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Chapter 7

Chapter 7 . Work and Energy. Introduction. Work, power, and energy – common terms used to describe changes in physical activity We will look at how scientists and engineers use work, power, and energy See how they are related See how they differ from everyday meanings. Objectives.

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Chapter 7

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  1. Chapter 7 Work and Energy

  2. Introduction • Work, power, and energy – common terms used to describe changes in physical activity • We will look at how scientists and engineers use work, power, and energy • See how they are related • See how they differ from everyday meanings

  3. Objectives • Distinguish common and technical definitions of work • Analyze how power is used and described in technical applications • Relate kinetic and potential energy to the law of conservation of mechanical energy

  4. Work: Common Definition • Common work: associated with physical or mental effort that leads to fatigue • Technical definition is not nearly as broad • Example: if you try to lift a heavy crate that will not budge, you would say that you have done work because you strained your muscles and are tired, but in the technical sense, no work was done because object did not move

  5. Work: Technical Definition • Example: if you move a crate across the floor, work would be done by you on the crate • Technical work requires work to be done by one object on another object • Ex: bulldozer pushing a boulder – work done by bulldozer on boulder • Limited meaning of work: work is done when a force acts through a distance

  6. Physical Definition of Work • Work is the product of the force in the direction of the motion and the displacement W = Fs W = work F = force applied in direction of motion s = displacement

  7. Work when trying to lift crate • Previous example when trying to lift, but unsuccessful • Couldn’t budge, so displacement = 0 • Therefore, the Force x displacement would also equal 0 • So, the work = 0 • No work was performed

  8. Units of Work • Metric W = Fs = Newton x meter = N m = Joule Abbreviated J Named after James P. Joule: English physicist who showed that heat is a form of energy • English W = Fs = pounds x feet = ft lb • Scalar quantity (has only magnitude) • No direction = not a vector

  9. Example • Find the amount of work done by a worker lifting 225 N of bricks to a height of 1.75 m. F = 225 N s = 1.75 m W = ? W = Fs = (225 N) (1.75 m) = 394 N m or 394 J

  10. Another Example • A worker pushes a 350 lb crate a distance of 30 ft by exerting a constant force of 40 lb. How much work does the person do? • W = Fs = (40 lb) (30 ft) = 1200 ft lb • Do not use weight of cart: use force in direction of motion (weight of cart force acts perpendicular to motion)

  11. Example: force is at an angle • A block is being pulled by a rope with a force 215 N that makes an angle of 30° with the level ground. Find the amount of work done. • Can only use force in direction of motion (horizontal force = Fx) W = Fs cos θ = (215 N) (15 m) cos 30° = 2790 J θ = angle between applied force and direction of motion

  12. Power: the rate of doing work P = W/t P = power W = Work t = time Units Metric: J/s = Watt (W) English: ft∙lb/s or horsepower(hp) 1 hp = 550 ft∙lb/s = 33000 ft∙lb/min

  13. Example • A freight elevator with operator weighs 5000 N. If it is raised to a height of 15.0 m in 10.0 s, how much power is developed? F = 5000 N s = 15.0 m t = 10.0 s P = W/t = Fs/t = (5000 N)(15.0 m)/(10.0 s) P = 7500 N∙m/s = 7500 W

  14. Example 2 • A pump is needed to lift 1500 L of water per minute a distance of 45.0 m. What power, in kW, must the pump be able to deliver (1 L H2O = 1 kg) Mass H2O = 1500 L x 1 kg/1 L = 1500 kg F = mg = (1500 kg)(9.8 m/s2) = 14700 N P = W/t = Fs/t = (14700 N)(45 m)/60 s P = 11000 W x 1 kW/1000 W = 11.0 kW

  15. Energy • Defined as the ability to do work • Different forms: mechanical, electrical, thermal, fluid, chemical, atomic, sound • Mechanical energy due to position, motion, or internal structure • Two types of mechanical energy • Potential: stored energy due to internal characteristics or position • Kinetic: due to mass and velocity of moving object

  16. Potential Energy • Internal potential energy: determined by the nature or condition of the substance • Ex: gasoline, compressed spring, stretched rubber band • Gravitational potential energy: determined by the position of the object relative to a particular reference level (based on pull of gravity)

  17. Potential Energy (PE) Formula • PE = mgh m = mass g = 9.80 m/s2 or 32.2 ft/s2 h = height above reference level • Units • Metric system: Joule (J) • English system: foot-pound (ft-lb)

  18. Example • A wrecking ball of mass 200 kg is poised 4.00 m above a concrete platform whose top is 2.00 m above the ground. • What is potential energy with respect to the platform? PE = mgh = (200 kg)(9.8 m/s2)(4.00 m) PE = 7840 J • What is potential energy with respect to the ground? PE = mgh = (200 kg)(9.8 m/s2)(6.00 m) PE = 11800 J

  19. Kinetic Energy (KE) • Kinetic energy is due to the mass and velocity of a moving object • Formula: KE = ½mv2 m = mass v = velocity • For pile driver: • ½mv2 = Fs

  20. Pile Driver Example • A pile driver with mass 10000 kg strikes a pile with a velocity of 10.0 m/s • What is the kinetic energy of the driver as it strikes the pile? KE = ½mv2 = ½(10000 kg)(10.0 m/s)2 KE = 500000 J or 500 kJ • If the pile is driven 20.0 cm into the ground, what force is applied to the driver as it strikes the pile? (Assume all KE is converted to work) KE = W = Fs → F = KE/s = 500000 J/0.20 m F = 2500000 N

  21. Kinetic Energy Example • A 60.0 g bullet is fired from a gun with 3150 J of kinetic energy. Find its velocity. KE = ½mv2 rearrange to: v = 2(KE) √ m v = 2(3150 J) = 324 m/s √ 0.0600 kg

  22. Conservation of Mechanical Energy • Relates kinetic and potential energy • The sum of the kinetic energy and potential energy in a system is constant if no resistant forces do work • Example: pendulum • Lift and hold before releasing (PE = maximum, KE = 0 no movement) • Release (at bottom PE =0, KE = max) • Between top and bottom KE + PE = constant • Bob would swing forever if not for friction

  23. Example: Roller coaster

  24. Energy in collisions • In an elastic collision, the total kinetic energy in the system before the collision equals the total kinetic energy in the system after the collision .

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