Chapter 14 Work Power and Machines 14 1
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Chapter 14 Work, Power, and Machines 14. 1 Work and Power
What Is Work? When does a force do work? In science, work is the product of force and distance.
What Is Work? For a force to do work on an object, the force must cause the object to move. • no movement=no work done. Any force not acting in the direction of motion does no work on an object.
Calculating Work = force x distance Units of Work The joule (J) is the SI unit of work. A joule is equal to 1 newton-meter. ****When using SI units in the work formula, the force is in newtons, and distance is in meters.
Calculating Work Using the Work Formula A weight lifter raises a 1600 newton barbell to a height of 2. 0 meters.
Calculating Work Using the Work Formula A weight lifter raises a 1600 newton barbell to a height of 2. 0 meters. W=fd W=1600 x 2 W= 3200 J
Work Practice 1. A crane uses an average force of 5200 N to lift a girder 25 m 2. The brakes on a bicycle apply 125 N of frictional force to the wheels as it travels 14. 0 m
Work Practice 1. A crane uses an average force of 5200 N to lift a girder 25 m W=fd W=5200 N x 25 m W = 130, 000 J 2. The brakes on a bicycle apply 125 N of frictional force to the wheels as it travels 14. 0 m W=fd W=125 N x 14 m W = 1750 J
Work Practice 3. While rowing, John exerts a force of 165 N per stroke while pulling the oar 0. 8 m. How much work is done in 30 strokes? 4. A 900 -N mountain climber scales a 100 -m cliff
Work Practice 3. While rowing, John exerts a force of 165 N per stroke while pulling the oar 0. 8 m. How much work is done in 30 strokes? W=fd W=165 N x 0. 8 m W=132 J 4. A 900 -N mountain climber scales a 100 m cliff W=fd W=900 N x 100 m W=90, 000 J
Work Practice 5. A turtle slowly crawls along carrying a bird feather on its back. It passes an elephant standing still with five large lions on its back. Who is doing more work, the turtle or the elephant? Explain.
Work Practice 5. A turtle slowly crawls along carrying a bird feather on its back. It passes an elephant standing still with five large lions on its back. Who is doing more work, the turtle or the elephant? Explain. W=fd The turtle, because the elephant is not moving. W=f x 0, therefore The elephant’s work is 0
What Is Power? How are work and power related? Power is the rate of doing work. To increase power, • increase the amount of work done in a given time • you can do a given amount of work in less time.
Calculating Power
Calculating Power When using SI units in the power formula, work is measured in joules (J), and time is measured in seconds (s). The SI unit of power is the watt (W), which is equal to one joule per second.
Calculating Power You exert a vertical force of 72 newtons to lift a box to a height of 1. 0 meter in a time of 2. 0 seconds. How much power is used to lift the box?
Calculating Power You exert a vertical force of 72 newtons to lift a box to a height of 1. 0 meter in a time of 2. 0 seconds. How much power is used to lift the box? W=fd W=72 N x 1 m W=72 J P=w/t P = 72 J/2 s P = 36 Watts
Calculating Power 1. Your family is moving to a new apartment. While lifting a box 1. 5 m straight up to put it on a truck, you exert an upward force of 200 N for 1. 0 s. How much power is required to do this?
Calculating Power 1. Your family is moving to a new apartment. While lifting a box 1. 5 m straight up to put it on a truck, you exert an upward force of 200 N for 1. 0 s. How much power is required to do this? W=fd W=200 N x 1. 5 m W = 300 J P=W/t P = 300 J / 1 s P = 300 w
Calculating Power 2. You lift a book from the floor to a bookshelf 1. 0 m above the ground. How much power is used if the upward force is 15. 0 N and you do the work in 2. 0 s?
Calculating Power 2. You lift a book from the floor to a bookshelf 1. 0 m above the ground. How much power is used if the upward force is 15. 0 N and you do the work in 2. 0 s? P = w/t P = (15 N x 1 m) / 2 s P = 7. 5 w
Calculating Power 3. You apply a horizontal force of 10. 0 N to pull a wheeled suitcase at a constant speed of 0. 5 m/s across flat ground. How much power is used? (Hint: The suitcase moves 0. 5 m/s. Consider how much work the force does each second and how work is related to power. )
Calculating Power 3. You apply a horizontal force of 10. 0 N to pull a wheeled suitcase at a constant speed of 0. 5 m/s across flat ground. How much power is used? (Hint: The suitcase moves 0. 5 m/s. Consider how much work the force does each second and how work is related to power. ) P=w/t P = 10 N x 0. 5 m / 1 s P = 5 w
Power Practice 1. John does 3960 J of work on the oars in 60 s 2. A mechanic does 5350 J of work to lift a car 0. 5 m in 50 s 3. Anna weighs 565 N and goes up 3. 25 m vertically by stairs. What is power if her time is 12. 6 s?
Power Practice 1. John does 3960 J of work on the oars in 60 s P = 3960 J / 60 s = 66 w 2. A mechanic does 5350 J of work to lift a car 0. 5 m in 50 s P = 5350 J /50 s = 107 w 3. Anna weighs 565 N and goes up 3. 25 m vertically by stairs. What is power if her time is 12. 6 s? P = 565 N x 3. 25 / 12. 6 s = 145. 73 w
James Watt and Horsepower Another common unit of power is the horsepower. One horsepower (hp) is equal to about 746 watts.
Power Practice Suppose you ride in a sleigh being pulled by horses at 16 km/h. Another sleigh being pulled at 10 km/h travels the same distance you do. Which horses are more powerful? How is speed related to power?
Power Practice Suppose you ride in a sleigh being pulled by horses at 16 km/h. Another sleigh being pulled at 10 km/h travels the same distance you do. Which horses are more powerful? How is speed related to power? 16 km/h because they are capable of doing more work (traveling farther in less time)
Assessment Questions 1. In which of the following cases is work being done on an object? a. pushing against a locked door b. suspending a heavy weight with a strong chain c. pulling a trailer up a hill d. carrying a box down a corridor
Assessment Questions 1. In which of the following cases is work being done on an object? a. pushing against a locked door b. suspending a heavy weight with a strong chain c. pulling a trailer up a hill d. carrying a box down a corridor
Assessment Questions 2. A tractor exerts a force of 20, 000 newtons to move a trailer 8 meters. How much work was done on the trailer? a. 2, 500 J b. 4, 000 J c. 20, 000 J d. 160, 000 J
Assessment Questions 2. A tractor exerts a force of 20, 000 newtons to move a trailer 8 meters. How much work was done on the trailer? a. 2, 500 J b. 4, 000 J c. 20, 000 J d. 160, 000 J
Assessment Questions 3. A car exerts a force of 500 newtons to pull a boat 100 meters in 10 seconds. How much power does the car use? a. 5000 W b. 6000 W c. 50 W d. 1000 W
Assessment Questions 3. A car exerts a force of 500 newtons to pull a boat 100 meters in 10 seconds. How much power does the car use? a. 5000 W b. 6000 W c. 50 W d. 1000 W
Assessment Questions 4. One horsepower is a unit of power equal to a. 0. 746 W. b. 1. 0 W. c. 746 W. d. 2, 000 W.
Assessment Questions 4. One horsepower is a unit of power equal to a. 0. 746 W. b. 1. 0 W. c. 746 W. d. 2, 000 W.
Chapter 14 Work, Power, and Machines 14. 2 Work and Machines
Machines Do Work A machine is a device that changes a force. Machines make work easier to do by –changing the size, direction, or distance over which a force acts.
Work Input and Work Output How are work input and work output related for a machine? Because of friction, the work done by a machine is always less than the work done on the machine.
Work Input and Work Output Work Input to a Machine • The force exerted on a machine is the input force. • The distance the input force acts through is the input distance. work input = input force X input distance
Work Input and Work Output of a Machine • force exerted by a machine = output force • The distance the output force is exerted through = output distance. work output of a machine = output force X output distance.
Work Input and Work Output All machines use some amount of input work to overcome friction.
Assessment Questions 1. What is the output distance of a machine that requires 2 newtons of force exerted over 6 meters and whose output force is 4 newtons? a. 2 meters b. 3 meters c. 6 meters d. 12 meters
Assessment Questions 1. What is the output distance of a machine that requires 2 newtons of force exerted over 6 meters and whose output force is 4 newtons? a. 2 meters b. 3 meters c. 6 meters d. 12 meters
Assessment Questions 2. The work output of a machine is always greater than the work input to the machine. True False
Assessment Questions 2. The work output of a machine is always greater than the work input to the machine. True False
Chapter 14 Work, Power, and Machines 14. 3 Mechanical Advantage and Efficiency
Mechanical Advantage The mechanical advantage of a machine is the number of times that the machine increases an input force. • MA greater than one multiplies the input force • MA less than one increases the distance and speed
Mechanical Advantage
Mechanical Advantage Ideal Mechanical Advantage The ideal mechanical advantage (IMA) of a machine is the mechanical advantage in the absence of friction. Because friction reduces mechanical advantage, engineers often design machines that use low-friction materials and lubricants.
Mechanical Advantage Because friction is always present, the actual mechanical advantage is always less than the ideal mechanical advantage
Calculating Mechanical Advantage
Calculating Mechanical Advantage Calculating IMA A woman drives her car up onto wheel ramps to perform some repairs. If she drives a distance of 1. 8 meters along the ramp to raise the car 0. 3 meter, what is the ideal mechanical advantage (IMA) of the wheel ramps?
Calculating Mechanical Advantage Calculating IMA A woman drives her car up onto wheel ramps to perform some repairs. If she drives a distance of 1. 8 meters along the ramp to raise the car 0. 3 meter, what is the ideal mechanical advantage (IMA) of the wheel ramps? Input distance = 1. 8 m Output distance = 0. 3 m IMA = input distance = 1. 8 m = 6 pit[it distance 0. 3 m
MA Example • Calculate the mechanical advantage of a ramp that is 5. 0 m long and 1. 5 m high
MA Example • Calculate the mechanical advantage of a ramp that is 5. 0 m long and 1. 5 m high IMA = input/output IMA = 5 m / 1. 5 m IMA =
Calculating Mechanical Advantage 1. A student working in a grocery store after school pushes several grocery carts together along a ramp. The ramp is 3 meters long and rises 0. 5 meter. What is the ideal mechanical advantage of the ramp?
Calculating Mechanical Advantage 1. A student working in a grocery store after school pushes several grocery carts together along a ramp. The ramp is 3 meters long and rises 0. 5 meter. What is the ideal mechanical advantage of the ramp? IMA = input distance / output distance IMA = 3 m /. 5 m IMA = 6
Calculating Mechanical Advantage 2. A construction worker moves a crowbar through a distance of 0. 50 m to lift a load 0. 05 m off of the ground. What is the IMA of the crowbar?
Calculating Mechanical Advantage 2. A construction worker moves a crowbar through a distance of 0. 50 m to lift a load 0. 05 m off of the ground. What is the IMA of the crowbar? IMA = input distance / output distance IMA =. 5 m /. 05 m IMA = 10
Calculating Mechanical Advantage 3. The IMA of a simple machine is 2. 5. If the output distance of the machine is 1. 0 m, what is the input distance?
Calculating Mechanical Advantage 3. The IMA of a simple machine is 2. 5. If the output distance of the machine is 1. 0 m, what is the input distance? IMA = input distance / output distance 2. 5 = input / 1 m 2. 5 m = input distance
MA Practice 1. A ramp is 6. 0 m long and 1. 5 m high 2. An automobile jack lifts a 9900 N car with an input force of 150 N 3. A sailor pulls down on a sail weighing 140 N with a force of 140 N
MA Practice 1. A ramp is 6. 0 m long and 1. 5 m high IMA = in distance / out distance IMA = 6 m / 1. 5 m IMA = 4 m 2. An automobile jack lifts a 9900 N car with an input force of 150 N MA = out force / in force MA = 9900 N / 150 N MA = 66 3. A sailor pulls down on a sail weighing 140 N with a force of 140 N MA = out force / in force MA = 140 N / 140 N MA = 1
Efficiency Why is the efficiency of a machine always less than 100 percent? The percentage of the work input that becomes work output is the efficiency of a machine. Because there is always some friction, the efficiency of any machine is always less than 100 percent.
Efficiency is usually expressed as a percentage.
Efficiency If a machine requires 10. 0 J of work input to operate, then the work output is 75% of 10. 0 J.
Efficiency Example • Alice and Jim calculate that they must do 1800 J of work to push a piano up a ramp. Because of friction, they actually must do 2400 J of work. What is the efficiency?
Efficiency Example • Alice and Jim calculate that they must do 1800 J of work to push a piano up a ramp. Because of friction, they actually must do 2400 J of work. What is the efficiency? Efficiency = work out / work in x 100% Eff = 1800 J / 2400 J x 100% Eff = 75%
How can efficiency be maximized? Reducing friction increases the efficiency of a machine. – Roller bearings reduce the friction of the rotating wheels because rolling friction is less than sliding friction. – To further reduce the rolling friction, the roller bearings are also lubricated with grease.
Assessment Questions 1. Which statement about the actual mechanical advantage of a machine is true? a. The actual mechanical advantage is greater than one if the input force is greater than the output force. b. The actual mechanical advantage of a machine is greater than its ideal mechanical advantage when the output force is greater than the input force. c. The actual mechanical advantage of a machine is always less than its ideal mechanical advantage. d. The actual mechanical advantage of a machine is never affected by friction.
Assessment Questions 1. Which statement about the actual mechanical advantage of a machine is true? a. The actual mechanical advantage is greater than one if the input force is greater than the output force. b. The actual mechanical advantage of a machine is greater than its ideal mechanical advantage when the output force is greater than the input force. c. The actual mechanical advantage of a machine is always less than its ideal mechanical advantage. d. The actual mechanical advantage of a machine is never affected by friction.
Assessment Questions 2. If a lever raises a large rock 0. 1 meters when the other end of the lever moves downward 2 meters, what is the ideal mechanical advantage of the lever? a. 0. 05 b. 0. 5 c. 2 d. 20
Assessment Questions 2. If a lever raises a large rock 0. 1 meters when the other end of the lever moves downward 2 meters, what is the ideal mechanical advantage of the lever? a. 0. 05 IMA = in dist / out dist b. 0. 5 IMA = 2 m /. 1 m c. 2 d. 20
Assessment Questions 3. A machine is used to accomplish 300 J of work. If the efficiency of the machine is 60 percent, what is the necessary work input? a. 180 J b. 360 J c. 500 J d. 750 J
Assessment Questions 3. A machine is used to accomplish 300 J of work. If the efficiency of the machine is 60 percent, what is the necessary work input? a. 180 J Eff = work out / work in x 100% b. 360 J 60% = 300 J / work in x 100% c. 500 J . 60 = 300 J / work in d. 750 J
Assessment Questions 4. The efficiency of any machine is less than 100% because of losses due to friction. True False
Assessment Questions 4. The efficiency of any machine is less than 100% because of losses due to friction. True False
Chapter 14 Work, Power, and Machines 14. 4 Simple Machines
What are the six types of simple machines? The six types of simple machines are • the lever • the wheel and axle • the inclined plane • the wedge • the screw • the pulley.
Levers What determines the mechanical advantage of the six types of simple machines? To calculate the ideal mechanical advantage of any lever, divide the input arm by the output arm.
Levers A lever is a rigid bar that is free to move around a fixed point. The fixed point the bar rotates around is the fulcrum.
Levers The input arm = the distance between the input force and the fulcrum. The output arm = the distance between the output force and the fulcrum. Levers are classified into three categories based on the locations of the input force, the output force, and the fulcrum.
Levers First-Class Levers The fulcrum of a first-class lever is always located between the input force and the output force. Depending on the fulcrum position, the mechanical advantage can be greater than 1, equal to 1, or less than 1.
Levers Second-Class Levers • In a second-class lever, the output force is located between the input force and the fulcrum. • The input distance is larger than the output distance. • The mechanical advantage of a second-class lever is always greater than 1.
Levers Third-Class Levers • The input force of a third-class lever is located between the fulcrum and the output force. • The output distance over which the third-class lever exerts its force is larger than the input distance. • The mechanical advantage of a thirdclass lever is always less than 1.
Wheel and Axle To calculate the ideal mechanical advantage of the wheel and axle, divide the radius (or diameter) where the input force is exerted by the radius (or diameter) where the output force is exerted.
Wheel and Axle A wheel and axle is a simple machine that consists of two disks or cylinders, each one with a different radius. The outer disk is the wheel and the inner cylinder is the axle. The wheel and the axle rotate together as a unit.
Wheel and Axle The input force can be exerted on the wheel or the axle. • If the force is applied to the wheel, the input distance is larger than the output distance. The mechanical advantage is greater than 1. • If the force is applied to the axle, the output distance is larger than the input distance. The mechanical advantage is less than 1.
Inclined Planes The ideal mechanical advantage of an inclined plane is the distance along the inclined plane divided by its change in height.
Inclined Planes An inclined plane is a slanted surface along which a force moves an object to a different elevation. • The distance traveled is the input distance. • The change in height of the ramp is its output distance. • The mechanical advantage of an inclined plane is greater than 1.
Wedges and Screws Wedges A wedge is a V-shaped object whose sides are two inclined planes sloped toward each other. A wedge has a mechanical advantage greater than 1.
Wedges and Screws A screw is an inclined plane wrapped around a cylinder. For two screws of the same length, the one whose threads are closer together moves forward less for each turn of the screw. A screw has a mechanical advantage greater than 1.
Pulleys The ideal mechanical advantage of a pulley or pulley system is equal to the number of rope sections supporting the load being lifted.
Pulleys A pulley is a simple machine that consists of a rope that fits into a groove in a wheel. • Pulleys produce an output force that is different in size, direction, or both, from that of the input force. • The mechanical advantage of a pulley can be equal to or greater than 1.
Pulleys Fixed Pulleys A fixed pulley is a wheel attached in a fixed location. The direction of the exerted force is changed by a fixed pulley, but the size of the force is not. The ideal mechanical advantage of a fixed pulley is always 1.
Pulleys Movable Pulley A movable pulley is attached to the object being moved rather than to a fixed location. • Both sections of the rope pull up with the same force. • The movable pulley has a mechanical advantage of 2.
Pulleys Pulley System A large mechanical advantage can be achieved by combining fixed and movable pulleys into a pulley system. • The mechanical advantage depends on how the pulleys are arranged. • The ideal mechanical advantage of a pulley system is equal to the number of rope sections supporting the load being lifted.
Compound Machines • A compound machine is a combination of two or more simple machines that operate together. Most of the machines you use are compound machines.
Assessment Questions 1. A bar that is rotating about a fixed point is called a a. fulcrum. b. lever. c. wedge. d. compound machine.
Assessment Questions 2. A 3 -meter-long ramp is used to lift a piano to a moving truck, which is 1 meter off the ground. What is the ideal mechanical advantage of the ramp? a. 1 b. 2 c. 3 d. 33
Assessment Questions 3. A machine, such as a bicycle, that combines many simple machines is known as a complex machine. True False
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