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If a billiard ball is hit in just the right way by a cue stick, the ball will roll without slipping immediately after losing contact with the stick. Consider a billiard ball (radius r, mass M) at rest on a horizontal pool table. A cue stick exerts a constant horizontal force F on the ball for a time t at a point that is a height h above the table’s surface (see Fig. 10–68). Assume that the coefficient of kinetic friction between the ball and table is
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- A solid ball of radius R = 0.1 m and mass M = 4 kg is placed at the top of a ramp of height h 5 m and 0 = 53°. If the coefficient of kinetic friction (u) between the ball and the ramp surface is 0.1 and it is known that the ball does not roll smoothly down the ramp (there is sliding), calculate the velocity of the ball's center of mass (v com ) at the bottom of the ramp. (Your result must be in units of m /s and include 2 digit after the decimal point. Maximum of 3% of error is accepted in your answer. Take g = 9.8 m / ?.) (Hint: I =MR)arrow_forward(II) A mallet consists of a uniform cylindrical head of mass 2.30 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7-42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory? 24.0 cm FIGURE 7-42 Problem 62. 8.00 cmarrow_forward(III) Two blocks are connected by a light string passing over a pulley of radius 0.15 m and moment of inertia I. The blocks move (towards the right) with an acceleration of 1.00 m/s? along their frictionless inclines (see Fig. 8–51). (a) Draw free-body diagrams for each of the two blocks and the pulley. (b) Determine Fta and FrB, the tensions in the two parts of the string. (c) Find the net torque acting on the pulley, and determine its moment of inertia, I. a= 1.00 m/s² FTA FTB mA = 8.0 kg mB = 10.0 kg 61% 32° FIGURE 8–51 Problem 46.arrow_forward
- •60 In Fig. 13-50, two satellites, A and B, both of mass m= 125 kg. move in the same circular orbit of radius r= 7.87 x 106 m around Earth but in opposite senses of rotation and therefore on a collision Earth course. (a) Find the total mechanical en- ergy EA + ER of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tan- gled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth's center or or- biting around Earth? Figure 13-50 Problem 60.arrow_forwardA ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches. (b) Repeat the calculation for the same ball if it slides up the hill without rolling.arrow_forward(b) On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman's moment of inertia about the axis of rotation is 5.00 kg-m² and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if anyarrow_forward
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- (II) A potter’s wheel is rotating around a vertical axis through its center at a frequency of 1.5 rev/s. The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 2.6-kg chunk of clay,approximately shaped as a flat disk of radius 7.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it? Ignore friction.arrow_forwardA small mass m on a string is rotating without friction in a circle. The string is shortened by pulling it through the axis of rotation without any external torque, Fig. 8–39. What happens to the angular velocity of the object? (a) It increases. (b) It decreases. (c) It remains the same. FIGURE 8–39 MisConceptual Questions 10 and 11.arrow_forward(5) Calculate the moment M about point A, that is created by force F, located at point B (units are in meters). For full credit, determine the correct answer by using vectors and the cross-product method. F = -2î + 4j – 1k (N) %D y pt B (6,2,0) X pt A (5,0,2)arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning