Review of Work and Power Work is done on an object when a force causes a displacement of the object. The object must move because of an applied force for work to be accomplished. Formula for work W = Fd W = work = nm (joule) or kg . m2/s2 F = force (mass x accleration) or kg x m/s2 d= distance (m)

power = work ÷ time interval Chapter 5 Power Power is a quantity that measures the rate at which work is done or energy is transformed. P = W/∆t power = work ÷ time interval Power is measured in watts

Kinetic Energy Kinetic Energy Chapter 5 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.

Kinetic Energy, continued Chapter 5 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 equals change in kinetic energy. Wnet = ∆KE net work = change in kinetic energy

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

Chapter 5 Elastic potential energy is the energy available for use when a deformed elastic object (such as a spring) returns to its original configuration.

Mechanical Energy Chapter 5 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)

Sample Problem Chapter 5 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.

Given: h = hi = 3.00 m m = 25.0 kg vi = 0.0 m/s hf = 0 m Unknown: Chapter 5 1. Define Given: h = hi = 3.00 m m = 25.0 kg vi = 0.0 m/s hf = 0 m Unknown: vf = ?

Chapter 5 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.

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

Therefore, the final kinetic energy is as follows: Chapter 5 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:

Substitute values into the equations: 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

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.

Chapter 5 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.