A teddy falls to the ground.

Transcription

1 Work and Power 1

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3 Work Work equals the product of an object's displacement and the force acting on the object. The force must act parallel to the object's direction of motion. Examples A weightlifter lifts a barbell. A teddy falls to the ground. The cart moves to the right Work = Force x Displacement Work is a scalar quantity. Work is measured in joules, J. (1 Nm = 1 J) In order to use the above equation, the force must be constant. 3

4 Special Cases Scenario 1 Positive work is done on an object when the force and displacement are in the same direction. Examples F a a) A rightward force acts on an object and it is displaced rightward. d b) Gravity acts on an object and it accelerates downwards. F g d Scenario 2 Negative work is done when the force and displacement are in opposite directions. Examples a) Friction acts leftward on an object that is displaced rightward. F f d b) Gravity acts downwards on an object that is displaced upwards. d F g 4

5 Sample Problems Work 1. Bubba pushes horizontally on a 20.0 kg crate with an 80.0 N force. If the crate is moved 10.0 m across the floor, how much work did Bubba do on the crate? 2. The third floor of a house is 8.0 m above street level. How much work must be done to lift a 1.50 x 10 2 kg refrigerator to the third floor? 3. A horizontal force of 805 N is applied to a present to move it across the floor at constant velocity. If the present is moved 22 m, how much work does friction do on the present? 5

6 Scenario 3 When is no work done on an object? a) No work is done when an applied force does not cause motion. A force is applied to the house, but it is not displaced. b) No work is done when there is uniform motion in the absence of a force. No force is required to keep a hockey puck sliding at constant velocity on a frictionless surface. Note: Work was done to start the puck moving, but no work is done to keep it moving at constant velocity. c) No work is done when the applied force is perpendicular to the object's motion. While the waiter applies an upward force on the tray to prevent it from falling, it is displaced rightwards. θ = 90 o F a v As the moon orbits the Earth, the force of gravity acts towards the center of the Earth. The moon's direction of motion is perpendicular to the force of gravity. F g v 6

7 Work and Power In physics, if a force causes the displacement of an object, we say that the force has done work on the object. Work is independent of time. Sometimes work can be done very quickly and sometimes work can be done very slowly. Example Teddy Bear Figgy Bubba Bubba runs up the stairs to find his teddy bear. He does a certain amount of work in short amount of time. His identical brother, Figgy, takes 3 hours to climb the same set of stairs. Both puppies do the same amount of work, but Bubba does the work in less time. The quantity which has to do with the rate at which a certain amount of work is done is called power. In this case, Bubba has a greater power rating than Figgy. 7

8 Power Power is the rate at which work is done. The standard unit of power is the watt, W. A watt is equal to a J/s. James Watt ( ) was a Scottish inventor and engineer whose improvements to the steam engine were fundamental to the changes wrought by the Industrial Revolution. Wikipedia For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. 1 horsepower 746 watts The term horsepower was coined by James Watt. He determined that a horse could do a certain amount of work per second; when he sold his steam engines, this measurement allowed him to estimate the worth of an engine in terms of the number of horses it would replace. Therefore, a six horsepower engine was capable of replacing six horses. Answer.com 8

9 P = Fv 9

10 Sample Problems 1. Two guys, Arnold and Walter, are in the gym lifting weights. Arnold lifts a 20.0 kg barbell over his head 10 times in one minute; Walter lifts 20.0 kg barbell over his head 10 times in 10 seconds. a) Which guy did more work? b) Which student delivers the most power? Arnold Walter 10

11 2. Nellie Newton decides to do some chin ups. If she lifts her 40.0 kg body a distance of 0.25 m in 2.0 s, then what is the power delivered by Nellie's biceps? 11

12 3. A horizontal force of 671 N is needed to pull a wagon across a horizontal floor at constant velocity. Bart drags the wagon using a rope held at an angle of 47 o. If the wagon is moved 3.4 m in 7.5 s, what power is developed? 12

13 Work Done by Changing Forces A force position graph can be used to determine work done whether: a force is constant. a force changes. work done = area under the curve Example 1 The graph below shows a constant force of 10.0 N acting over a displacment of 4.0 m. The area under the force position line is given by the shaded rectangle. The work done by the force is 40 J. 13

14 Example 2 The force position graph below shows a force that starts at zero and increases to 10.0 N over a displacment of 4.0 m. In this case, the area under the curve the forms a triangle. The work done on the object is 20 J. 14

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16 Textbook, page 229 Answers A. 180 J B. 65 J 16

17 a) b) c) d) 17

18 Textbook, page

19 Forces Applied at Angles When a force is applied to an object at an angle, only part of the force causes the object's horizontal displacement. Example Consider the force of a chain pulling upwards and rightwards on a cat in order to persuade the cat to move to the right. θ F F x (No cat was harmed during the creation of this example...) d F x is the horizontal component of the force which causes the cat to be displaced to the right. This component is found by muliplying the force, F, by the cosine of the angle, θ. (1) Sometimes the work equation is written as follows: (2) If we combine equations (1) and (2), we get: where F = force (N), d = displacement (m) and the angle theta, θ, is the angle between the force and the displacement. 19

20 Caution! Theta, θ, is defined as the angle between the force and displacement. 38 o In this situation, F and d are in the same direction. Therefore, the angle between them is 0 o. Just because an angle is given doesn't mean it has to be used! 20