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Understanding Work and Energy

Learn the definitions of work and energy, how they relate to force and displacement, and how to calculate work and potential energy. Get familiar with kinetic energy and the work-energy theorem.

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Understanding Work and Energy

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  1. Chapter 5 Section 1 Work Preview • Objectives • Definition of Work

  2. Chapter 5 Section 1 Work Objectives • Recognizethe difference between the scientific and ordinary definitions of work. • Definework by relating it to force and displacement. • Identifywhere work is being performed in a variety of situations. • Calculatethe net work done when many forces are applied to an object.

  3. Chapter 5 Section 1 Work Definition of Work • Work is done on an object when a force causes a displacement of the object. • Workis done only when components of a force are parallel to a displacement.

  4. Chapter 5 Section 1 Work Definition of Work

  5. Chapter 5 Section 1 Work Sign Conventions for Work Click below to watch the Visual Concept. Visual Concept

  6. Chapter 5 Section 2 Energy Preview • Objectives • Kinetic Energy • Sample Problem

  7. Chapter 5 Section 2 Energy Objectives • Identifyseveral forms of energy. • Calculatekinetic energy for an object. • Applythe work–kinetic energy theorem to solve problems. • Distinguishbetween kinetic and potential energy. • Classifydifferent types of potential energy. • Calculatethe potential energy associated with an object’s position.

  8. Chapter 5 Section 2 Energy Kinetic Energy • Kinetic Energy The energy of an object that is due to the object’s motion is called kinetic energy. • Kinetic energy depends on speed and mass.

  9. Chapter 5 Section 2 Energy Kinetic Energy Click below to watch the Visual Concept. Visual Concept

  10. Chapter 5 Section 2 Energy Kinetic Energy, continued • Work-Kinetic Energy Theorem • The net work done by all the forces acting on an object is equal to the change in the object’s kinetic energy. • The net work done on a body equals its change in kinetic energy. Wnet= ∆KE net work = change in kinetic energy

  11. Chapter 5 Section 2 Energy Work-Kinetic Energy Theorem Click below to watch the Visual Concept. Visual Concept

  12. Chapter 5 Section 2 Energy Sample Problem Work-Kinetic Energy Theorem On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

  13. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 1. Define Given: m = 10.0 kg vi = 2.2 m/s vf = 0 m/s µk = 0.10 Unknown: d = ?

  14. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 2. Plan Choose an equation or situation: This problem can be solved using the definition of work and the work-kinetic energy theorem. Wnet = Fnetdcosq The net work done on the sled is provided by the force of kinetic friction. Wnet = Fkdcosq = µkmgdcosq

  15. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 2. Plan, continued The force of kinetic friction is in the direction opposite d, q = 180°. Because the sled comes to rest, the final kinetic energy is zero. Wnet = ∆KE = KEf - KEi = –(1/2)mvi2 Use the work-kinetic energy theorem, and solve for d.

  16. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 3. Calculate Substitute values into the equation:

  17. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 4. Evaluate According to Newton’s second law, the acceleration of the sled is about -1 m/s2 and the time it takes the sled to stop is about 2 s. Thus, the distance the sled traveled in the given amount of time should be less than the distance it would have traveled in the absence of friction. 2.5 m < (2.2 m/s)(2 s) = 4.4 m

  18. Chapter 5 Section 2 Energy Potential Energy • Potential Energy is the energy associated with an object because of the position, shape, or condition of the object. • Gravitational potential energy is the potential energy stored in the gravitational fields of interacting bodies. • Gravitational potential energy depends on height from a zero level. PEg= mgh gravitational PE = mass  free-fall acceleration  height

  19. Chapter 5 Section 2 Energy Potential Energy Click below to watch the Visual Concept. Visual Concept

  20. Chapter 5 Section 2 Energy Potential Energy, continued • Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration. • The symbol k is called the spring constant, a parameter that measures the spring’s resistance to being compressed or stretched.

  21. Chapter 5 Section 2 Energy Elastic Potential Energy

  22. Chapter 5 Section 2 Energy Spring Constant Click below to watch the Visual Concept. Visual Concept

  23. Chapter 5 Section 2 Energy Sample Problem Potential Energy A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?

  24. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 1. Define Given:m = 70.0 kg k = 71.8 N/m g = 9.81 m/s2 h = 50.0 m – 44.0 m = 6.0 m x = 44.0 m – 15.0 m = 29.0 m PE = 0 J at river level Unknown:PEtot= ?

  25. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 2. Plan Choose an equation or situation: The zero level for gravitational potential energy is chosen to be at the surface of the water. The total potential energy is the sum of the gravitational and elastic potential energy.

  26. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 3. Calculate Substitute the values into the equations and solve:

  27. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 4. Evaluate One way to evaluate the answer is to make an order-of-magnitude estimate. The gravitational potential energy is on the order of 102 kg  10 m/s2 10 m = 104 J. The elastic potential energy is on the order of 1  102 N/m  102 m2 = 104 J. Thus, the total potential energy should be on the order of 2  104 J. This number is close to the actual answer.

  28. Section 3 Conservation of Energy Chapter 5 Preview • Objectives • Conserved Quantities • Mechanical Energy • Sample Problem

  29. Section 3 Conservation of Energy Chapter 5 Objectives • Identifysituations in which conservation of mechanical energy is valid. • Recognizethe forms that conserved energy can take. • Solveproblems using conservation of mechanical energy.

  30. Section 3 Conservation ofEnergy Chapter 5 Conserved Quantities • When we say that something isconserved,we mean that it remains constant.

  31. Section 3 Conservation ofEnergy Chapter 5 Mechanical Energy • Mechanical energyis the sum of kinetic energy and all forms of potential energy associated with an object or group of objects. ME = KE + ∑PE • Mechanical energy is often conserved. MEi = MEf initial mechanical energy = final mechanical energy (in the absence of friction)

  32. Section 3 Conservation of Energy Chapter 5 Conservation of Mechanical Energy Click below to watch the Visual Concept. Visual Concept

  33. Section 3 Conservation ofEnergy Chapter 5 Sample Problem Conservation of Mechanical Energy Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg.

  34. Section 3 Conservation ofEnergy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 1. Define Given: h = hi = 3.00 m m = 25.0 kg vi = 0.0 m/s hf = 0 m Unknown: vf = ?

  35. Section 3 Conservation ofEnergy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 2. Plan Choose an equation or situation: The slide is frictionless, so mechanical energy is conserved. Kinetic energy and gravitational potential energy are the only forms of energy present.

  36. Section 3 Conservation ofEnergy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 2. Plan, continued The zero level chosen for gravitational potential energy is the bottom of the slide. Because the child ends at the zero level, the final gravitational potential energy is zero. PEg,f = 0

  37. Section 3 Conservation ofEnergy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 2. Plan, continued The initial gravitational potential energy at the top of the slide is PEg,i = mghi = mgh Because the child starts at rest, the initial kinetic energy at the top is zero. KEi = 0 Therefore, the final kinetic energy is as follows:

  38. Section 3 Conservation ofEnergy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 3. Calculate Substitute values into the equations: PEg,i = (25.0 kg)(9.81 m/s2)(3.00 m) = 736 J KEf = (1/2)(25.0 kg)vf2 Now use the calculated quantities to evaluate the final velocity. MEi = MEf PEi + KEi = PEf + KEf 736 J + 0 J = 0 J + (0.500)(25.0 kg)vf2 vf = 7.67 m/s

  39. Section 3 Conservation ofEnergy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 4. Evaluate The expression for the square of the final speed can be written as follows: Notice that the masses cancel, so the final speed does not depend on the mass of the child. This result makes sense because the acceleration of an object due to gravity does not depend on the mass of the object.

  40. Section 3 Conservation ofEnergy Chapter 5 Mechanical Energy, continued • Mechanical Energy is not conserved in the presence of friction. • As a sanding block slides on a piece of wood, energy (in the form of heat) is dissipated into the block and surface.

  41. Chapter 5 Section 4 Power Preview • Objectives • Rate of Energy Transfer

  42. Chapter 5 Section 4 Power Objectives • Relatethe concepts of energy, time, and power. • Calculatepower in two different ways. • Explainthe effect of machines on work and power.

  43. Chapter 5 Section 4 Power Rate of Energy Transfer • Poweris a quantity that measures the rate at which work is done or energy is transformed. P = W/∆t power = work ÷ time interval • An alternate equation for power in terms of force and speed is P = Fv power = force  speed

  44. Chapter 5 Section 4 Power Power Click below to watch the Visual Concept. Visual Concept

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