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Chapter 6 Work and Machines

6.1 Work vs. Impulse It takes Energy to push something and make it move. 2 conditions 1.) Force Exerted. 2.) How long force is exerted. For… Impulse = “how long” means time. Work = “how long” means distance

What is Work? Work makes something move! Work-the transfer of energy that occurs when a force makes an object move. 2 conditions 1.) Force must make the object move. 2.)Movement must be in the same direction as force.

Is this work? Examples: Lifting a barbell? Holding a barbell steady? Carrying barbell across the gym? Why?

Formula to calculate work Work(J)=Force(N)*distance (m) Or: W= Fd

Try this! Alexander has a mass of 70 kg. His apartment is on the second floor, 5 meters from the ground level. How much work does he do against gravity each time he climbs the stairs to his apartment? 1. W=fd 2. W= (70 kg x 10 m/s 2 ) (5 m) 3. W= 3500 J

Try this! How much additional work does Alexander have to do if he is carrying 5 kg of groceries? 1. W=fd 2. W= (75 kg x 10 m/s 2 ) (5 m) 3. W= 3750 J

Try this! A car engine does 50,000 J of work to accelerate at 10 m/s 2 for 5 m. What is the mass of the car? 1. F = W ÷ d 2. F = 50,000 J ÷ 5 m 3. F = 10,000 N 4. F = m x a 5. 10,000 N = 10 m/s 2 x m 6. Mass = 1000 kg

POWER! Power-amount of work done in one second. Rate at which work is done SI unit = Watts (W) 1 kilowatt = 1000 W Formula Power (Watts) = Work (Joules) / Time(seconds) P = W/t

Problem A roller coaster is pulled up a hill by a chain attached to a motor. The roller coaster has a total mass of 10,000 kg. If it takes 20 s to pull the roller coaster up a 50 m hill, how powerful is the motor? P = W/t; W = Fxd W = (10,000 kg x 10 m/s 2 ) x 50 m P = 5,000,000 J ÷ 20 s = 250 kW

ANOTHER PROBLEM… What would the motor’s power be if it took 40 s to pull the same roller coaster up the hill? P = W/t P = 5,000,000 J / 40 s P = 125 kW

YET ANOTHER PROBLEM… What is the power of a 70 kg person who climbs a 10-meter high hill in 45 s? P = W/t; W=Fd P = (70 kg x 10 m/s 2 ) x 10 m / 45 s P = 156 W

TIEING IT ALL TOGETHER Power is also the rate at which energy is transferred. Power (Watts) = Energy transferred (Joules) time (seconds) P= E/t EX: Power used by lightbulb is the amount of electrical E used each second.

Work and Energy Energy-the ability to cause change or to do work Types of energy: Potential = energy of position. m x g x h or F x h. Kinetic = energy of motion ½ m x v 2 transfer of energy always occurs when work is done!

Mechanical Energy Includes both Potential and Kinetic Energy The sum of the kinetic and potential energy in a system.

Work – Energy Theorem Work is equal to change in Energy (could be potential or kinetic) Work = ΔKE or ΔPE

Work – Energy Theorem Energy is required to change the motion of an object (speed up or slow down) The more motion an object has, the more KE the object has. Work = Δ KE, therefore the more KE the more work required to change the object’s motion.

Work and Energy Height of the weight, Δ y = distance the tractor travels, d. Ideal situation: constant speed and negligible friction - therefore F tractor = F weight PE is given by F Δ y, & W tractor on the weight equals Fd So W = ΔE

Try this! How much work is needed to lift an object that weighs 500 N to a height of 4 m? How does this work compare to the change in PE for that object? 1. W=fd or PE = m x g x h 2. W= (500N) (4m) or PE = 500 N x 4 m 3. W= 2000 J or PE = 2000 J 4. They are the same!

Try this! A tractor accelerates a 100 kg trailer from rest to a velocity of 5 m/s over a distance of 1.25 m. How much work is required and how does this work compare to the change in KE for that object? What is the acceleration of the trailer? 1. W=fd or KE = ½ m x v 2 2. W= (100 kg x 10 m/s 2 ) (1.25 m) or KE = ½ 100 kg x W= 1250 J or KE = 1250 J 4. They are the same! 5. F = ma; a = 10 m/s 2

Try this! A car traveling along a level road at speed “v” slams on the brakes and skids to a stop. If the force of friction on the car is half the car’s weight, how far does the car slide? 1. W=Fd or ΔKE = ½ m x v 2 2. Fd = ½ m v 2 3. d = ½ m v 2 ÷ F; F = ½ m g 4. d = v 2 ÷ g 5. Stopping distance is proportional to v 2

6.8 Machines Machine - a device that makes doing work easier. ↑ force that can be applied on an object. ↑ the distance over which a force can be applied. Changing the direction of the force applied

Work done by Machines Input force-force that is applied to the machine. F in Output force- force applied by the machine. F out

Energy is always conserved! Your energy is transferred to machine Machine transfers energy to the object. Some energy changes to heat due to friction W out is never greater than W in Conserving Energy

Work done by Machines If Friction is negligible, meaning not present, then we can say the following: Work input = Work output (Fd) in = (Fd) out

Simple Machines 6 classes of machines: Lever Inclined plane Pulley Wheel & axle Wedge Screw

1. Lever Lever- A bar that is free to pivot or turn around a fixed point.

Parts of a Levers Fulcrum- fixed point Input Arm- Distance from fulcrum to part where input force is applied. ( E =effort force) Output arm-Distance from fulcrum to part where output force is applied. (R =resistance Force)

First Class levers Fulcrum is between the output ( R ) & input force (E). Forces move in opposite directions Ex: See saw INPUT FORCE OUTPUT FORCE

Second Class Levers Output force between the input force & fulcrum. EX: Car door, wheelbarrow OUTPUT FORCE INPUT FORCE FULCRUM

Third Class Lever The input force is between output force and fulcrum. EX: Your arm, hockey stick, baseball bat. OUTPUT FORCE FULCRUM INPUT FORCE

Mechanical Advantage Mechanical advantage-the ratio of the output force to the input force MA = output force (N) input force (N) The mechanical advantage of a machine without friction is the ideal mechanical advantage. (IMA)

Ideal MA (lever) IMA= Length of input arm (m) Length of output arm (m) IMA = L input ÷ L output

Example Problem A lever has a mechanical advantage of 4. Its input arm is 60 cm long. How long is its output arm? 1. MA = Lin ÷ Lout 2. 4 = 60 ÷ Lout 3. Lout = 15 cm

Example Problem What is the mechanical advantage of a lever with an input arm of 25 cm and an output arm of 100 cm? 1. MA = Lin ÷ Lout 2. MA = 25 cm ÷ 100 cm 3. MA = 0.25

Example Problem A lever has an input arm of 100 cm and an output arm of 10 cm. What is the mechanical advantage of this lever? Given the mechanical advantage, how much input force is needed to lift a 100-N load? 1. MA = Lin ÷ Lout 2. MA = 100 cm ÷ 10 cm = MA = Fout ÷ Fin; 10 = 100-N ÷ Fin 5. Fin = 10 N

Example Problem You want to use a lever to lift a 2000 N rock. The maximum force you can exert is 500 N. Draw a lever that will allow you to lift the rock. Label the input force, output force, fulcrum, input arm and output arm. Specify measurements for the input and output arms.

2. Pulleys Pulley – grooved wheel w/ a rope or chain, or cable running along a groove. Modified 1 st class lever Can change direction of input force or increase output force Three types!

PULLEYS 1. Fixed Pulley- Changes only direction of force. IMA = 1 EX: Elevator cable OUTPUT FORCE INPUT FORCE FULCRUM

PULLEYS 2. Moveable pulley- one end of the rope is fixed & wheel is free to move. Multiplies force  Force required = weight ÷ IMA Output force = 8 N Input force = 4 N IMA = 2 String attached to ceiling is another person who can support ½ weight of the load. If the weight of the load is equal to 8 N, you only need to exert a force of 4 N in order to support and lift the load. 8N

PULLEYS 3. Block & Tackle- System of fixed & moveable pulleys IMA= # of ropes that support the weight. Force required = weight ÷ IMA Fixed Pulley Moveable Pulley IMA = 2

Efficiency Efficiency- a measure of how much of the work put into a machine is changed into useful output work by the machine. efficiency ( %) = output work (J) input work (J) X 100 ↑ Efficiency by reducing friction – Lubrcant ex: oil or grease, ball bearings, etc…

Work & Energy Work - the transfer of energy that occurs when a force makes an object move. 2 conditions 1.) Force must make the object move. 2.)Movement must be in the same direction as force. W = F x d

Work & Energy Work - the transfer of energy that occurs when a force makes an object move. Types of energy: Potential = energy of position. m x g x h or F x h. Kinetic = energy of motion ½ m x v 2 Work must equal CHANGE IN ENERGY!

Work & Energy Power-amount of work done in one second. Rate at which work is done Formula P = W/t

Work & Energy Machine - a device that makes doing work easier. ↑ force that can be applied on an object. ↑ the distance over which a force can be applied. Changing the direction of the force applied Win = Wout or (Fd)in = (Fd)out

Simple Machines 6 classes of machines: Lever Inclined plane Pulley Wheel & axle Wedge Screw

Mechanical Advantage Mechanical advantage-the ratio of the output force to the input force MA = output force (N) input force (N) MA lever = Lin/Lout MA pulley = # ropes supporting weight

Efficiency Efficiency- a measure of how much of the work put into a machine is changed into useful output work by the machine. efficiency ( %) = output work (J) input work (J) X 100 ↑ Efficiency by reducing friction