Week 5 Recitation Problems PDF

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Carnegie Mellon University 33-141 Recitation

Physics Department Tuesday Week 5

Problem X.5.1) Three identical bricks are pushed across a table at constant velocity as shown below. The hand pushes horizontally, there is (static) friction between the bricks, and kinetic friction between the bricks and the table. A

motion B

Consider the stack of two bricks on the left as system A, and the single brick on the right as system B. (a) Compare the net force on A to that on B. How do you arrive at your conclusion? (b) Draw separate free-body diagrams for A and B. Make sure the label for each force indicates the types of force, the object on which the force is exerted, and the object exerting the force. (c) Is the magnitude of the force exerted by A on B greater than, less than, or equal to the force exerted by B on A? (d) Identify any third law pairs appearing in your two free-body diagrams. Is your answer to (c) consistent with these? (e) If the mass of each brick is m, the coefficient of static friction between the bricks is µs, the coefficient of kinetic friction between the bricks and the table is µk, and the bricks are moving at constant velocity v, determine the magnitude of all the forces in your free-body diagrams.

Problem 4.28) A person pulls horizontally on block B in Fig.E4.28, causing both blocks to move together as a unit. While this system is moving, make a carefully labeled free-body diagram of block A if (a) the table is frictionless (b) there is friction between block B and the table and the pull is equal to the friction force on block B due to the table.

Problem 5.35) Two crates connected by a rope lie on a horizontal surface (Fig. E5.35). Crate A has mass ma and crate B has mass mb. The coefficient of kinetic friction between each crate and the surface is μk. The crates are pulled to the right at constant velocity by  a horizontal force F . In terms of ma, mb, and μk calculate  (a) the magnitude of the force F

(b) the tension in the rope connecting the blocks. Include the free-body diagram or diagrams you used to determine each answer.

Problem 5.6) A large wrecking ball (mass m) is held in place by two light steel cables (Fig. E5.6). (a) Find the tension TB in the cable that makes an angle θ with the vertical.

θ

(b) Find the tension TA in the horizontal cable?

Problem 5.15) Atwood’s Machine. A load of bricks (mass mb) hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight (mass mc) is suspended from the other end of the rope, as shown in Fig. E5.15. The system is released from rest. (a) Draw two free-body diagrams, one for the load of bricks and one for the counterweight. (b) What is the magnitude of the upward acceleration of the load of bricks? (c) What is the tension in the rope while the load is moving? How does the tension compare to the weight of the load of bricks? To the weight of the counterweight?

mc

mb

Carnegie Mellon University 33-141 Recitation

Physics Department Thursday Week 5

Problem X.5.2 A box of flies is resting on a scale. Does it make a difference if the flies are all resting on floor of the box, or if they are hovering in the air? What if the flies are flying up at constant speed? What if the flies are accelerating up?

Problem X.5.3 A block of mass m is sliding down a plane inclined at an angle θ. The coefficient of kinetic friction between the block and the plane is µk. (a) Draw a free body diagram for the block. Choose an appropriate coordinate system, and decompose the vectors into their components. (b) Write down a constraint on the motion (this is really additional information about the normal force). (c) Apply Newton’s II law, and solve to determine the acceleration of the block. (d) Run the following cross-checks (i) Check the units (ii) Look at the general trends. What happens to the acceleration of the block as the angle θ increases? (iii) Check limiting cases. What is the acceleration of the block for θ = 0? What is the acceleration of the block for θ = 90º? (iv) For what values of θ is the box speeding up? For what values of θ is the box slowing down?

Problems from: University Physics, 13th edition, by H. D. Young & R. A. Freedman, Pearson Addison Wesley, 2012. Problem 8.52) Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets combined, this is essentially the position of the center of mass of the solar system.) Does the center of mass lie inside or outside the sun? Mass of Sun: msun = 1.99 x 1030 kg Mass of Jupiter: mjupiter = 1.90 x 1027 kg Orbital Radius of Jupiter: Ro = 7.78 x 1011 m

Problem X.5.4 The table below lists some approximate values for the coefficients of static and kinetic friction. Note that we almost always see µs > µk and we always see µs ≥ µk. What kind of world would it be if µk > µs?

Problem X.5.5 (a) What force on the rope must be exerted by the person in Fig.(a) in order to hold up the block, or equivalently to move it upward at constant speed? The rope wraps twice around the top of the top pulley and the bottom of the bottom pulley. (Assume that the segment of rope attached to the center of the top pulley is essentially vertical.) (b) Now consider the case where the person (with mass m) stands on the block, as shown in Fig. (b). What force is now required?

Problem X.5.6 A box (mass m1) resting on a horizontal, frictionless surface is attached to a mass m2 by a thin, light wire that passes over a frictionless pulley. The pulley is a solid disk with radius R and mass mp. After the system is released find: (a) The acceleration of the box (b) The tension in the wire on either side of the pulley (c) The force that the axle exerts on the pulley

Problem 5.89) Block A in Fig.P5.89 weighs WA, and block B weighs WB. The coefficient of kinetic friction between all surfaces is µk. Find the magnitude of the horizontal force necessary to drag block B to the left at constant speed if A and B are connected by a light, flexible cord passing around a fixed, frictionless pulley.

Problem 5.34) Consider the system shown in Fig.E5.34. Block A weighs WA and block B weighs WB. Once block B is set into downward motion, it descends at a constant speed. (a) Calculate the coefficient of kinetic friction between block A and the tabletop. (b) A cat, also of weight WA, falls asleep on top of block A. If block B is now set into downward motion, what is its acceleration (magnitude and direction)?...