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Kreutter: Work and Energy Lesson 1: How Do We Ever Get Anything Done Around Here? 1.1 Observe and find a pattern In these three experiments, we will study the ability for a group of objects to smash a piece of chalk. a) Consider a 1-kg block with a flat bottom with a string attached to the top and Earth as your system. There is also a piece of chalk sitting below the block. You pull up on the string so that the 1-kg block slowly rises 0.5 m above the piece of chalk. After this lifting process, you release the block. It falls and breaks the chalk. 1 kg Lift 1 kg chalk b) Consider a 1-kg dynamics cart that can roll on a low-friction horizontal dynamics track as your system. There is also a piece of chalk that is taped to the fixed, vertical end of the track. You push the cart so that it rolls faster and faster toward the chalk at the end of the dynamics track and the cart breaks the chalk when it hits it. wall Push c) wall Now consider a slingshot that holds a piece of chalk as your system. You slowly pull back on the sling. When you release the sling, the chalk shoots out at a high speed and hits the wall, causing the chalk to break. Complete this table. Experiment Draw an arrow indicating the direction of the external force you exerted on each of the system objects that you studied (𝐹⃗Y on S). Draw an arrow indicating the displacement of the system object while you were exerting the force (𝑑⃗). Adapted from PUM ©2010, Rutgers, The State University of New Jersey a) b) c) Kreutter: Work and Energy d) Look for a pattern of what was done to the systems that we studied to give them the chalk-smashing potential. Then, devise a new physical quantity to describe this pattern. 1.2 Observe and find a pattern Now, suppose that a friend decides to save the chalk in the first two experiments by exerting, with her hands, an opposing force on the block or on the cart after they are released. In each case, she pushes on the moving object opposite to the direction of its velocity. Below, give the direction of the external force your friend exerts on the moving object relative to its displacement as she stops it, thus causing the system to lose its potential to break the chalk. a) After lifting the block, you release the block and it starts falling. Your friend then starts pushing upward on the falling block, slowing it down, and the block does not break the chalk. b) You push the cart so that it rolls faster and faster. You then stop pushing. Just before the cart reaches the chalk, your friend pushes it in a direction opposite to its direction of motion. This causes the cart to slow down and stop so that it does not break the chalk. Complete this table. Experiment Draw an arrow indicating the direction of the external force your friend exerted on the system object that you studied (𝐹⃗Y on S). a) b) Draw an arrow indicating the displacement of the system object while your friend was exerting the force (𝑑⃗). c) How could you modify the definition of the quantity you devised in the previous activity to account for the system’s loss of the chalk-breaking potential due to your friend’s intervention? Adapted from PUM ©2010, Rutgers, The State University of New Jersey Kreutter: Work and Energy 1.3 Observe and find a pattern : Consider Earth and a 1-kg block as your system. a) You hold a string tied to a block so that it stays about 1 cm above a table. A piece of chalk is placed on the table under the block. If you release the block and it falls on the chalk, the chalk will not break (it’s too close to the chalk). Next you slowly walk about 2 m beside the table, continually keeping the block 1 cm above the surface. After walking the 2 m, the block hangs over a second, identical piece of chalk. Draw the force exerted by the string on the block and the displacement of the block as you walked the 2 m. b) Discuss whether the vertical force the string exerted on the block while moving it horizontally above the tabletop caused Earth and block to have a better chance of breaking the second piece of chalk than the first piece. c) Revise the quantity you devised in the last two activities to account for this result. Your revision will involve the angle between the external force exerted on the system and the system object’s displacement. We call this quantity work. 1.4 Observe and find a pattern (if you know trigonometry) Ki Ugi 0 a) Consider a 1-kg dynamics cart a system. You pull it at angle θ causing it to roll on a low-friction horizontal dynamics track toward a piece of chalk that is taped to the fixed, vertical end of the track. You pull the cart so that it rolls faster and faster toward the chalk at the end of the dynamics track and breaks the chalk when it hits it. Draw the force exerted by you on the cart and the displacement of the cart while you were pulling it. b) Discuss whether the angled force exerted on the cart while moving it horizontally gave it a better chance of breaking the piece of chalk than the force exerted in activity 1.1 part (b). Adapted from PUM ©2010, Rutgers, The State University of New Jersey Kreutter: Work and Energy c) What trigonometric function would help you determine the system’s increase in chalk-smashing ability? Is this consistent with the increase, decrease, and no change in chalk-smashing potential for activities 1.1-1.3? d) Revise the quantity you devised in the last three activities to account for this result. Your revision will involve the angle between the external force exerted on the system and the system object’s displacement. We call this quantity work. Work done by a constant force on an object is equal to the product of the force magnitude and displacement magnitude with a positive sign (W = FW on B *d) if the force and displacement are in the same direction and the product of the force and displacement with the negative sign (W = -FW on B * d) if they are in the opposite direction. If the force and displacement of the object are perpendicular to each other, the force does NO work! The units of work are Joules (J). One joule is equal to one Newton·Meter, or one kg·m2/s2. 1.5 Regular Problem Jeff did 573 J of work on a sled. He pulled the sled for a distance of 30 m. Represent the sled as a box. Draw the direction of the force Jeff exerts on the sled and the direction of the sled’s displacement. What is the average force that he exerted on the system? 1.6 Regular Problem Steve slowly lifts a 20 kg barbell 1 meter vertically. Represent the barbell as a box. Draw the direction of the force Steve exerts on the barbell and the direction of the barbell’s displacement. How much work does he do on the barbell? What assumptions did you make? 1.7 Regular Problem If Natasha slows a moving grocery cart by pulling on it exerting a force of 23 N over 2.3 m, what will be the work she does on it? Represent the cart as a box. Draw the direction of the force Natasha exerts on the cart and the direction of the cart’s displacement. What assumptions did you make? Adapted from PUM ©2010, Rutgers, The State University of New Jersey Kreutter: Work and Energy In problem 1.7 Natasha did negative work on the box. Notice that when the force exerted on the object and the object’s displacement are in the opposite directions, the force does NEGATIVE work! 1.8 Regular Problem Jessica, at a constant slow speed, moved a 1 kg book from a 2 m high shelf to the floor. Represent the book as a box. Draw the direction of the force Jessica exerts on the book and the direction of the book’s displacement. How much work did she do on the book? 1.9 Reason Dylan is trying to lift his bike into the back of his pick-up truck of height h. He attaches a light string to it and pulls it vertically upward. If the bike is the system, what kind of work do Dylan and Earth do on the bike? i. Dylan does positive work on the bike. Earth does positive work on the bike. ii. Dylan does positive work on the bike. Earth does negative work on the bike. iii. Dylan does negative work on the bike. Earth does positive work on the bike. iv. Dylan does negative work on the bike. Earth does negative work on the bike. Homework 1.12 Relate Describe a situation when you have done: a) +1 J of work on a system. b) -1 J of work on a system. c) 0 J of work on a system. 1.13 Regular Problem While working out, a man lifts a 10-kg object a vertical distance of 0.80 m. He then carries it for 10 m where he sets it down a vertical distance of 0.80 m. How much work does he do on the object when he picks the object up, when he carries it, and when he sets it back down? What is the total work that he does on it? Adapted from PUM ©2010, Rutgers, The State University of New Jersey Kreutter: Work and Energy 1.14 Observe and Explain In another situation, you stretch a block-spring system and then release the block. The block slides toward the wall and smashes a piece of chalk. Label whether the ability of the block-spring-wall system to crush the chalk increases, decreases, or remains the same between each step. Is this process consistent with the pattern we observed today between the net force exerted on an object and the displacement of the object? 1.15 Regular Problem Sara drops a 1 kg ball from the top of a cliff. It falls vertically with a constant acceleration (9.8 m/s2). What object (if any) exerts a force that does work on the ball (system)? How much work has been done on the ball if it falls 10 m? Sketch the situation. Draw the direction of the force exerted on the ball and the direction of the displacement. 1.16 Regular Problem Minh is riding the elevator up to the top floor of a shopping mall. He moves with a constant velocity from the ground level to the floor above (5 m high). Estimate the work done on Minh by the elevator. To calculate the force exerted on Minh, choose him as the system and draw a force diagram. 1.17 Regular Problem Shelly is now riding up the same elevator as Minh in the previous problem. She is going to the fifth floor so as the elevator goes from the ground level to the first floor, it accelerates at a rate of 1.0 m/s2. Estimate the work done on Shelly by the elevator during this part of the trip if her mass is 2/3 the mass of Minh. To calculate the force exerted by the elevator on Shelly, choose her as the system and draw a force diagram. Adapted from PUM ©2010, Rutgers, The State University of New Jersey Kreutter: Work and Energy 1.18 Regular Problem As Shelly goes from the fourth floor to the fifth floor the elevator slows to a stop from 2.0 m/s. Estimate the work done on Shelly by the elevator as it goes from the fourth to fifth floor. To calculate the force exerted by the elevator on Shelly, choose her as the system and draw a force diagram. 1.19 Evaluate Heather, Minh and Danny are arguing about the units of work. Minh says that the units of work are pounds i inches, Heather thinks that the units of work are in Joules, and Danny thinks they are Newtons imeters. Which of them is right? Explain your answer. What are your assumptions? 1.20 Regular Problem Kate is waiting in the security line at the airport and has to keep picking up her suitcase, moving forward, and setting it down again. Calculate the work done by Kate on her 15-kg suitcase when (a) slowly lifting it 0.80 m upward, (b) when holding it and slowly moving forward 1.0 m, and (c) when lowering it 0.80 m down again. Work-Trigonometry Section: In this section, students will use trigonometry to express work done for a more general range of situations. Work System W = Fp on s cos() d Magnitude of displacement—always positive Magnitude of force—always positive Angle between 𝐹⃗ and 𝑑⃗ Adapted from PUM ©2010, Rutgers, The State University of New Jersey Kreutter: Work and Energy Did You Know? Work W: Work is a physical quantity that is equal to the product of the magnitude of the average force FEx on O that an external environmental object exerts on a system object, the magnitude of the system object’s displacement d, and the cosine of the angle between FEx on O and d. W = (FEx on O cos ) d 1.21 Regular Problem Suzanne is pulling a sled up a hill that makes a 24 angle with the horizontal. She keeps the rope parallel to the hill and exerts a 150-N force on it. How much work will she do if she pulls the sled 150 m? 1.22 Regular Problem A 4 kg grocery cart rolls down a 3 m long incline with an angle of 10°. How much work does Earth do on the cart? 1.23 Regular Problem Juan pushes a box at an angle to the horizontal, doing 250 J of work over a distance of 10 m. If the force exerted is 30 N, what is the angle between the force exerted by Juan on the box and the horizontal? 1.24 Regular Problem To clean the floor, David exerts a 40 N force on a broom handle to push it 2 m. If the broom handle makes a 40° angle with the floor, what is the work done by David on the broom? If the broom handle were angled at 65° would David do more or less work? Explain your answer. 1.25 Regular Problem Tara pushes a baby carriage at an angle 35° to the horizontal over a distance of 20 m on her way to the playground. If she does 600 J of work on the carriage, what force does she have to exert on the carriage? 1.26 Regular Problem Komila is driving her car alongside a river. Theo is water skiing in the river and holding onto a rope attached to Komila’s car. The force exerted by the rope on Theo is 400 N, and the rope makes an angle of 15° with the river. Calculate the work done by the rope in pulling Theo 300 m up the river. Assume he does not fall into the water. 1.27 Regular Problem Dustin exerts 200 N of force on a box sitting on a horizontal surface. He does not do any work on the box. How is this possible? Explain your answer. Reflect: How does work in physics compare to work in real life? What is the same? What is different? Ask your relatives what they think the word “work” means in physics and then try to teach them what you know. What difficulties did they have? Share them tomorrow in class. Adapted from PUM ©2010, Rutgers, The State University of New Jersey