg y 1 We therefore define the gravitational potential energy:

Gravitational Potential Energy The quantity is (A) the kinetic energy of the object. (B) the gravitational potential energy of the object. (C) the work done on the object by the force. (D) the power supplied to the object by the force.

Gravitational Potential Energy (Problem) How high will a 1. 85 kg rock go if thrown straight up by someone who does 80. 0 J of work on it? Neglect air resistance. Gravity does -80 J while stopping the rock.

Systems and Energy Conservation The sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign. This allows us to define the total mechanical energy: And its conservation:

Systems and Energy Conservation If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height. y So the first hill must be the highest, unless the track has chains/magnets along the way.

Systems and Energy Conservation All three of these balls have the same initial kinetic energy; as the change in potential energy is also the same for all three. Their speeds just before they hit the bottom are the same as well.

Systems and Energy Conservation Ball dropped from rest falls freely from a height h. Find its final speed. h v

Power is the rate at which work is done – In the SI system, the units of power are watts (W): The difference between walking and running up the stairs is power – the change in gravitational potential energy is the same.

Power is also needed for acceleration and for moving against the force of gravity. The average power can be written in terms of the force and the average velocity: v F FR d

Power A box that weighs 57. 5 kg is lifted a distance of 20. 0 m straight up by a rope. The job is done in 10. 0 s. What power is developed in watts and kilowatts? 1. 15 x 103 W = 1. 15 k. W

Work An electric motor develops 65 k. W of power as it lifts a loaded elevator 17. 5 m in 35. 0 s. How much force does the motor exert? 1. 3 x 105 N

Power (Problem) A 1000 kg sports car accelerates from rest to 20 m/s in 5. 0 s. What is the average power delivered by the engine?

Review Work done by a constant force is the displacement times the component of force in the direction of the displacement. Kinetic energy is the energy of motion. Work–energy theorem: the net work done on an object is equal to the change in its kinetic energy. Potential energy is the energy of position or configuration.

Review The total energy of the universe, or of an isolated system, is conserved. Total mechanical energy is the sum of kinetic and potential energy. It is conserved in a conservative system. The net work done by forces is equal to the change in the total mechanical energy. Power is the rate at which work is done.