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

Section 1 Work Chapter 5 Definition of Work

Sign Conventions for Work Section 1 Work Chapter 5 Sign Conventions for Work

Chapter 5 Kinetic Energy Section 2 Energy Chapter 5 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.

Section 2 Energy Chapter 5 Kinetic Energy

net work = change in kinetic energy Section 2 Energy Chapter 5 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

Work-Kinetic Energy Theorem Section 2 Energy Chapter 5 Work-Kinetic Energy Theorem

Chapter 5 Work-Kinetic Energy Theorem Section 2 Energy Chapter 5 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?

Chapter 5 Work-Kinetic Energy Theorem 1. Define Given: m = 10.0 kg Section 2 Energy Chapter 5 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 = ?

gravitational PE = mass  free-fall acceleration  height Section 2 Energy Chapter 5 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

Section 2 Energy Chapter 5 Potential Energy

Section 2 Energy Chapter 5 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.

Elastic Potential Energy Section 2 Energy Chapter 5 Elastic Potential Energy

Section 2 Energy Chapter 5 Spring Constant

Chapter 5 Sample Problem Potential Energy Section 2 Energy Chapter 5 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?

Sample Problem, continued Section 2 Energy Chapter 5 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 = ?

Sample Problem, continued Section 2 Energy Chapter 5 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.

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

Sample Problem, continued Section 2 Energy Chapter 5 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.

Chapter 5 Conserved Quantities Section 3 Conservation of Energy Chapter 5 Conserved Quantities When we say that something is conserved, we mean that it remains constant.

Chapter 5 Mechanical Energy Section 3 Conservation of Energy Chapter 5 Mechanical Energy Mechanical energy is 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)

Conservation of Mechanical Energy Section 3 Conservation of Energy Chapter 5 Conservation of Mechanical Energy

Chapter 5 Sample Problem Conservation of Mechanical Energy Section 3 Conservation of Energy 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.

Sample Problem, continued Section 3 Conservation of Energy 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 = ?

Sample Problem, continued Section 3 Conservation of Energy 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.

Sample Problem, continued Section 3 Conservation of Energy 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

Sample Problem, continued Section 3 Conservation of Energy 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:

Sample Problem, continued Section 3 Conservation of Energy 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

Sample Problem, continued Section 3 Conservation of Energy 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.

Mechanical Energy, continued Section 3 Conservation of Energy 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.

Chapter 5 Objectives Relate the concepts of energy, time, and power. Section 4 Power Chapter 5 Objectives Relate the concepts of energy, time, and power. Calculate power in two different ways. Explain the effect of machines on work and power.

Rate of Energy Transfer Section 4 Power Chapter 5 Rate of Energy Transfer Power is 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

Section 4 Power Chapter 5 Power