## Chapter 7 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Book on a Table A book weighing 5 N rests on top of a table. Part A A downward force of magnitude 5 N is exerted on the book by the force of ANSWER: Part B An upward force of magnitude _____ is exerted on the _____ by the table. the table gravity inertia . ANSWER: Part C Do the downward force in Part A and the upward force in Part B constitute a 3rd law pair? You did not open hints for this part. ANSWER: Part D The reaction to the force in Part A is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____ . You did not open hints for this part. ANSWER: 6 N / table 5 N / table 5 N / book 6 N / book yes no Part E The reaction to the force in Part B is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____. ANSWER: Part F Which of Newton’s laws dictates that the forces in Parts A and B are equal and opposite? ANSWER: Part G Which of Newton’s laws dictates that the forces in Parts B and E are equal and opposite? ANSWER: 5 N / earth / book / upward 5 N / book / table / upward 5 N / book / earth / upward 5 N / earth / book / downward 5 N / table / book / upward 5 N / table / earth / upward 5 N / book / table / upward 5 N / table / book / downward 5 N / earth / book / downward Newton’s 1st or 2nd law Newton’s 3rd law Blocks in an Elevator Ranking Task Three blocks are stacked on top of each other inside an elevator as shown in the figure. Answer the following questions with reference to the eight forces defined as follows. the force of the 3 block on the 2 block, , the force of the 2 block on the 3 block, , the force of the 3 block on the 1 block, , the force of the 1 block on the 3 block, , the force of the 2 block on the 1 block, , the force of the 1 block on the 2 block, , the force of the 1 block on the floor, , and the force of the floor on the 1 block, . Part A Assume the elevator is at rest. Rank the magnitude of the forces. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Newton’s 1st or 2nd law Newton’s 3rd law kg kg F3 on 2 kg kg F2 on 3 kg kg F3 on 1 kg kg F1 on 3 kg kg F2 on 1 kg kg F1 on 2 kg F1 on floor kg Ffloor on 1 Part B This question will be shown after you complete previous question(s). Newton’s 3rd Law Discussed Learning Goal: To understand Newton’s 3rd law, which states that a physical interaction always generates a pair of forces on the two interacting bodies. In Principia, Newton wrote: To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. (translation by Cajori) The phrase after the colon (often omitted from textbooks) makes it clear that this is a statement about the nature of force. The central idea is that physical interactions (e.g., due to gravity, bodies touching, or electric forces) cause forces to arise between pairs of bodies. Each pairwise interaction produces a pair of opposite forces, one acting on each body. In summary, each physical interaction between two bodies generates a pair of forces. Whatever the physical cause of the interaction, the force on body A from body B is equal in magnitude and opposite in direction to the force on body B from body A. Incidentally, Newton states that the word “action” denotes both (a) the force due to an interaction and (b) the changes in momentum that it imparts to the two interacting bodies. If you haven’t learned about momentum, don’t worry; for now this is just a statement about the origin of forces. Mark each of the following statements as true or false. If a statement refers to “two bodies” interacting via some force, you are not to assume that these two bodies have the same mass. Part A Every force has one and only one 3rd law pair force. ANSWER: Part B The two forces in each pair act in opposite directions. ANSWER: Part C The two forces in each pair can either both act on the same body or they can act on different bodies. ANSWER: true false true false Part D The two forces in each pair may have different physical origins (for instance, one of the forces could be due to gravity, and its pair force could be due to friction or electric charge). ANSWER: Part E The two forces of a 3rd law pair always act on different bodies. ANSWER: Part F Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.) You did not open hints for this part. ANSWER: true false true false true false Part G According to Newton’s 3rd law, the force on the (smaller) moon due to the (larger) earth is ANSWER: Pulling Three Blocks Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force . The magnitude of the tension in the string between blocks B and C is = 3.00 . Assume that each block has mass = 0.400 . true false greater in magnitude and antiparallel to the force on the earth due to the moon. greater in magnitude and parallel to the force on the earth due to the moon. equal in magnitude but antiparallel to the force on the earth due to the moon. equal in magnitude and parallel to the force on the earth due to the moon. smaller in magnitude and antiparallel to the force on the earth due to the moon. smaller in magnitude and parallel to the force on the earth due to the moon. F T N m kg Part A What is the magnitude of the force? Express your answer numerically in newtons. You did not open hints for this part. ANSWER: Part B What is the tension in the string between block A and block B? Express your answer numerically in newtons You did not open hints for this part. ANSWER: Pulling Two Blocks In the situation shown in the figure, a person is pulling with a constant, nonzero force on string 1, which is attached to block A. Block A is also attached to block B via string 2, as shown. For this problem, assume that neither string stretches and that friction is negligible. Both blocks have finite (nonzero) mass. F F = N TAB TAB = N F Part A Which one of the following statements correctly descibes the relationship between the accelerations of blocks A and B? You did not open hints for this part. ANSWER: Part B How does the magnitude of the tension in string 1, , compare with the tension in string 2, ? You did not open hints for this part. Block A has a larger acceleration than block B. Block B has a larger acceleration than block A. Both blocks have the same acceleration. More information is needed to determine the relationship between the accelerations. T1 T2 ANSWER: Tension in a Massless Rope Learning Goal: To understand the concept of tension and the relationship between tension and force. This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let and (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless, so that its weight is negligible compared with the tension. (This is not a ridiculous approximation–modern rope materials such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.) Consider the three sections of rope labeled a, b, and c in the figure. At point 1, a downward force of magnitude acts on section a. At point 1, an upward force of magnitude acts on section b. At point 1, the tension in the rope is . At point 2, a downward force of magnitude acts on section b. At point 2, an upward force of magnitude acts on section c. At point 2, the tension in the rope is . Assume, too, that the rope is at equilibrium. Part A What is the magnitude of the downward force on section a? Express your answer in terms of the tension . ANSWER: More information is needed to determine the relationship between and . T1 > T2 T1 = T2 T1 < T2 T1 T2 Fu Fd Fad Fbu T1 Fbd Fcu T2 Fad T1 Part B What is the magnitude of the upward force on section b? Express your answer in terms of the tension . ANSWER: Part C The magnitude of the upward force on c, , and the magnitude of the downward force on b, , are equal because of which of Newton's laws? ANSWER: Part D The magnitude of the force is ____ . ANSWER: Fad = Fbu T1 Fbu = Fcu Fbd 1st 2nd 3rd Fbu Fbd Part E Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces? You did not open hints for this part. ANSWER: Part F The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true? Check all that apply. ANSWER: less than greater than equal to Fu > Fd Fu = Fd Fu < Fd The tension in the rope is everywhere the same. The magnitudes of the forces exerted on the two objects by the rope are the same. The forces exerted on the two objects by the rope must be in opposite directions. The forces exerted on the two objects by the rope must be in the direction of the rope. Two Hanging Masses Two blocks with masses and hang one under the other. For this problem, take the positive direction to be upward, and use for the magnitude of the acceleration due to gravity. Case 1: Blocks at rest For Parts A and B assume the blocks are at rest. Part A Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: M1 M2 g T2 M1 M2 g Part B Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: Case 2: Accelerating blocks For Parts C and D the blocks are now accelerating upward (due to the tension in the strings) with acceleration of magnitude . Part C Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , , and . You did not open hints for this part. ANSWER: T2 = T1 M1 M2 g T1 = a T2 M1 M2 a g Part D Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , , and . You did not open hints for this part. ANSWER: Video Tutor: Suspended Balls: Which String Breaks? First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the question at right. You can watch the video again at any point. T2 = T1 M1 M2 a g T1 = Part A A heavy crate is attached to the wall by a light rope, as shown in the figure. Another rope hangs off the opposite edge of the box. If you slowly increase the force on the free rope by pulling on it in a horizontal direction, which rope will break? Ignore friction and the mass of the ropes. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The rope attached to the wall will break. The rope that you are pulling on will break. Both ropes are equally likely to break.

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