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Friction: A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. 1) What is the acceleration of the block? (A) F/m (B) Fcos /m (C) (F-f)/m (D) (Fcos-f)/m (E) (Fsin-mg)/m 2) What is the coefficient of friction between the block and the surface? (A) f/mg (B) mg/f (C) (mg-Fcos)/f (D) f/(mg-Fcos) (E) f/(mg-Fsin) 3) Consider the system shown in the figure above. Block A has mass mA and block B has mass mB. Once block B is set into downward motion, it descends at a constant speed. Assume that the mass and friction of the pulley are negligible. Which of the following is equivalent to the coefficient of kinetic friction μk between block A and the table top? (A) mA mB (B) mA / mB (C) mB / mA (D) mA mB g (E) | mB - mA | During an experiment, a crate is pulled along a rough horizontal surface by a constant force F. The vector F has a component along the x direction of magnitude Fx. The experiment is repeated several times, with different values of Fx each time. 4) Choose the graph that most accurately depicts the relationship among fs, Fx, and Fmin. Let the point Fmin, along the horizontal axis, represent the minimum force required to accelerate the crate. 5) Choose the graph that most accurately depicts the relationship among fk, Fx, and Fmin. 6) A block rests on an incline that makes an angle with the horizontal. The block remains at rest as is slowly increased. What happens to the magnitudes of the normal force and the static friction force of the incline on the block? (A) (B) (C) (D) (E) Both increase Both decrease Both remain the same The normal force increases while the friction force decreases. The friction force increases while the normal force decreases. Resultant Vectors: 7) Two forces act on a 1-kg object. The first force has a magnitude of 30 N and is directed 45° north of east. The second force is 30 N, 45° north of west. What is the acceleration of the object resulting from the action of these two forces? (A) 42.43 m/s2, 45° north of east (B) 84.85 m/s2, 45° north of east (C) 28.28 m/s2, north (D) 84.85 m/s2, south (E) 42.43 m/s2, north Free Body Diagrams: 8) An object of weight W is suspended from the center of a massless string as shown to the right. The tension at any point in the string is (A) 2Wcos (B) ½Wcos (C) Wcos (D) W/(2cos ) (E) W/cos 9) A block of weight W is pulled along a horizontal surface at constant speed v by a force F, which acts at an angle of with the horizontal, as shown to the right. The normal force exerted on the block by the surface has magnitude (A) W - F cos (B) W - Fsin (C) W (D) W + Fsin (E) W + Fcos 10) A 400-newton weight is suspended by two cords as shown in the figure above. The tension in the slanted cord is (A) 50 N (B) 100 N (C) 150 N (D) 200 N (E) 250 N F=ma 11) A 2000-kg truck is traveling along a straight, level road at a constant speed of 107 m/s when the driver removes his foot from the accelerator. After 36.0 s, the truck’s speed is 35.0 m/s. What is the magnitude of the average net force acting on the truck during the 36.0 s interval? (A) 200 N (B) 2000 N (C) 4000 N (D) 40000 N (E) 400 N 12) When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension in the string between the blocks is (A) 2 F (B) F/5 (C) (1/4)F (D) 5 F (E) F 4 13) Two 0.60-kilogram objects are connected by a thread that passes over a light, frictionless pulley, as shown above. The objects are initially held at rest. If a third object with a mass of 0.30 kilogram is added on top of one of the 0.60-kilogram objects as shown and the objects are released, the magnitude of the acceleration of the 0.30-kilogram object is most nearly (A) 9.8 m/s2 (B) 6.0 m/s2 (C) 3.0 m/s2 (D) 2.0 m/s2 (E) 1.0 m/s2 Inclines: 14) A block of mass 5 kilograms lies on a frictionless inclined plane at an angle of θ = 37°. The magnitude of the force F necessary to pull the block up the plane with constant speed is: (A) 29.5 N (B) 42.5 N (C) 49.5 N (D) 50.5 N (E) 58 N Third Law: 15) Two blocks are pushed along a horizontal frictionless surface by a force of 20 N to the right, as shown above. The force that the 2-kg block exerts on the 3-kg block is (A) 8 N to the left (B) 8 N to the right (C) 10 N to the left (D) 12 N to the right (E) 20 N to the left Graphs: Velocity (m/s) 16) The figure to the right shows the velocity versus time curve for a car traveling along a straight line. Which of the following statements is false? B (A) No net force acts on the car during interval B. C (B) Net forces act on the car during intervals A and C. A (C) Opposing forces may be acting on the car during interval B. (D) Opposing forces may be acting on the car during interval C. (E) The magnitude of the net force acting during interval A is less Time (s) than that during interval C. Two forces are exerted on an object of mass m in the x direction as illustrated in the free-body diagram above. Assume that these are the only forces acting on the object. 17) Which of the curves labeled A to D on the graph below could be a plot of vx(t), the velocity of the object in the x direction as a function of time? (A) A (B) B (C) C (D) D (E) None 18) Which of the curves labeled A to D on the graph below could be a plot of x(t), the position of the object along the x axis as a function of time? (A) A (B) B (C) C (D) D (E) None of these Putting it all together: Free Response: 1. A helicopter holding a 60-kilogram package suspended from a rope 7.0 meters long accelerates upward at a rate of 5.2 m/s2. Neglect air resistance on the package. a. On the diagram below, draw and label all of the forces acting on the package. b. Determine the tension in the rope. c. When the upward velocity of the helicopter is 30 meters per second, the rope is cut and the helicopter continues to accelerate upward at 5.2 m/s2. Determine the distance between the helicopter and the package 2.0 seconds after the rope is cut.