Three things necessary to do Work in Physics: There must be an applied force F. There must be a change in displacement x (velocity). The force must have a component along the displacement (or velocity). F q x
If a force does not affect displacement, it does no work. The force F exerted on the pot by the man does work. F W The earth exerts a force W on pot, but does no work even though there is displacement.
Work = Force component X displacement Definition of Work Work is a scalar quantity equal to the product of the displacement x and the component of the force Fx in the direction of the displacement. Work = Force component X displacement Work = Fx x
Positive Work F x Force F contributes to displacement x. Example: If F = 40 N and x = 4 m, then Work = (40 N)(4 m) = 160 Nm Work = 160 J 1 Nm = 1 Joule (J)
Negative Work x f The friction force f opposes the displacement. Example: If f = -10 N and x = 4 m, then Work = (-10 N)(4 m) = - 40 J Work = - 40 J
Resultant Work or Net Work Resultant work is the algebraic sum of the individual works of each force. F x f Example: F = 40 N, f = -10 N and x = 4 m Work = (40 N)(4 m) + (-10 N)(4 m) Work = 120 J
Work of a Force at an Angle x = 12 m F = 70 N 60o Work = Fx x Work = (F cos ) x Work = (70 N) Cos 600 (12 m) = 420 J Only the x-component of the force does work! Work = 420 J
Work Done by a Varying Force For a force that varies, work done is the area under the force vs. distance curve.
Work and Kinetic Energy A resultant force changes the velocity of an object and does work on that object. m vo vf x F
The Work-Energy Theorem Work is equal to the change in ½mv2 If we define kinetic energy as ½mv2 then we can state a very important physical principle: The Work-Energy Theorem: The work done by a resultant force is equal to the change in kinetic energy that it produces.
Problem Solving Using Conservation of Mechanical Energy If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height. It does not matter on path taken. Because gravity is the only force doing work. Why not normal force? © 2014 Pearson Education, Inc.
Conservative and Nonconservative Forces If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force. © 2014 Pearson Education, Inc.
6-5 Conservative and Nonconservative Forces Potential energy can only be defined for conservative forces. © 2014 Pearson Education, Inc.
Conservative and Nonconservative Forces Therefore, we distinguish between the work done by conservative forces and the work done by nonconservative forces. We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies:
Work Done by a Constant Force The work done by a non conservative force is also equal to the following. In this case energy is being added to the system. © 2014 Pearson Education, Inc.
6-9 Energy Conservation with Dissipative Processes; Solving Problems If there is a nonconservative force such as friction, where do the kinetic and potential energies go? They become heat; the actual temperature rise of the materials involved can be calculated. © 2014 Pearson Education, Inc.
Power Power is the rate at which work is done— In the SI system, the units of power are watts: 1W = 1 J/s The difference between walking and running up these stairs is power— the change in gravitational potential energy is the same. (6-17) © 2014 Pearson Education, Inc.
Power Power is also needed for acceleration and for moving against the force of gravity. The average power can be written in terms of the force and the average velocity: (6-18)