Work and Energy Work Done W Fd Units

Work and Energy • Work Done • W = Fd • Units and Direction • Positive and Negative Work • When Work = 0

Work • Work (W) is the energy transferred to an object when a force acting on the object moves it through a distance • W=Fxd o F = the magnitude of force acting on the object parallel to d = the displacement

Work Done • Work is done when you lift an object • Work is done to a bow when you bend it and work is done to the arrow when it’s fired • Work is done to make a car accelerate

Work • Consider a situation where you are pulling a bag on wheels at an angle Θ to the displacement • The force parallel to the displacement = FcosΘ

Work Done – Try It • W = Fd W=? F = 10 cos 30 d = 20 W = 10 cos 30 x 20 m = 173 N m = 1. 7 x 102 N m

Units and Direction • Work is scalar and has no direction • Its units are N m = J • 1 J = 1 kg m 2/s 2 Stop at 3: 42

Positive or Negative Work • If the force and displacement are in the same direction, work is “+”. If F and d are in opposite directions, work is “-” • Work is positive, negative, or zero, depending on the angle between the force and the displacement. • d=r • Try an example on your own for each

If velocity is constant, isn’t a = 0 and therefore, F = 0 and W = 0? • Whenever you talk about the work done, you must be very careful to specify which force does the work. • i. e. if the object is moving at a constant v • Wfriction= Ff x d F = 10 N F = 10 cos 180° x 1 = -10 J • Wapp = Fapp x d = 10 cos 0° x 1 = 10 J x = +1 m • Wnet = Fnet x d =0 x 1=0 J friction ext The net work is 0 but there is still work being done.

Check Your Understanding An airport terminal employee is pushing a line of carts at a constant velocity with a horizontal force of magnitude 95 N. How much work is done in pushing the carts 16 m in the direction of the applied force? Express the answer in kilojoules. Answers: 1. 5 k. J

Check Your Understanding 2000. 0 N of force is applied to a cable used to tow a car as seen below 20. 0 km. How much work is being done? Your answer should be in megajoules (1, 000 J = 1 MJ). Answer: 25. 7 MJ

Check Your Understanding A store clerk moved a 4. 4 -kg box of soap without acceleration along a shelf by pushing it with a horizontal force of magnitude 8. 1 N. If the employee did 5. 9 J of work on the box, how far did the box move? Answer: 0. 73 m

Check Your Understanding A toboggan carrying two children (total mass = 85 kg) reaches its maximum speed at the bottom of a hill, and then glides to a stop in 21 m along a horizontal surface. The coefficient of kinetic friction between the toboggan and the snowy surface is 0. 11. a) Draw an FBD of the toboggan when it is moving on the horizontal surface. b) Determine the magnitude of kinetic friction acting on the toboggan. Answers: b) FK = 92 N [backwards]

Check Your Understanding A toboggan carrying two children (total mass = 85 kg) reaches its maximum speed at the bottom of a hill, and then glides to a stop in 21 m along a horizontal surface. The coefficient of kinetic friction between the toboggan and the snowy surface is 0. 11. c) Calculate the work done by the kinetic friction. FK = 92 N [backwards] Answer: W = -1. 9 x 103 J

Check Your Understanding A bag of groceries of mass 8. 1 kg is raised vertically without acceleration from the floor to a countertop, over a distance of 92 cm. Determine a) the force needed to raise the bag without acceleration b) the work done on the bag of groceries against the force of gravity Answers: a) 79 N [up] b) 73 J

Check Your Understanding A student pushes against a large maple tree with a force of magnitude 250 N. How much work does the student do on the tree? Answer: W = 0 because d = 0

Check Your Understanding A 500 -kg meteoroid is travelling through space far from any measurable force of gravity (F approaches 0). If it travels at 10, 000 km/h for 100 years, how much work is done on the meteoroid? Answer: W approaches 0 J because F approaches 0

Check Your Understanding You are walking east at 30 m/s while holding a box of mass 10 kg still on your shoulder. You walk 20 m, how much work is being done on the box? Answer: 0 J because Θ = 90°

Zero Work Done - Summary When W = 0 • if d = 0 • if F = 0 • if Θ = 90° cos 90 = 0 – F is perpendicular to d