Measures of Effort & Motion; Conservation Laws 4/23/2008 Work, Energy, Power Measures of Effort & Motion; Conservation Laws Lecture 9 https://www.youtube.com/watch?v=k60jGJfV8oU

What is Work? Pushing a car? Picking up a weight? Holding a weight up? 11/23/2017

What is Work? You do work on an object when you move it. The rate at which you do work is your power output. When you do work on an object, you transfer energy from one object to another.

Work Done by a Constant Force The definition of work, when the force is parallel to the displacement:

Work work = force  displacement W = F · d 4/23/2008 Work work = force  displacement W = F · d Work can be done by you, as well as on you Work is a measure of expended energy Lecture 9

Work = Fx x dx = F x cosθ x d A m/s^2 B kg * m^2 / s^2 C N * m/s^2 Units of Work Work = Fx x dx = F x cosθ x d What are the SI units for Work? A m/s^2 B kg * m^2 / s^2 C N * m/s^2

Work = Fx x dx = F x cosθ x d A m/s^2 B kg * m^2 / s^2 C N * m/s^2 Units of Work Work = Fx x dx = F x cosθ x d What are the SI units for Work? A m/s^2 B kg * m^2 / s^2 C N * m/s^2

Work is measured in Joules Joules are the unit of energy One joule of work is done when a force of 1 N acts on a system over a displacement of 1m

W = F•D What is the work if: The force on the box is 10 Newtons The distance pushed is 5 meters

W = F•D What is the work if: The force on the box is 10 Newtons The distance pushed is 5 meters W = Fx x dx W = 10 x 5 = 50 J

How Much Work is Done? A friend’s car is stuck on the ice. You push down on the car to provide more friction for the tires (Ff = FN) allowing the car’s tires to propel it forward 5 meters onto less slippery ground. How much work did you do? 11/23/2017

Work Done? A friend’s car is stuck on the ice. You push down on the car to provide more friction for the tires (Ff = FN) allowing the car’s tires to propel it forward 5 meters onto less slippery ground. How much work did you do? W = F x cosθ x d W = F (cos 90°) d W = F (0) d W = 0 J 11/23/2017

Negative, Positive, Zero Work

What is the work if: The force on the box is 8 Newtons The distance pushed is 2 meters The angle is 30 degrees

Only the force in the direction of the displacement “counts” Only a component of the force is doing work W = Fx x dx = F x cosθ x d

Work = F x cos x d W = Fx x dx = F x cosθ x d What is the work if: The force on the box is 8 Newtons; the distance pushed is 2 meters; The angle is 30 degrees W = 8 x cos(30) x 2 = 13.86 J

https://www.youtube.com/watch?v=azbpj0pwl0k 11/23/2017

Machines can make work easy (ramps, levers) 4/23/2008 Work Machines can make work easy (ramps, levers) Apply less force over larger distance for same work Lecture 9

Working at an advantage 4/23/2008 Working at an advantage Work = Force  Distance Work = Force  Distance Lecture 9

Ramps Larger Force Small Force Short Distance Long Distance M 4/23/2008 Ramps Larger Force Small Force Short Distance Long Distance M Lecture 9

Whiteboard Team Challenge Grab a whiteboard and get ready to play… “You better work!” 11/23/2017

1) To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no

1) To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.

2) Friction and Work I A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1) friction does no work at all 2) friction does negative work 3) friction does positive work

2) Friction and Work I A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1) friction does no work at all 2) friction does negative work 3) friction does positive work Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work: W = F d cos q since  = 180o, then W < 0. f N mg displacement Pull

3) Friction and Work II Can friction ever do positive work? 1) yes 2) no

3) Friction and Work II Can friction ever do positive work? 1) yes 2) no Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move.

4) Play Ball! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work

4) Play Ball! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos q ), since  = 180o, then W < 0. Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher?

5) Tension and Work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? 1) tension does no work at all 2) tension does negative work 3) tension does positive work

5) Tension and Work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? 1) tension does no work at all 2) tension does negative work 3) tension does positive work No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work: W = F d cos q since  = 90o, then W = 0. v T Follow-up: Is there a force in the direction of the velocity?