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Mechanics: PX132 / 2005 Dr. Rudolf A. Römer 1. Motion and Newton's Laws 1.1. Conceptual Questions on Newton's 1st and 2nd Laws In this problem, you are given a diagram representing the motion of an object--a motion diagram. The dots represent the object's position at moments separated by equal intervals of time. The dots are connected by arrows representing the object's average velocity during the corresponding time interval. Your goal is to use this motion diagram to determine the direction of the net force acting on the object. You will then determine which force diagrams and which situations may correspond to such a motion. Left: Motion diagram Right: Force diagrams for questions D, E, F, G A. What is the direction of the net force acting on the object at position A? B. What is the direction of the net force acting on the object at position B? C. What is the direction of the net force acting on the object at position C? The next four questions are related to the force diagrams numbered 1 to 6. These diagrams represent the forces acting on a moving object. The number next to each arrow represents the magnitude of the force in newtons. D. Which of these diagrams may possibly correspond to the situation at point A on the motion diagram? E. Which of these diagrams may possibly correspond to the situation at point B on the motion diagram? F. Which of these diagrams may possibly correspond to the situation at point C on the motion diagram? G. Which of these diagrams correspond to a situation where the moving object (not necessarily the one shown in the motion diagram) is changing its velocity? At this point, we stop although the question continues on the web with parts H, I, J. You are welcome to answer them if you wish. http://www.warwick.ac.uk/go/PX132/ Example Set 1 of 3 Mechanics: PX132 / 2005 Dr. Rudolf A. Römer 1.2. Pulling Three Blocks Pulling three identical blocks, each connected to the next by a string. Find total force needed to pull the blocks given tension in one of the strings. Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force F . The magnitude of the tension in the string between blocks B and C is T .Assume that each block has mass m . A. What is the magnitude aB of the acceleration of block B? Express your answer in terms of T and m . B. What is the magnitude a of the acceleration of the three blocks? Express your answer in terms of m and F . C. What is the magnitude F of the force F ? Express the magnitude of the force in terms of T. 1.3. Tension in a Massless Rope This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let Fu and Fd (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 labelled a, b, and c in the figure on the right. - At point 1, a downward force of magnitude Fad acts on section a. - At point 1, an upward force of magnitude Fbu acts on section b. - At point 1, the tension in the rope is T1 . - At point 2, a downward force of magnitude Fbd acts on section b. - At point 2, an upward force of magnitude Fcu acts on section c. - At point 2, the tension in the rope is T2 . . Assume, too, that the rope is stationary. A. What is the magnitude Fad of the downward force on section a? B. What is the magnitude Fbu of the upward force on section b? C. The magnitude of the upward force on c, Fcu , and the magnitude of the downward force on b, Fbd , are equal to T2 because of which of Newton's laws? http://www.warwick.ac.uk/go/PX132/ Example Set 2 of 3 Mechanics: PX132 / 2005 Dr. Rudolf A. Römer D. The magnitude of the force Fbu is ____ Fbd . E. Fbu = Fbd because of Newton's ______ law. F. Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces? G. A massless rope is attached at its ends to two stationary objects (e.g., two trees or two cars). For this situation, indicate whether the following statements are true or false: 1. The tension in the rope is everywhere the same. 2. The magnitudes of the forces exerted on the two objects are the same. 3. The forces exerted on the two objects must be in opposite directions. 4. The forces exerted on the two objects must be in the direction of the rope. Separate your answers with commas (e.g., t,f,f,t). 1.4. Jumping to the Ground [UP11 Problem 4.46] A 75.0-kg man steps off a platform 3.10 m above the ground. He keeps his legs straight as he falls, but at the moment his feet touch the ground his knees begin to bend, and, treated as a particle, he moves an additional 0.60 m before coming to rest. A. What is his speed at the instant his feet touch the ground? B. Treating him as a particle, what is the magnitude of his acceleration as he slows down, if the acceleration is assumed to be constant? C. What is the direction of his acceleration as he slows down? D. Use Newton's laws and the results of part (B) to calculate the average force his feet exert on the ground while he slows down. Express this force in newtons. E. Calculate the average force his feet exert on the ground while he slows down. Express this force as a multiple of his weight. 1.5. Three identical links [UP11 Problem 4.52] ASSESSED A student tries to raise a chain consisting of three identical links. Each link has a mass of m . The three-piece chain is connected to a string and then suspended vertically, with the student holding the upper end of the string and pulling upward. Because of the student's pull, an upward force of magnitude F is applied to the chain by the string. Use Newton's laws to answer the following questions. A. Find the acceleration of the chain (Take the free fall acceleration to be g .). B. Find the force exerted by the top link on the middle link. http://www.warwick.ac.uk/go/PX132/ Example Set 3 of 3

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