i jn 613 U r,h ( 1()j. ) W LA cfr (a) Hector lifts the before after j-c vr cp i I / /SE fr before after J r ); L(- /fj \ Represent and Reason

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1 Word description of Sketch the initial and J Complete the workenergy bar chart for this Complete the table that follows. Consider a 20 N brick sitting on a table which is I m high. 4.1 Represent and Reason Lesson 4: Such Great Heights ( 1()j. ) i jn cfr no energy, you must have been describing the ability to smash the chalk if it were on the table. the table. Since you have decided that when the block was on the table, the system begins with final state, the 20 J of energy actually measures the system s ability to smash a piece of chalk on The energy of each system measures its ability to smash a particular piece of chalk. For Hectors L( /ft! evl Compare and contrast Hector s situation with Eva s situation to help you answer this. amount. You found different initial potential energies for each system, though. How can this be? c) When dropped, the bricks in parts (a) and (b) will both smash the chalk on the floor the same W LA J r ); Write an equation relating these quantities: \/ 40 J floor. /fj \ 20 also hanging over a piece of chalk on the 0 Hector s brick. It is 20J spot right next to /SE from the floor to a identical brick 2 m (b) Eva lifts an fr before after :, Write an equation relating these quantities: w chalk on the floor..2oj horizontally so it is moves the brick 20J table. He then 1 40J the surface of the brick I mupoffof (a) Hector lifts the before after held over a piece of 0 system. a process. final state. Circle the I process Ii jc vr cp i I / I 4t. + j KREU ThF WORK MD ENE. V 613 U r,h

2 d) Redraw your workenergy bar chart for Hector, but now describe the ability to smash chalk on the floor. Below, relate the quantities mathematically. Uq / 1) 40 J 20 J 0 20 J 40J before after IUi+U±Kfu+uII raourenerbarcjart for Eva, but use it to represent the system s ability to smash the chalk on the table. Is the final state identical to Hector s final state in part (a)? Below, relate the quantities mathematically. 20 J 40J before after When calculating the gravitational potential energy of a system, you must pick a reference level When an object is at this reference level, the gravitational potential energy of the system is zero. 4.2 Reason You smash open walnuts on a picnic table by lifting a block from the table to a height of 1 above the walnuts and then dropping the block on the walnuts. m a) Draw a workenergy bar chart and a diagram for the initial and final states representing the blockearth system s ability to smash these walnuts as you lift the block. V III Your friend is in a tree house that is 10 m above the picnic table, Your friend has walnuts for a snack in his tree house, b) Draw a workenergy bar chart and a diagram for the initial and final states representing the blockearth system s ability to smash these walnuts in the tree house as you lift the block I m above the picnic table,

3 1j KREUTTER: WORK AND ENERGY 3 LA jj (L L the gravitational potential energy of the blockearth system at any moment. the change in gravitational potential energy of the system (iu9) in order to find the expression for on the block equals the change in a quantity: mgyf mgy 1? Relate the work done on the system to d) Examine the expression that you derived in part c. Do you see that the work that the cable did Substitute this expression into the expression in part b. force that the cable exerts on the block in terms of its mass and the gravitational constant g. c) Draw a force diagram for the block during this process. Use it to find an expression for the O ) Substitute this into the expression in part a. b) Write an expression for the work the cable does on the block during its displacement f LI 4 1 a) Comple e a wo energy ar c art for this expression 0 and Earth. Below is a picture of the initial and final states of the process. The system for analysis is the block drops the massive block onto the top of the pole, which is at height y = 0. The massive block has a mass m. constant speed from a height y above the pole to a height yabove the pole. The crane then into granite stone. To hammer the poles into the ground, a crane lifts a massive block at a slow To build the foundation for a new skyscraper, a construction company needs to drive metal poles 43 Derive the Relationship for Gravitational Potential Energy does a negative value represent about the ability of the system to accomplish a task? lh i tt c) In parts a) and b), you have a system with negative gravitational potential energy. What

4 4.5 Evaluate the Relation 7 [ 4. 4 bu The change in gravitational potential energy of the blockearth system is caused by the work done by the cable on the block. From that relationship, we find the accepted value for the gravitational potential energy of a system at a given moment is equal to Ug = mgy, where y represents the height with respect to the reference level. The gravitational potential energy of the system describes its ability to smash a piece of chalk at the reference level, where Ug Test the Relation You are the head engineer for the construction company discussed in the last problem. Before you build the machine to drive the poles into the ground, you need to test whether the ability of the blockearth system to do something (to smash chalk or clay, to dent Styrofoam, to splash water, etc.) depends on the mass of the block and the initial height of the block above the target. r V y u epe Describe two experiments that you can perform to test these relatiqn$ps. k How many variables can you and independent variables? Lii Jr L change in this exèriment? What will be your dçpendent in Y Ii lncicda sketch. What does the relationship predict will happen? What are your assupiptions? IC$: 4i I 1)b( You are performing an experiment involving a track that you can tilt at different angles and a marble. Tape a Styrofoam cup to your lab table. Your goal is to let the marble roll down the track and have it land in the cup. The only rule is that you cannot move the cup. a) Design and perform an experiment that will allow you to find a pattern in the location of the marble from which you can release it and it lands in a cup (make sure that you try at least 4 different locations that work). b) Draw a picture of the experiment and describe what you did. c) Record the data you collected and deqlde what the best way to represent it is. (Mjke your own data table). V IE?

5 d) Describe the pattern you found in words and mathematicaljy. t e) Use your knowledge of energy to relate the location of the marble and its ability to land in the cup, Compare your pattern to the definition of the gravitational potential energy of the system. Use any necessary representations to help with your explanation. Are the two relationships consistent? How do you know? 4.6 Reason r Imagine that you could use one of two ramps to slowly move a 7kg cart to a position that is 2 m above the ground. 3m 15m a) Using a workenergy bar chart, determine how much work you will have to do to move the cart up each ramp slowly. r b) Determine the value of the force that you will need to exert on the cart to slowly push it up each ramp. 4.7 Reason I You slowly lift a box from the floor to the top of a table and do 310 J of work on the box. Now lift the same box quickly from the floor to the top of the table. It ends at rest on the table. a) How does the work you did on the system now compare to the previous situation where you lifted the box slowly? i. More work was done on the box when it was lifted quickly. ii. iii. iv. The same amount of work was done on the box when it was lifted quickly. Less work was done on the box when it was lifted quickly. No work was done on the box when it was lifted quickly.

6 ,1 tr b) In the second experiment identif the time intervals and displacements when you did positive and negative work on the box. What is the total work being done? How does it compare to the work you do when you lift the box very slowly? What if you lift the box with even higher acceleration at the beginning will you do more total work lifting the box to the same height? () fl. c) Think of how your answers are reaated to the change of gravitational potential energy of the system boxearth in all situations. Explain. The work that you did on the boxearth system in the previous activity is equal to the change in gravitational potential energy of that system. if the systems energy change in two experiments is the same, the external work done on it should the same too. 4.9 Equation jeopardy Homework Write a problem that would require the mathematical equation below to solve it. IOJ=m*9,8(N/kg)(15m_3m) 4.10 Reason When you crushed the chalk with a block, you released the 5 kg block from a height of I m above the chalk. What is the gravitational potential energy of the blockearth system before you released it? What did you set ap your reference level? Io a 4.11 Reason A skier slides down an icy hill. He has a mass of 70 kg and begins 50 m above the bottom of the hill. What is the skiers kinetic energy at the bottom of the hill? What is his kinetic energy when he is % of the way down the hill? What system did you choose for analysis?

7 4.8 Represent and Reason the direction of motion. Because the cart rolls, its kinetic energy increases. Earth does positive no initial kinetic energy. Earth pulls down on the cart; the surface exerts a force perpendicular to Case A: Our system is the cart only; therefore it does not have any potential energy. There is also incline and the final state is when it is moving fast at the bottom. Imagine that a cart is rolling down an inclined plane. The initial state is when it is on top of the 2 :ii ow K, + Ug,i +Us+_ I before after Case,p: V &: I before after Case r K1 + Ug,i + Us,i + W = K + Ugif + Usj+A jjiz Draw a diagram for the situation and Complete the bar chart for this process and relate the circle the system. quantities mathematically. the cart rolls down, some of this energy is transformed into kinetic energy. Earth does not do any Case B: The system is the cart and Earth together. It has initial gravitational potential energy. As direction of motion. work and the surface of the plane does no work because the force is perpendicular to the work because it is internal to the system. KREUTTER: WORK AND ENERGY 7

8 4.12 Reason Jeff and Jim are both demolition experts skilled in using a wrecking ball to destroy old buildings. The motion of the wrecking ball is shown below. When asked to draw workenergy bar charts for the motion of the wrecking ball, Jeff and Jim drew the bar charts below. Jeff s Jim s before after before after JiJ1 L!L_±!4jj4n K, Ui,, +W I( Ur Us, EZ{ + 0 a) When would Jeff s be correct and when would jim s be correct? Be sure to state the initial and final states, what objects you are including in the system, and where you are defining the reference level for zero gravitational potential energy. f 4 b) How should Jim and Jeff label their workenergy bar charts to prevent any more confusion? I c) Shouldn t they include the work due to the force that the rope exerts on the ball on both charts? Explain your answer with a force diagram.

9 4i3 Represent and Reason Imagine that you throw a baseball out of your dorm room window on the fifth floor to a friend standing outside on the ground level, Determine which of the following workenergy bar charts could represent this situation. Decide what is included in the system and state the reference level for the gravitational potential energy for each correct bar chart. before K k Ur after before after K, L, U, W R7Uc U,j AU,,t before after before after jus,+jj IJMJ 1 Reflect: Look back at everything that you learned about gravitational potential energy. Make a list of things that are important to know about this physical quantity. Compare your list to your classmate s list,