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**Conceptual Physics Fundamentals**

Chapter 5: MOMEMTUM AND ENERGY

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**This lecture will help you understand:**

Momentum Impulse Impulse Changes Momentum Bouncing Conservation of Momentum Collisions Energy Work Potential Energy Work-Energy Theorem Conservation of Energy Power Machines Efficiency Sources of Energy

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Momentum and Energy “Human history becomes more and more a race between education and catastrophe.” —H. G. Wells

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**Momentum a property of moving things means inertia in motion**

more specifically, mass of an object multiplied by its velocity in equation form: mass velocity (momentum = mv)

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Momentum example: A moving boulder has more momentum than a stone rolling at the same speed. A fast boulder has more momentum than a slow boulder. A boulder at rest has no momentum.

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**A moving object has ________________.**

Momentum CHECK YOUR NEIGHBOR A moving object has ________________. A. momentum energy speed all of the above D. all of the above.

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**A moving object has ________________.**

Momentum CHECK YOUR ANSWER A moving object has ________________. A. momentum energy speed all of the above D. all of the above.

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**When the speed of an object is doubled, its momentum ________________.**

CHECK YOUR NEIGHBOR When the speed of an object is doubled, its momentum ________________. A. remains unchanged in accord with the conservation of momentum doubles quadruples decreases B. doubles.

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**When the speed of an object is doubled, its momentum ________________.**

CHECK YOUR ANSWER When the speed of an object is doubled, its momentum ________________. A. remains unchanged in accord with the conservation of momentum doubles quadruples decreases B. doubles.

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**Impulse Impulse example: product of force and time (force time)**

in equation form: impulse = Ft example: A brief force applied over a short time interval produces a smaller change in momentum than the same force applied over a longer time interval. or If you push with the same force for twice the time, you impart twice the impulse and produce twice the change in momentum.

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**Impulse Changes Momentum**

The greater the impulse exerted on something, the greater the change in momentum. in equation form: Ft = (mv)

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**Impulse Changes Momentum**

CHECK YOUR NEIGHBOR When the force that produces an impulse acts for twice as much time, the impulse is ________________. A. not changed doubled quadrupled halved B. increased by twice.

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**Impulse Changes Momentum**

CHECK YOUR ANSWER When the force that produces an impulse acts for twice as much time, the impulse is ________________. A. not changed doubled quadrupled halved B. increased by twice.

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**Impulse Changes Momentum**

Case 1: increasing momentum Apply the greatest force for as long as possible, and you extend the time of contact. Force can vary throughout the duration of contact. examples: golfer swings a club and follows through baseball player hits a ball and follows through

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**Impulse Changes Momentum**

CHECK YOUR NEIGHBOR A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater ________________. A. average force impulse both of the above neither of the above B. impulse.

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**Impulse Changes Momentum**

CHECK YOUR ANSWER A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater ________________. A. average force impulse both of the above neither of the above Explanation: The force on the cannonball will be the same for a short- or long-barreled cannon. The longer barrel provides for a longer time for the force to act, and therefore, a greater impulse. (The long barrel also provides a longer distance for the force to act, providing greater work and greater kinetic energy of the cannonball.) B. impulse.

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**Impulse Changes Momentum**

Case 2: decreasing momentum over a long time extend the time during which momentum is reduced

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**Impulse Changes Momentum**

CHECK YOUR NEIGHBOR A fast-moving car hitting a haystack or a cement wall produces vastly different results. 1. Do both experience the same change in momentum? 2. Do both experience the same impulse? 3. Do both experience the same force? A. yes for all three yes for 1 and 2 no for all three no for 1 and 2 B. Yes for 1 and 2.

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**Impulse Changes Momentum**

CHECK YOUR ANSWER A fast-moving car hitting a haystack or hitting a cement wall produces vastly different results. 1. Do both experience the same change in momentum? 2. Do both experience the same impulse? 3. Do both experience the same force? A. yes for all three yes for 1 and 2 no for all three no for 1 and 2 Explanation: Although stopping the momentum is the same whether done slowly or quickly, the force is vastly different. Be sure to distinguish between momentum, impulse, and force. B. Yes for 1 and 2.

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**Impulse Changes Momentum**

CHECK YOUR NEIGHBOR When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? (Careful!) A. no, both are the same yes, less if it lands on the carpet no, less if it lands on a hard floor no, more if it lands on a hard floor A. No, both are the same.

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**Impulse Changes Momentum**

CHECK YOUR ANSWER When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? (Careful!) A. no, both are the same yes, less if it lands on the carpet no, less if it lands on a hard floor no, more if it lands on a hard floor Explanation: The momentum becomes zero in both cases, so both change by the same amount. Although the momentum change and impulse are the same, the force is less when the time of momentum change is extended. Be careful to distinguish between force, impulse, and momentum. A. No, both are the same.

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**Impulse Changes Momentum**

examples: When a car is out of control, it is better to hit a haystack than a concrete wall. physics reason: same impulse either way, but extension of hitting time reduces the force

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**Impulse Changes Momentum**

example (continued): In jumping, bend your knees when your feet make contact with the ground because the extension of time during your momentum decrease reduces the force on you. In boxing, ride with the punch.

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**Impulse Changes Momentum**

Case 3: decreasing momentum over a short time short time interval produces large force example: Karate expert splits a stack of bricks by bringing her arm and hand swiftly against the bricks with considerable momentum. Time of contact is brief and force of impact is huge.

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**Bouncing Impulses are generally greater when objects bounce. example:**

Catching a falling flower pot from a shelf with your hands: You provide the impulse to reduce its momentum to zero. If you throw the flower pot up again, you provide an additional impulse. This “double impulse” occurs when something bounces.

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Bouncing Pelton wheel designed to “bounce” water when it makes a U-turn as it impacts the curved paddle

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**Conservation of Momentum**

Law of conservation of momentum: In the absence of an external force, the momentum of a system remains unchanged.

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**Conservation of Momentum**

examples: When a cannon is fired, the force on cannonball inside the cannon barrel is equal and opposite to the force of the cannonball on the cannon. The cannonball gains momentum, while the cannon gains an equal amount of momentum in the opposite direction—the cannon recoils. When no external force is present, no external impulse is present, and no change in momentum is possible.

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**Conservation of Momentum**

examples (continued): Internal molecular forces within a baseball come in pairs, cancel one another out, and have no effect on the momentum of the ball. Molecular forces within a baseball have no effect on its momentum. Pushing against a car’s dashboard has no effect on its momentum.

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**Collisions For all collisions in the absence of external forces**

net momentum before collision equals net momentum after collision in equation form: (net mv)before = (net mv)after

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**Collisions elastic collision**

occurs when colliding objects rebound without lasting deformation or any generation of heat

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**Collisions inelastic collision**

occurs when colliding objects result in deformation and/or the generation of heat

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**Collisions example of elastic collision:**

single car moving at 10 m/s collides with another car of the same mass, m, at rest From the conservation of momentum, (net mv)before = (net mv)after (m 10)before = (2m V)after V = 5 m/s

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**Collisions CHECK YOUR NEIGHBOR**

Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is ________________. A. the same half twice none of the above B. half.

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**Collisions CHECK YOUR ANSWER**

Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is ________________. A. the same half twice none of the above Explanation: After the collision, the mass of the moving freight cars has doubled. Can you see that their speed is half the initial velocity of freight car A? B. half.

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**Energy A combination of energy and matter make up the universe. Energy**

mover of substances both a thing and a process observed when it is being transferred or being transformed a conserved quantity

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**Energy Matter property of a system that enables it to do work**

anything that can be turned into heat example: electromagnetic waves from the Sun Matter substance we can see, smell, and, feel occupies space

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**Work Work Two things occur whenever work is done:**

involves force and distance is force distance in equation form: W = Fd Two things occur whenever work is done: application of force movement of something by that force

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**Work CHECK YOUR NEIGHBOR**

If you push against a stationary brick wall for several minutes, you do no work ________________. A. on the wall at all both of the above none of the above A. on the wall.

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Work CHECK YOUR ANSWER If you push against a stationary brick wall for several minutes, you do no work ________________. A. on the wall at all both of the above none of the above Explanation: You may do work on your muscles, but not on the wall. A. on the wall.

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Work examples: twice as much work is done in lifting two loads one- story high versus lifting one load the same vertical distance reason: force needed to lift twice the load is twice as much twice as much work is done in lifting a load two stories instead of one story reason: distance is twice as great

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**Work example: Unit of work: Newton-meter (Nm) or Joule (J)**

A weightlifter raising a barbell from the floor does work on the barbell. Unit of work: Newton-meter (Nm) or Joule (J)

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**Work CHECK YOUR NEIGHBOR**

Work is done in lifting a barbell. How much work is done in lifting a barbell that is twice as heavy the same distance? A. twice as much half as much the same depends on the speed of the lift A. Twice as much.

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Work CHECK YOUR ANSWER Work is done in lifting a barbell. How much work is done in lifting a barbell that is twice as heavy the same distance? A. twice as much half as much the same depends on the speed of the lift Explanation: This is in accord with work = force distance. Twice the force for the same distance means twice the work done on the barbell. A. Twice as much.

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**Work CHECK YOUR NEIGHBOR**

You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is ________________. A. less than twice as much twice as much more than twice as much zero B. twice as much.

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Work CHECK YOUR ANSWER You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is ________________. A. less than twice as much twice as much more than twice as much zero B. twice as much.

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**Potential Energy Potential Energy example:**

stored energy held in readiness with a potential for doing work example: A stretched bow has stored energy that can do work on an arrow. A stretched rubber band of a slingshot has stored energy and is capable of doing work.

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**Potential Energy Gravitational potential energy**

potential energy due to elevated position example: water in an elevated reservoir raised ram of a pile driver equal to the work done (force required to move it upward the vertical distance moved against gravity) in lifting it in equation form: PE = mgh

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**Potential Energy CHECK YOUR NEIGHBOR**

Does a car hoisted for repairs in a service station have increased potential energy relative to the floor? A. yes no sometimes not enough information A. Yes.

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**Potential Energy CHECK YOUR ANSWER**

Does a car hoisted for repairs in a service station have increased potential energy relative to the floor? A. yes no sometimes not enough information Comment: If the car were twice as heavy, its increase in potential energy would be twice as great. A. Yes.

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Potential Energy example: Potential energy of 10-N ball is the same in all 3 cases because work done in elevating it is the same.

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**Kinetic Energy Kinetic Energy energy of motion**

depends on the mass of the object and its speed include the proportional constant 1/2 and KE = 1/2 mass speed squared If object speed is doubled kinetic energy is quadrupled

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**Must a car with momentum have kinetic energy?**

CHECK YOUR NEIGHBOR Must a car with momentum have kinetic energy? A. yes, due to motion alone yes, when motion is nonaccelerated yes, because speed is a scalar and velocity is a vector quantity no A. Yes, due to motion alone.

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**Must a car with momentum have kinetic energy?**

CHECK YOUR ANSWER Must a car with momentum have kinetic energy? A. yes, due to motion alone yes, when momentum is nonaccelerated yes, because speed is a scalar and velocity is a vector quantity no Explanation: Acceleration, speed being a scalar, and velocity being a vector quantity, are irrelevant. Any moving object has both momentum and kinetic energy. A. Yes, due to motion alone.

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**Kinetic Energy Kinetic energy and work of a moving object**

equal to the work required to bring it from rest to that speed, or the work the object can do while being brought to rest in equation form: net force distance = kinetic energy, or Fd = 1/2 mv2

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**Work-Energy Theorem Work-energy theorem**

gain or reduction of energy is the result of work in equation form: work = change in kinetic energy (W = KE) doubling speed of an object requires 4 times the work also applies to changes in potential energy

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**Work-Energy Theorem applies to decreasing speed**

reducing the speed of an object or bringing it to a halt example: applying the brakes to slow a moving car, work is done on it (the friction force supplied by the brakes distance)

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**Work-Energy Theorem CHECK YOUR NEIGHBOR**

Consider a problem that asks for the distance of a fast-moving crate sliding across a factory floor and then coming to a stop. The most useful equation for solving this problem is ________________. A. F = ma B. Ft = mv C. KE = 1/2mv2 D. Fd = 1/2mv2 D. Fd = 1/2mv2.

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**Work-Energy Theorem CHECK YOUR ANSWER**

Consider a problem that asks for the distance of a fast-moving crate sliding across a factory floor and then coming to a stop. The most useful equation for solving this problem is ________________. A. F = ma B. Ft = mv C. KE = 1/2mv2 D. Fd = 1/2mv2 Comment: The work-energy theorem is the physicist’s favorite starting point for solving many motion-related problems. D. Fd = 1/2mv2.

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**Work-Energy Theorem CHECK YOUR NEIGHBOR**

The work done in bringing a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping distance is ________________. A. actually less about the same twice none of the above D. none of the above.

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**Work-Energy Theorem CHECK YOUR ANSWER**

The work done in bringing a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping distance is ________________. A. actually less about the same twice none of the above Explanation: Twice the speed means four times the kinetic energy and four times the stopping distance. D. none of the above.

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**Conservation of Energy**

Law of conservation of energy Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

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**Conservation of Energy**

example: energy transforms without net loss or net gain in the operation of a pile driver

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**Conservation of Energy A situation to ponder…**

Consider the system of a bow and arrow. In drawing the bow, we do work on the system and give it potential energy. When the bowstring is released, most of the potential energy is transferred to the arrow as kinetic energy, and some as heat to the bow.

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**A situation to ponder… CHECK YOUR NEIGHBOR**

Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then ________________. A. energy is not conserved 10 joules go to warming the bow 10 joules go to warming the target 10 joules are mysteriously missing B. 10 joules go to warming the bow.

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**A situation to ponder… CHECK YOUR ANSWER**

Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then ________________. A. energy is not conserved 10 joules go to warming the bow 10 joules go to warming the target 10 joules are mysteriously missing Explanation: The total energy of the drawn bow, which includes the poised arrow is 50 joules. The arrow gets 40 joules and the remaining 10 joules warms the bow—still in the initial system. B. 10 joules go to warming the bow.

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**Kinetic Energy and Momentum Compared**

Similarities between momentum and kinetic energy Both are properties of moving things. Difference between momentum and kinetic energy Momentum is a vector quantity; therefore it is directional and can be cancelled. Kinetic energy is a scalar quantity and can never be cancelled.

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**Kinetic Energy and Momentum Compared**

velocity dependence Momentum depends on velocity. Kinetic energy depends on the square of velocity. example: An object moving with twice the velocity of another with the same mass, has twice the momentum but four times the kinetic energy.

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Power Power measure of how fast work is done in equation form:

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Power example: A worker uses more power running up the stairs than climbing the same stairs slowly. Twice the power of an engine can do twice the work of one engine in the same amount of time, or twice the work of one engine in half the time or at a rate at which energy is changed from one form to another.

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Power Unit of power joule per second, called the watt after James Watt, developer of the steam engine 1 joule/second = 1 watt 1 kilowatt = 1000 watts

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**Power CHECK YOUR NEIGHBOR**

A job can be done slowly or quickly. Both may require the same amount of work, but different amounts of ________________. A. energy momentum power impulse C. power.

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**Power CHECK YOUR ANSWER**

A job can be done slowly or quickly. Both may require the same amount of work, but different amounts of ________________. A. energy momentum power impulse Comment: Power is the rate at which work is done. C. power.

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Machines Machine device for multiplying forces or changing the direction of forces cannot create energy but can transform energy from one form to another, or transfer energy from one location to another cannot multiply work or energy

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**Machines Principle of a machine conservation of energy concept:**

work input = work output input force input distance = output force output distance (force distance)input = (force distance)output

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**Machines Simplest machine lever**

rotates on a point of support called the fulcrum allows small force over a large distance and large force over a short distance

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Machines pulley operates like a lever with equal arms— changes the direction of the input force example: This pulley arrangement can allow a load to be lifted with half the input force.

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**Machines operates as a system of pulleys (block and tackle)**

multiplies force

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**Machines CHECK YOUR NEIGHBOR**

In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises ________________. A. 50 centimeters 45 centimeters 25 centimeters none of the above C. 25 centimeters.

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**Machines CHECK YOUR ANSWER**

In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises ________________. A. 50 centimeters 45 centimeters 25 centimeters none of the above Explanation: Work in = work out; Fd in = Fd out. One-fourth of 1 m = 25 cm. C. 25 centimeters.

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**Efficiency Efficiency**

percentage of work put into a machine that is converted into useful work output in equation form:

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**Efficiency CHECK YOUR NEIGHBOR**

A certain machine is 30% efficient. This means the machine will convert ________________. A. 30% of the energy input to useful work—70% of the energy input will be wasted 70% of the energy input to useful work—30% of the energy input will be wasted both of the above none of the above A. 30% of the energy input to useful work—70% of the energy input will be wasted.

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**Efficiency CHECK YOUR ANSWER**

A certain machine is 30% efficient. This means the machine will convert ________________. A. 30% of the energy input to useful work—70% of the energy input will be wasted 70% of the energy input to useful work—30% of the energy input will be wasted both of the above none of the above A. 30% of the energy input to useful work—70% of the energy input will be wasted.

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**Sources of Energy Sun example:**

Sunlight evaporates water; water falls as rain; rain flows into rivers and into generator turbines, then back to the sea to repeat the cycle. Sunlight can transform into electricity by photovoltaic cells. Wind power turns generator turbines.

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**Sources of Energy Concentrated energy nuclear power**

stored in uranium and plutonium byproduct is geothermal energy held in underground reservoirs of hot water to provide steam that can drive turbogenerators

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Sources of Energy dry-rock geothermal power is a producer of electricity Water is put into cavities in deep, dry, hot rock. Water turns to steam and reaches a turbine, at the surface. After exiting the turbine, it is returned to the cavity for reuse.

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