Work, Power, and Machines

What is Work? transfer of energy to a body by application of a force that causes body to move in direction of force. W = F  d

What is Work? Chapter 12 SI units: joules (J). 1 J = 1 N•m = 1 kg•m2/s2

F W d WORK W = ? W = Fd F = 190 N W = (190 N) (2.0 m) d = 2.0 m Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N? GIVEN: W = ? F = 190 N d = 2.0 m WORK: W = Fd W = (190 N) (2.0 m) W = 380 J F W d

F W d WORK W = ? W = Fd F = 5200 N W = (5200 N) (25 m) d = 25 m A crane uses an average force of 5200 N to lift a girder 25 m. How much work does the crane do on the girder? GIVEN: W = ? F = 5200 N d = 25 m WORK: W = Fd W = (5200 N) (25 m) W = 130,000 J or 1. 3 x 105 J F W d

F W d WORK W = ? W = Fd F = 1 N W = (1 N) (1 m) d = 1m W = 1 J An apple weighing 1 N falls through a distance of 1 m. How much work is done on the apple by the force of gravity? GIVEN: W = ? F = 1 N d = 1m WORK: W = Fd W = (1 N) (1 m) W = 1 J F W d

Power Chapter 12 rate at which work is done or energy is transformed. SI Unit: watts. watt (W) = 1 J/s Power = work time p= W/t

p W t POWER p = ? p = W/t W = 1 x 105 J p = 1 x 105 J / 20 s t = 20 s It takes 100 kJ of work to lift an elevator 18 m. If this is done in 20 s, what is the average power of the elevator during the process? GIVEN: p = ? W = 1 x 105 J t = 20 s WORK: p = W/t p = 1 x 105 J / 20 s p = 5 x 103 W or 5 kW p W t

p W t POWER p = ? p = W/t W = 3960 J p = 3960 J / 60 s t = 60 s While rowing across the lake during a race, John does 3960 J of work on the oars in 60.0 s. What is his power output in watts? GIVEN: p = ? W = 3960 J t = 60 s WORK: p = W/t p = 3960 J / 60 s p = 66.0 W p W t

p W t POWER p = ? p = W/t W = 5350 J p = 5350 J / 50 s t = 50 s Using a jack, a mechanic does 5350 J of work to lift a car 0.500 m in 50.0 s. What is the mechanic’s power output? GIVEN: p = ? W = 5350 J t = 50 s WORK: p = W/t p = 5350 J / 50 s p = 107 W p W t

Machines Machines multiply and redirect forces. help people by redistributing work put into them. change either size or direction of input force. allows same amount of work to be done by either decreasing distance while increasing force or by decreasing force while increasing distance.

Force and Work Chapter 12

Mechanical Advantage id od of if ma ma tells how much a machine multiplies force or increases distance. mechanical advantage = output force = input distance input force output distance ma id od ma of if

MECHANICAL ADVANTAGE id od ma = ? ma = id/od id = 5.0 m Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high. GIVEN: ma = ? id = 5.0 m od = 1.5 m WORK: ma = id/od ma = 5.0 m / 1.5 m ma = 3.3 ma id od

MECHANICAL ADVANTAGE id od ma = ? ma = id/od id = 6.0 m Calculate the mechanical advantage of a ramp that is 6.0 m long and 1.5 m high. GIVEN: ma = ? id = 6.0 m od = 1.5 m WORK: ma = id/od ma = 6.0 m / 1.5 m ma = 4 ma id od

MECHANICAL ADVANTAGE of if ma = ? ma = of/if of = 9900 N Determine the mechanical advantage of an automobile jack that lifts a 9900 N car with an input force of 150 N. GIVEN: ma = ? of = 9900 N if = 150 N WORK: ma = of/if ma = 9900 N / 150 N ma = 66 ma of if

SIMPLE MACHINES

The Lever Family simple machines One of six basic types of machines which are basis for all other forms of machines. have a rigid arm and a fulcrum. six types divided into two families. lever family: inclined plane family: simple lever (3 types) simple inclined plane pulley wedge wheel and axle screw

First Class Levers fulcrum located between points of application of input and output forces.

fulcrum is at one end of arm and input force is applied to other end. Second Class Levers fulcrum is at one end of arm and input force is applied to other end.

Third Class Levers multiply distance rather than force. have a mechanical advantage of less than 1.

Pulleys are modified levers. point in middle of a pulley is like fulcrum of a lever. single, fixed pulley has a m. a. of 1. block and tackle: Multiple pulleys working together

Wheel & Axle a lever or pulley connected to a shaft. steering wheel of a car, screwdrivers, and cranks

The Inclined Plane Family multiply and redirect force. turns small input force into large output force by spreading work out over a large distance.

Simple Inclined Plane Changes both magnitude & direction of force

Wedge Functions as two inclined planes back to back. Turns single downward force into two forces directed out to sides.

Screw an inclined plane wrapped around a cylinder.

Compound Machines Chapter 12 machine made of more than one simple machine Examples : scissors two first class levers joined at a common fulcrum car jack combination of lever with a large screw

What is Energy?

Energy Chapter 12 Energy: ability to do work. When you do work on an object, you transfer energy to that object. Whenever work is done, energy is transformed or transferred to another system. SI Units: joules (J)

Potential Energy Elastic potential energy: energy that an object has because of position, shape, or condition stored energy. Elastic potential energy: energy stored in any type of stretched or compressed elastic material, (spring or a rubber band). Gravitational potential energy energy stored in gravitational field which exists between any two or more objects.

Gravitational Potential Energy depends on both mass and height. PE = mgh The height can be relative. height used in above equation is usually measured from ground. However, it can be a relative height between two points, such as between two branches in a tree.

GRAVITATIONAL POTENTIAL ENERGY A 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff? GIVEN: m = 65 kg h = 35 m g= 9.8 m/s2 PE = ? WORK: PE = mgh PE = (65 kg) (35 m) (9.8 m/s2) PE = 2.2 x 104 kg•m2/s2 2.2 x 104 J

Kinetic Energy energy of a moving object due to object’s motion depends on mass and speed. depends on speed more than mass.

KE = ? m = 44 kg v= 31 m/s KE = ½ mv2 KE = ½ (44 kg) (31 m/s)2 KINETIC ENERGY What is the kinetic energy of a 44 kg cheetah running at 31 m/s? GIVEN: KE = ? m = 44 kg v= 31 m/s WORK: KE = ½ mv2 KE = ½ (44 kg) (31 m/s)2 KE = 2.1 x 104 kg x m2/s2 or 2.1 x104 J

KE = ? m = 1500 kg v= 29 m/s KE = ½ mv2 KE = ½ (1500 kg) (29 m/s)2 KINETIC ENERGY Calculate the kinetic energy in joules of a 1500 kg car moving at 29 m/s. GIVEN: KE = ? m = 1500 kg v= 29 m/s WORK: KE = ½ mv2 KE = ½ (1500 kg) (29 m/s)2 KE = 6.3 x105 J

KE = ? m = 1500 kg v= 18 m/s KE = ½ mv2 KE = ½ (1500 kg) (18 m/s)2 KINETIC ENERGY Calculate the kinetic energy in joules of a 1500 kg car moving at 18 m/s. GIVEN: KE = ? m = 1500 kg v= 18 m/s WORK: KE = ½ mv2 KE = ½ (1500 kg) (18 m/s)2 KE = 2.4 x105 J

Other Forms of Energy mechanical energy: amount of work an object can do because of object’s kinetic & potential energies you can SEE it Large scale basis nonmechanical energy. you CANNOT SEE it X rays, microwaves Small scale basis (atomic)

Other Forms of Energy Chapter 12 Photosynthesis Atoms and molecules kinetic energy of particles related to heat and temperature. Chemical reactions Breaking bonds exothermic/endothermic Photosynthesis turn energy in sunlight into chemical energy.

Other Forms of Energy nuclear fusion reactions Combining of atomic nuclei Electricity. derived from flow of charged particles bolt of lightning or in a wire. electromagnetic waves. Light energy from sun

CONSERVATION OF ENERGY

Energy Transformations readily changes from one form to another. Potential energy changes into kinetic energy. car goes down a hill on a roller coaster, potential energy changes to kinetic energy. Kinetic energy changes into potential energy. kinetic energy a car has at bottom of a hill can do work to carry car up another hill.

Energy Transformations Mechanical energy can change to nonmechanical energy as a result of friction, air resistance, or other means.

The Law of Conservation of Energy energy cannot be created or destroyed. doesn’t disappear, it changes to another form. if total energy in a system increases, it must be due to energy that enters the system from an external source.

SYSTEMS open systems (most) closed system when flow of energy into and out of a system is small enough that it can be ignored open systems (most) exchange energy with the space that surrounds them.

Efficiency of Machines Not all of the work done by a machine is useful work. cannot do more work than work required to operate machine. Because of friction, work output of a machine is always somewhat less than work input. Efficiency: ratio of useful work out to work in. measure of how much useful work it can do. expressed as a percentage.

Efficiency of Machines Efficiency Equation Machines need energy input. Because energy always leaks out of a system, every machine needs at least a small amount of energy input to keep going.

eff = ? uwo = 140 J wi= 180 J wi eff = uwo/wi eff = 140 J / 180 J EFFICIENCY A sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope in order to raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the pulley? Express your answer as a percentage. GIVEN: eff = ? uwo = 140 J wi= 180 J WORK: eff = uwo/wi eff = 140 J / 180 J eff = 0.78 or 78 % eff uwo wi

eff = ? uwo = 1800 J wi= 2400 J wi eff = uwo/wi eff = 1800 J / 2400 J EFFICIENCY Alice & Jim calculate that they must do 1800 J of work to push a piano up a ramp. However, because they must also overcome friction, they must actually do 2400 J of work. What is the efficiency of the ramp? GIVEN: eff = ? uwo = 1800 J wi= 2400 J WORK: eff = uwo/wi eff = 1800 J / 2400 J eff = 0.75 or 75 % eff uwo wi

eff = 25% uwo = 1200 J wi= ? wi wi = uwo/eff wi = 1200 J / .25 EFFICIENCY It takes 1200 J of work to lift the car high enough to change a tire. How much work must be done by the person operating the jack if the jack is 25% efficient GIVEN: eff = 25% uwo = 1200 J wi= ? WORK: wi = uwo/eff wi = 1200 J / .25 wi = 4800 J eff uwo wi