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Chapter 6 Energy and Oscillations

Chapter 6 Energy and Oscillations. Energy and Oscillations. A swinging pendant always returns to the same point (almost) after each swing. What is conserved in this motion? . Simple Machines. A simple machine multiplies the effect of an applied force. For example, a lever , and a pulley.

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Chapter 6 Energy and Oscillations

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  1. Chapter 6Energy and Oscillations

  2. Energy and Oscillations A swinging pendant always returns to the same point (almost) after each swing. What is conserved in this motion?

  3. Simple Machines • A simple machine multiplies the effect of an applied force. • For example, a lever , and a pulley. The mechanical advantage of a simple machine is the ratio of the output force to the input force. The price to pay is to move through a larger distance.

  4. Work • Work is equal to the force applied times the distance moved (only force in the parallel direction of motion). • Work = Force x Distance: W = F d units: 1 joule (J) = 1 Nm In Simple Machine, Work output = Work input

  5. Work and Power • Only forces parallel to the motion do work. • Power is the rate of doing work • Power = Work divided by Time: P = W / t units: 1 watt (W) = 1 J / s

  6. Example (Box 6.1) • A crate is pulled a distance of 4 m across the floor under the influence of a 50N force applied by a rope to the crate. What is the work done on the crate by the 50N force if • a) the rope is horizontal, parallel to the floor? • b) the rope pulls at an angle to the floor, so that the horizontal component of the 50N force is 30N?

  7. A string is used to pull a wooden block across the floor without accelerating the block. The string makes an angle to the horizontal. Does the force applied via the string do work on the block? Example If there is a frictional force opposing the motion of the block, does this frictional force do work on the block? What is the work done by the vertical component of the force?

  8. A force of 50 N is used to drag a crate 4 m across a floor. The force is directed at an angle upward from the crate as shown. What is the work done by the horizontal component of the force? Example What is the work done by the vertical component of the force? What is the total work done by the 50-N force?

  9. Kinetic Energy • Kinetic energy is the energy associated with an object’s motion. Doing work on an object can increase its kinetic energy. Work Done =Increase of Energy Starting from rest on a frictionless floor, you move a 100-kg crate by applying a net force of 50N for a time 4s. Find a) what is the acceleration of the crate? b) what is the final speed of the crate? c) how far will the crate go in this time? d) the work done on the crate. e) the final kinetic energy of the crate.

  10. Negative Work • Negative work is the work done by a force acting in a direction opposite to the object’s motion. • For example, a car skidding to a stop. What force is acting to slow the car? Does the force do any work on the car?

  11. Potential Energy • Potential energy is the energy that an object has by virtue of its position or its status related to the motion of the object . It represents stored energy that can be released later. • gravitational potential energy • The work done to raise the object is equal to the gravitational potential energy that the object gains.

  12. Potential Energy • The term potential energy implies storing energy to be released later. • For example, the gravitational potential energy of the crate can be converted to kinetic energy. • There are other types of potential energy, such as the elastic potential energy (energy stored in springs) and chemical potential energy, etc.

  13. Work is done on a large crate to tilt the crate so that it is balanced on one edge, rather than sitting squarely on the floor as it was at first. Has the potential energy of the crate increased? Example

  14. Conservative forces: Forces such as gravity and elastic force. The work done against conservative forces will increase the system’s potential energy that can be completely recovered later. • Gravity and elastic forces are conservative. • Friction is not conservative.

  15. Energy Conversion Energy can change from one form to another. Examples: Kinetic energy to gravitational potential energy Gravitational energy to kinetic energy Kinetic energy to elastic energy (example: pole vaulter) Kinetic energy to heat

  16. Conservation of Energy • Conservation of energy In energy conversion, the total energy of all forms (the kinetic plus potential energies) of a system remains constant if no work is done to the system.

  17. Example

  18. Example E. 12. At the low point in its swing, a pendulum bob with a mass of 2.0kg has a velocity of 5m/s. a. What is its kinetic energy at the low point? b. Ignore air resistance, how high will the bob swing above the low point before reversing direction?

  19. Example • Work done in pulling a sled up a hill produces an increase in potential energyof the sled and rider. • This initial energy is converted to kinetic energyas they slide down the hill. • In any of the point, the total energy (PE+KE if other energy is ignored) is a constant.

  20. Example • E. 14. A sled and rider with a combined mass of 50kg are at the top of a hill a height of 15 m above the level ground below. The sled is given a push providing an initial kinetic energy at the top of the hill of 1600J. •  Choosing a reference level at the bottom of the hill, what is the potential energy of the sled and the rider at the top of the hill? • After the push, what is the total mechanical energy of the sled and the rider at the top of the hill? • If the friction can be ignored, what will be the kinetic energy of the sled and rider at the bottom of the hill?

  21. Any work done by frictional forces isnegative. • That work removesmechanical energy from the system.

  22. A sled and rider with a total mass of 40 kg are perched at the top of the hill shown. Suppose that 2000 J of work is done against friction as the sled travels from the top (at 40 m) to the second hump (at 30 m). Will the sled make it to the top of the second hump if no kinetic energy is given to the sled at the start of its motion? Example

  23. Springs and Simple Harmonic Motion • Simple harmonic motion occurs when the energy of a system repeatedly changes from potential energy to kinetic energy and vise versa. Energy added by doing work to stretch the spring is transformed back and forth between potential energy and kinetic energy.

  24. The horizontal position x of the mass on the spring is plotted against time as the mass moves back and forth. • The period T is the time taken for one complete cycle. • The frequency f is the number of cycles per unit time. • The amplitude is the maximum distance from equilibrium.

  25. A restoring force is a force that exerts a push or a pull back towards equilibrium. • A restoring force that increases in direct proportion to the distance from equilibrium results in simple harmonic motion.

  26. U.S. Energy and Future US Energy Flow Trend (2002) Unit: Quadrillion BTUs (quads)

  27. Renewable Energy and Energy Efficiency • Fossil Fuels • Oil, coal, natural gas • Renewable Energy Sources • Solar energy, wind

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