3) Figure 4 illustrates a fireman (Bill) having mass M1 standing on a scale, which is positioned on a solid horizontal surface. An ideal rope extends vertically upward from Bill's hands, up and over an ideal pulley having a fixed axis of rotation. The rope extends vertically downward from the pulley to a block having mass M2. Bill is controlling the motion of the block by pulling on the rope downward (if the block is traveling upward) or by allowing the rope to controllably slide through his hands (if the block is traveling downward).
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- The Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. The pulley can be approximated by a uniform disk with mass m, = 6.13 kg and 17.9 kg radius r, = 0.150 m. The hanging masses are m and mg = 12.9 kg. Calculate the magnitude of the masses' acceleration a and the tension in the left and right ends of the rope, Ti and TR, respectively. m/s? a = N Ti = m. MR TRIf an astronaut on the International Space Station accidentally left a wrench in space, the wrench would burn up as it re-entered the Earth's atmosphere, long before it hit the Earth. This question is about what would happen before that. Figure 1 Before After A wrench with a mass of 0.29 kg began at rest at a distance of d1 = 4.12 x 10° meters from the center of the Earth. The wrench then began falling toward Earth. Sometime later, the wrench was at a distance of d2 = 3.98 x 10° meters from the center of the Earth. Assume that the only significant force acting on the wrench was the gravitational force exerted by the Earth. The mass of the Earth is 5.97 x 1024 kg. Newton's gravitational constant is G = 6.67 x 1011 m³/(kg s²) (the denominator is kilograms to the first power times seconds squared) Calculate the speed of the wrench in units of meters per second when it is at a distance d2 from the center of the Earth.PRINTER VERSION BACK NEXT Chapter 10, Problem 051 GO In the figure, block 1 has mass m, - 488 g, block 2 has mass m, = 551 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.78 cm. When released from rest, block 2 falls 71 9 cm in 5 27 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T, (the tension force on the block 2) and (c) tension T, (the tension force on the block 1)? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia? Caution: Try to avoid rounding off answers along the way to the solution. Use g = 9.81 m/s. m2 (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
- While working as an intern in a blacksmith's shop, you realize that the brake on the sharpening stone (a stone uniform disk) is no longer working. To stop the rotation at the end of the day, you put your knowledge of physics to good use and use a steel axe to stop the rotation. You press the steel axe against the stone using a radial force of 19.5 N. The stone is originally rotating at a rate of 85 revolutions per minute (out of the page), has a radius of 0.350 m, and a mass of 91.0 kg. Choose out of the page to be positive. a) Given a coefficient of kinetic friction between the stone and the axe equal to 0.20, what is the angular acceleration of the sharpening stone? b) What angular displacement did the stone turn through from its initial angular speed to when the stone stops rotating?pulley m Figure 8-78 Problem 97. Type your answers in all of the blanks and submit X, ** In Figure 8-78, a rope is wound around a horizontal disk (Md = 2.90 kg and Rd = 20.0 cm), passed across a pulley (with negligible mass), and connected to a hanging 4.00 kg mass. Initially, the mass is held in place, and the system is at rest. The mass is then released and descends in response to the force of gravity. The rope does not slip on the pulley or the horizontal disk. Both the pulley and the disk rotate on bearings that are effectively frictionless. Using energy considerations, (a) find the angular speed of the disk after the mass has descended 1.20 m. Type your answer here rad/s. Please type your answer to submit (b) calculate the acceleration of the mass. Type your answer here m/s2Problem 5: A 2.0 kg block, lying on a smooth table, is connected to another 5.0 kg block by means of a weightless cord passing over, without slipping, a cylindrical pulley of 2.0 kg mass and 10.0 cm radius placed at the edge of the table. The system is released from rest at t = 0. Consider g=9.8 m/s2. (a) In 0.3s the 5.0 kg block will drop by ________ (b) The tension in the part of cord connected horizontally to the 2.0 kg block is ________
- Block 1 with mass m1=502 kg rests on a horizontal ledge with negligible friction. This block is then attached to a string that passes over a pulley, and the other end of the string is attached to the hanging block 2 of mass m2=251 kg, as shown. The pulley is a uniform disk of radius 9.40 cm and mass 1.770 kg. Calculate the speed of block 2 after it is released from rest and falls a distance of 2.15 m. What is the angular speed of the pulley at the instant when block 2 has fallen a distance of 2.15 m?For each of the situations below, determine which forms of Newton's second law (N2L) are appropriate: N2L rotation, N2L translation, either, or both. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it. You are asked to find the angular acceleration of a low-friction pulley due to a mass hanging from it by a rope. You are asked to determine the maximum height of a spinning ball that is thrown upwards. You are asked to calculate the time it takes a ball to roll down an inclined plane. You are asked to find the tangential acceleration of a small satellite in a circular orbit that results from it firing its thruster. You are asked to determine the orbital period of a small satellite around Earth.Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 10.7 seconds to get up to its full speed of f1 = 78 revolutions per minute.Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 16 times while accelerating uniformly. a)Calculate the angular speed described in Case 1, given as f1 = 78 revolutions per minute, into units of radians/second. d)Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).