M 2M A block of mass M = 2.26 kg is at rest on a horizontal, frictionless surface. On one side a relaxed spring with a spring constant k = 169 N/m connects it to a wall; on the other side, a light string passing over a frictionless pulley connects it to another block, mass 2M, as shown. The pulley has a moment of inertia / = 4.9 x 10³ kg m² and a radius R = 0.053 m. A short time after the hanging block is released (from rest) it has fallen through a height of 0.091 m. At this point determine: a) the combined (total) kinetic energy of the blocks-and-pulley system J b) the rotational kinetic energy of the pulley. Krotal Krot = mJ
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- A string is wrapped around a disk of mass m = 2.2 kg and radius R = 0.08 m. Starting from rest, you pull the string with a constant force F = 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x = 0.12 m, your hand has moved a distance of d = 0.27 m. m d (a) At this instant, what is the speed of the center of mass of the disk? Vcm = m/s (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? Krot = Additional Materials M eBookAn object of mass m, = 4.60 kg is connected by a light cord to an object of mass m, = 3.00 kg on a frictionless surface (see figure). The pulley rotates about a frictionless axle and has a moment of inertia of 0.520 kg m and a radius of 0.290 m. Assume that the cord does not slip on the pulley. 2 T2 (a) Find the acceleration of the two masses. m/s2 (b) Find the tensions T, and 12 T. T = T2 =An object of mass m, = 5.00 kg is connected by a light cord to an object of mass m, = 3.00 kg on a frictionless surface (see figure). The pulley rotates about a frictionless axle and has a moment of inertia of 0.560 kg · m2 and a radius of 0.290 m. Assume that the cord does not slip on the pulley. m2 medic ocume logy (a) Find the acceleration of the two masses. m/s2 (b) Find the tensions T, and T2. cer 3 T1 = T2 = Need Help? Read It na's docum
- The motion of spinning a hula hoop around one's hips can be modeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is less than R, the radius of the hoop. Suppose Maria spins a hula hoop with a mass of 0.74 kg and a radius of 0.67 m around her waist. The rotation axis is perpendicular to the plane of the hoop, but approximately 0.45 m from the center of the hoop. (a) What is the rotational inertia of the hoop in this case? 0.45 X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg. m² (b) If the hula hoop is rotating with an angular speed of 13.3 rad/s, what is its rotational kinetic energy? 0.74 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. JA puck of mass m = 1.10 kg slides in a circle of radius r = 19.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 4.10 kg by a cord through a hole in the table. What speed keeps the cylinder at rest?Two buckets of mass ?1=17.5 kg and ?2=15.1 kg are attached to the ends of a massless rope which passes over a pulley with a mass of ?p=8.53 kg and a radius of ?p=0.450 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction. The buckets are released from rest and begin to move. If the larger bucket is a distance ?0=2.05 m above the ground when it is released, with what speed ? will it hit the ground?
- The massive pully has moment of inertia I = 1/2MR2. Calculate the downward acceleration of the hanging mass (as a positive number, in m/s²). %3D • M = 700 grams %3D • m = 70 grams • R = 9 cm M, R mA 170-kg merry-go-round of radius 2.10 m is rotated by pulling a rope that is wrapped around its edge. What is the magnitude of the force (assume it to be constant) on the rope needed to bring the merry- go-round from rest to an angular speed of 0.400 rev/s in 3.00 s? (The moment of inertia of merry-go- round is 1/2MR2).Am1= 19.0-kg object and a m 2 = 9.0-kg object are suspended, joined by a cord that passes over a pulley with a radius of R = 30.0 cm and a mass of M = 3.00 kg as seen in the Figure. The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest d = 5.00 m apart. Treat the pulley as a uniform disk, and determine the speeds of the two objects as they pass each other. (Your result must be in units of m /s and include 2 digit after the decimal point. Maximum of 4% of error is accepted in your answer. Take g = 9.80 m/s 2.) Hint: For solid cylinder of disk the moment of inertia about an axis through center of mass is IcOM = MR %3D d.
- = - = 6. A mass M₁ 10 kg resting on a horizontal frictionless surface is attached to a M₂ = 7 kg weight by a light wire that passes over a frictionless pulley. See figure. The pulley has the shape of a uniform disk of mass M3 4 kg and radius R 0.3 m. After the system is released, find (a) the tension in the wire on both sides of the pulley, (b) the acceleration of M₁, and (c) the horizontal and vertical forces that the axle exerts on the pulley. M1 M 3 M2Zorch, an archenemy of Superman, decides to slow the Earth's rotation to once per 30.5 h by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.60 x 10' N (comparable to a Saturn V rocket's thrust). Assume the Earth's initial rotation is exactly once per 24.0 h to find how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains. The Earth's mass is 5.98 × 1024 kg and its radius is 6.38 x 106 m.) Additional Materials |Reading