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Energy and Systems

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Unit 3: Energy and Systems Chapter 7: Machines, Work, and Energy 7.1 Work, Energy and Power 7.2 Simple Machines 7.3 Efficiency

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7.1 Investigation: Force, Work, and Machines Key Question: How do simple machines affect work? Objectives: Build a simple machine that multiplies force. Measure and compare input and output forces and distances for different pulley setups. Calculate and compare work input and work output.

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Work Doing work always means transferring energy. The energy may be transferred to the object to which you apply the force, or it may go elsewhere. The work you do in stretching a rubber band is stored as potential energy by the rubber band. The rubber band can then use the energy to do work on a paper airplane by giving it kinetic energy.

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Doing work To do the greatest amount of work, you must apply force in the same direction the object will move. If forces A, B, and C have equal strengths, force C will do the most work because it is entirely in the direction of the motion.

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Work done against gravity Many situations involve work done by or against the force of gravity. It does not matter whether you lift an object straight up or you carry it up the stairs. The total work done against gravity is the same no matter what path you take.

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Work done against gravity W = mgh height object raised (m) gravity (m/sec 2 ) work (joules) mass (g)

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Alexander has a mass of 70 kilograms. His apartment is on the second floor, 5 meters up from ground level. How much work does he do against gravity each time he climbs the stairs to his apartment? Calculating work Looking for: …work. Given: … mass (70 kg) and height (5 m). You know that g = 9.8 m/s 2. Relationships: Use: F g = mg and W = Fd Solution: The force is equal to Alexander’s weight. F g = (70 kg)(9.8 m/s 2 ) F g = 686 N Use the force to calculate the work. W = Fd W = (686 N)(5 m) W = 3,430 J

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Work Energy Theorem The work-energy theorem says that the work done by a system equals the change in kinetic energy of that system. To understand how work and kinetic energy are related, let’s suppose a ball of mass (m) is at rest. A force (F) is applied and creates an acceleration (a). After moving a distance (d), the ball has reached a speed (v).

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Work Energy Theorem The work done on the ball is its mass times acceleration times distance. When an object starts from rest, you can relate distance traveled, acceleration, and time using the formula that includes all three.

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Work Energy Theorem Using this relationship, you can replace distance in the equation for work and combine similar terms. Mathematically, v = at, therefore v 2 = a 2 t 2.

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A car with a mass of 1,000 kg is going straight ahead at a speed of 10 m/s. The brakes can supply a force of 10,000 N. Calculate: a) the kinetic energy of the car. b) the distance it takes to stop. Calculating kinetic energy Looking for: … kinetic energy and distance to stop the car. Given: … mass (1,000 kg), speed (10 m/s) and force (10,000 N). Relationships: Use equations: E k = mv 2 and W = Fd Solution: E k = (1,000 kg)(10 m/s) 2 = 50,000 J To stop the car, work done by the brakes reduces the E k to zero. 50,000 J = (10,000 N) × d d = 5 meters

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Power The rate at which work is done is called power. It makes a difference how fast you do work. The unit for power is equal to the unit of work (joules) divided by the unit of time (seconds).

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Power Michael and Jim do the same amount of work. Michael’s power is greater because he gets the work done in less time. To find Michael’s power, divide his work (200 J) by his time (1 s).

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Power James Watt, a Scottish engineer, invented the steam engine. James Watt explained power as the number of horses his engine could replace. One horsepower still equals 746 watts.

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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 20s to pull the roller coaster up a 50 m hill, what is the power produced by the motor? Calculating power Looking for: … power of the motor. Given: … mass (10,000 kg), time (20 s), and height (50 m). Relationships: Use: F g = mg W = Fd P = W/t Solution: Calculate the weight of the roller coaster: F g = (10,000 kg)(9.8 m/s 2 ) = 98,000 N Calculate the work: W = (98,000 N)(50 m) = 4,900,000 J or 4.9 × 10 6 J Calculate the power: P = (4.9 × 10 6 J) (20 s) = 245,000 W or 2.45 × 10 5 W

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Unit 3: Energy and Systems Chapter 7: Machines, Work, and Energy 7.1 Work, Energy and Power 7.2 Simple Machines 7.3 Efficiency

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7.2 Investigation: Work and Energy Key Question: How does a system get energy? Objectives: Use force and distance data gathered during experiments to create graphs; and, then analyzethe data and graphs to calculate work. Derive the formula for the speed of a car from force and mass data. Analyze data to determine the relationship between the work done by a force and the energy of a body.

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Using Machines A machine is a device with moving parts that work together to accomplish a task. A bicycle is a good example.

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Using Machines The input includes everything you do to make the machine accomplish a task, like pushing on the bicycle pedals. The output is what the machine does for you, like going fast or climbing a steep hill.

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Forces in Machines A simple machine is an unpowered mechanical device, such as a lever.

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Mechanical advantage Machines multiply forces. The mechanical advantage of a machine is the ratio of the output force to the input force. One person could lift an elephant—quite a heavy load—with a properly designed system of ropes and pulleys!

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What is the mechanical advantage of a lever that allows Jorge to lift a 24-newton box with a force of 4 newtons? Calculating mechanical advantage Looking for: … mechanical advantage. Given: … input force (4 N) and the output force (24 N) Relationships: Use: M A = F o ÷ F i Solution: M A = (24 N) ÷ (4 N) M A = 6

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Work and Machines A rope and pulley machine illustrates a rule that is true for all processes that transform energy. The output work done by a simple machine can never exceed the input work done on the machine.

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A jack is used to lift one side of a car in order to replace a tire. To lift the car, the jack handle moves 30 cm for every 1 cm that the car is lifted. If a force of 150 N is applied to the jack handle, what force is applied to the car by the jack? You can assume all of the input work goes into producing output work. Calculating mechanical advantage Looking for: … output force in newtons. Given: … input force (150 N), input distance (30 cm =.03 m) and output distance (1 cm =.01 m) Relationships: Use: Work = Fd and Input work (W i ) = Output work (W o ) Solution: W i = (150 N)(0.30 m) = 45 J = W o W o = 45 J = F × 0.01 m F = 45 J ÷ 0.01 m = 4,500 N

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How a lever works A lever includes a stiff structure (the lever) that rotates around a fixed point called the fulcrum.

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The Lever Levers are useful because you can arrange the fulcrum and the input arm and output arm to adjust the mechanical advantage of the lever.

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Three types of levers The three types of levers are classified by the location of the input and output forces relative to the fulcrum: — first class lever — second class lever — third class lever

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Calculating the position of the fulcrum A lever has a mechanical advantage of 4. Its input arm is 60 cm long. How long is its output arm? Looking for: … length of output arm. Given: … mechanical advantage (4) and input arm length (60 cm) Relationships: Use: M A = L i ÷ L o Solution: 4 = 60 cm ÷ L o L o = 60 cm ÷ 4 = 15 cm

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Tension in ropes and strings Recall that ropes and strings carry tension forces along their length. If the rope is not moving, its tension is equal to the force pulling on each end.

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Rope & Pulleys The block-and-tackle machine is a simple machine using one rope and multiple pulleys. The rope and pulleys can be arranged to create different amounts of mechanical advantage.

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Gears Many machines require that rotating motion be transmitted from one place to another. Gears change force and speed.

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Designing Gear Machines The gear ratio is the ratio of output turns to input turns. You can predict how force and speed are affected when gears turn by knowing the number of teeth for each gear. T o = N i T i N o Number of teeth on input gear Turns of output gear Turns of input gear Number of teeth on input gear

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Ramps A ramp is a simple machine that allows you to raise a heavy object with less force than you would need to lift it straight up.

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Ramps The mechanical advantage of a ramp is the ramp length divided by the height of the ramp.

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Screws A screw is a rotating ramp. You find the mechanical advantage of a screw by dividing its circumference by the lead.

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Unit 3: Energy and Systems Chapter 7: Machines, Work, and Energy 7.1 Work, Energy and Power 7.2 Simple Machines 7.3 Efficiency

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7.3 Investigation: Energy and Efficiency Key Question: How well is energy transformed from one form to another? Objectives: Explain the meaning of efficiency and describe why processes are not 100 percent efficient. Describe the energy conversions involved as the Energy Car travels along the SmartTrack and collides with a rubber band. Explore the effects of changing variables, such as mass and tension, on the efficiency of a process.

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Efficiency Every process that is done by machines can be simplified in terms of work: Work input: the work or energy supplied to the process (or machine). Work output: the work or energy that comes out of the process (or machine).

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Efficiency and Friction Friction is a force that opposes motion. Friction converts energy of motion to heat. It is important to remember that the energy does not disappear. Energy is converted to other forms of energy that are not always useful.

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Efficiency A machine would have an efficiency of 100 % if the work output of the machine is equal to the work input. A machine that is 75 % efficient can produce three joules of output work for every four joules of input work What percentage of the energy is “lost” due to friction?

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Efficiency The efficiency of a machine is the ratio of usable output work divided by total input work. Efficiency is usually expressed in percent. Efficiency = W o W i Output work (J) Input work (J) x 100%

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Efficiency and time The efficiency is less than 100 percent for virtually all processes that convert energy to any other form except heat. Scientists believe this is connected to why time flows forward and not backward.

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Time runs forward Once energy is transformed into heat, the energy cannot ever completely get back into its original form. Because 100 % of the heat energy cannot get back to potential or kinetic energy, any process with less than 100 percent efficiency is irreversible. Irreversible processes can only go forward in time. Since processes in our universe almost always lose a little energy to friction, time cannot run backward.

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Electric Wind In a library textbook called Explaining Physics, fourteen year old William Kamkwamba read that if you spin a coil of wire inside a magnetic field, an electric current is created. An idea began to take shape in William’s mind. If he could build a windmill, he could have light in the evenings!

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