Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 7 Work and Kinetic Energy

Dr. Jie Zou PHY 1151G Department of Physics2 Outline Work Done by a Constant Force Case 1: Work done when the force is in the direction of the displacement Case 2: Work done when the force is at an angle to the displacement Negative Work Finding Total Work Various Examples

Dr. Jie Zou PHY 1151G Department of Physics3 Work Done by a Force in the Direction of the Displacement Definition of work when force is in the direction of displacement: W = Fd. SI units for work: newton-meter (N  m) = joule (J) The work W is zero if the distance d is zero, regardless of how great the force might be.

Dr. Jie Zou PHY 1151G Department of Physics4 An Example An intern pushes a 72-kg patient on a 15-kg gurney, producing an acceleration of 0.60 m/s 2. How much work does the intern do by pushing the patient and gurney through a distance of 2.5 m? Assume the gurney moves without friction.

Dr. Jie Zou PHY 1151G Department of Physics5 Work Done by a Force at an Angle to the Displacement Definition of work when the angle between the force and displacement is  : W = (F cos  )d = Fd cos . When  = 0 , force is in the same direction as the displacement and W = Fd cos 0  = Fd. When  = 90 , where force and displacement are at right angles to each other, W = Fd cos 90  = 0.

Dr. Jie Zou PHY 1151G Department of Physics6 An Example A 75.0-kg person slides a distance of 5.00 m on a straight water slide, dropping through a vertical height of 2.50 m. How much work does gravity do on the person?

Dr. Jie Zou PHY 1151G Department of Physics7 Negative Work Whenever we calculate work we must be careful about its sign, and not just assume it to be positive.

Dr. Jie Zou PHY 1151G Department of Physics8 Finding Total Work Method 1: If force F 1 does work W 1, force F 2 does work W 2, and so on, the total work is: W total = W 1 + W 2 +… =  W i. Method 2: The total work can also be calculated by first performing a vector sum of all the forces acting on an object to find the resultant (total or net) force  F and then using the basic definition of work: W total = (  F)d cos . Here  is the angle between the total force  F and the displacement d.

Dr. Jie Zou PHY 1151G Department of Physics9 An Example A car of mass m coasts down a hill inclined at an angle  below the horizontal. The car is acted on by three forces: (i) the normal force exerted by the road, (ii) a force due to air resistance, and (iii) the force of gravity. Find the total work done on the car as it travels a distance d along the road.

Dr. Jie Zou PHY 1151G Department of Physics10 Homework See online homework assignment at