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Work & Energy

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**Introductory Physics – Kinematics and Mechanics**

Distance and displacement Speed and Velocity Acceleration Kinematic formulas Forces – Contact and Non-contact Newton’s laws of motion Gravity and Friction

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Forces Do Work x Here, the force is exerted on the car to get it to move from rest. In physics, we say that the force F did work on the car.

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**Kinetic Frictional Force Does Work**

x Here, the frictional force was exerted on the sled to slow it to a stop. In physics, we say that the frictional force did work on the sled.

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**Work Done by a Constant Force**

Definition: Work Done by a Constant Force The work done on an object by a constant force F is where F is the magnitude of the force, x is the magnitude of the displacement, and is the angle between the force and the displacement. The SI Unit for work is newton · meter = joule (J).

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Accelerating a Crate The truck is accelerating at a rate of m/s2. The mass of the crate is 120-kg and it does not slip. The magnitude of the displacement is 65 m. What is the total work done on the crate by all of the forces acting on it?

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**The angle between the displacement and the normal force is 90 degrees.**

The angle between the displacement and the weight is also 90 degrees.

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**The angle between the displacement**

and the friction force is 0 degrees.

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**Find the work done if the force is 45.0-N, the angle is 50.0 **

x x Find the work done if the force is 45.0-N, the angle is 50.0 degrees, and the displacement is 75.0 m.

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**If you do some work, you expect to get something for it.**

Right! In physics, when a net force does some work on an object, the result is a change in the kinetic energy of the object.

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Kinetic Energy Definition: Kinetic Energy The kinetic energy of an object with mass m and speed v is The SI Unit for Kinetic Energy is joule (J).

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Work – Energy Theorem When a net external force does work W on an object, the kinetic energy of the object changes from its initial value of KE0 to a final value KEF, the difference between the two values is equal to the work:

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x Find the distance x the sled slides, if the magnitude of the kinetic frictional force is 35 N and the combined mass of the sled and rider is 70.0 kg.

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**Using Energy - Example Accelerating a Car**

A car is waiting for a traffic light to change. How much energy do you need to accelerate the 1500-kg car from 0 to 22 m/s? Gasoline Used? Each liter of gas has an energy equivalent of 3.3 107 J.

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**Using Energy Accelerating a Car**

A certain amount of energy is used to accelerate a car from 0 m/s to a speed v. How much more energy is required to accelerate from v to 2v?

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**Gravitational Potential Energy**

The work done by the force of gravity on an object is: This is equal to the gravitational potential energy PE that an object has by virtue of its position relative to the surface of the earth. That position is measured by the height h of the object relative to an arbitrary zero level. PE = mgh

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**A dam blocks the passage of a river and generates electricity**

A dam blocks the passage of a river and generates electricity. Approximately, kg of water fall each second through a height of 19 m. How much potential energy is converted to kinetic energy each second?

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**Conservation of Mechanical Energy**

Principle of Conservation of Mechanical Energy The total mechanical energy E = KE + PE of an object remains constant as the object moves, provided that the net work done by non-conservative forces is zero. Conservative Forces Gravitational Force Elastic Spring Force Electric Force Non-Conservative Forces Friction Normal Force Propulsion Force of a Rocket or a Motor

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**Conservation of Mechanical Energy**

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**Conservation of Mechanical Energy - Example**

Daredevil Jumping A motorcyclist attempts to leap a canyon by driving horizontally off a cliff. When it leaves the cliff, the cycle has a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle hits the ground on the other side.

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**Conservation of Mechanical Energy - Example**

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A quarter is dropped from rest from the fifth floor of a very tall building. The speed of the quarter is v just before striking the ground. From what floor would the quarter have to be dropped from rest for the speed just before striking the ground to be approximately 2v? Ignore all air resistance effects to determine your answer. For fall from 5th story…

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**For 2vf multiply both side by 2 and find the new initial height.**

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**Principle of Conservation of Energy**

Energy can neither be created nor destroyed, but can only be converted from one form to another. Forms of Energy: Chemical – Nuclear – Radiant – Thermal – Sound – Electrical - Mechanical

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Fuels store energy. Each liter of gas has an energy equivalent of 3.3 107 J. This is equivalent to… one Burger King value meal is J. So, 6 such meals equals one liter of gasoline. one kilogram of coal a 100 W computer monitor on for 90 hours

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Food Calories Usually, the energy content of food is expressed in Calories. The energy stored in food is a form of chemical energy that is released as we digest it. One Calorie = 1000 calories = 4186 J. 1 cup of lettuce = 10 Calories = J 1 cup of carrots = 45 Calories = J 12 ounce light beer = 95 Calories = J plain baked potato = 145 Calories = J piece of apple pie = 405 Calories = 1.7 million J 1 cup of rice = 670 Calories = 2.8 million J double cheeseburger = 1050 Calories = 4.4 million J

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**Food Calories One Million Joules**

Suppose a 65-kg hiker eats a 250 C snack. So the snack contains… One Million Joules If this were all (100 %) converted into potential energy mg(hF h0), we can find the equivalent change in height.

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Efficiency Not all of the energy is converted to usable work, some goes to other things such as producing an increase in body temperature. A more realistic estimate would be that 25% of the food calories would be used up in climbing, the rest goes to other things. The net result of all of this is that the climber could only climb a quarter of the way, about 400 m on that 250-Calorie snack. Similarly, in a moving car the chemical energy of the gasoline is converted into kinetic energy, electrical energy, and heat.

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Power Average Power Average power Pave is the average rate of work W is done; and it’s obtained by dividing W by the time required to perform the work: The SI unit for power is: joule/s = watt (W)

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**Power P = E / t = ½ mgh / t = ½ (57 000 kg)(9.8 m/s2)(19 m) / (1 s)**

A dam blocks the passage of a river and generates electricity. Approximately, kg of water fall each second through a height of 19 m. If one half of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated? P = E / t = ½ mgh / t = ½ ( kg)(9.8 m/s2)(19 m) / (1 s) = 5.3 x 106 J / s = 5300 kW kilowatt - hour One kilowatt-hour is the amount of work or energy generated when one kilowatt of power is supplied for a time of one hour.

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Power A television is rated at 150 watts. (a) What is the cost of operating the TV for 5 hours if the utility charges $0.11 per kilowatt-hour? (b) How many joules of energy are purchased? (a) E = Pt = (150 W)(5 h) = 750 W-h = 0.75 kW-h Cost = (0.75 kW-h)($0.11/kW-h) = $0.08 (b)

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**Power Clock radio = 10 W Hair dryer = 1200 – 1875 W**

Coffee maker = 900 – 1200 W Microwave oven = 750 – 1100 W Clothes washer = 350 – 500 W Laptop = 50 – 100 W Clothes dryer = 1800 – 5000 W Dishwasher = 1200 – 2400 W (using the drying feature greatly increases energy consumption) Fans Heater (portable) = 750 – 1500 Ceiling = 65–175 W Clothes iron = W Window = 55–250 W Toaster = 800 – 1400 W Furnace = 750 W VCR/DVD = 17–21 / 20–25 W Whole house = 240 – 750 Refrigerator (frost-free, 16 cubic feet) = 725 W Televisions (color) Water heater = 4500 – 5500 W 19" = 65 – 110 W 27" = 113 W 36" = 133 W 53“ - 61" Projection = 170 W Flat screen = 120 W

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Work Done by a Constant Force Work is done when a force F pushes a car through a displacement s. Work = Force X Distance. Work is a scalar. Unit: N.m =

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