phys124s11-hw01 - HW 1 Solutions Equilibrium of a Mobile...

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HW 1 Solutions Equilibrium of a Mobile Conceptual Question ( Conceptual Question). The artist Anya Calderona constructs the mobile shown in the figure. In the illustrated configuration, the mobile is perfectly balanced. If Anya decides to make the star twice as massive, and not change the length of any crossbar or the location of any object, what does she have to do with the mass of the smiley face to keep the mobile in perfect balance? Note that she may have to change masses of other objects to keep the entire structure balanced. Answer : make it twice as massive. Test Your Understanding 10.3: Rigid-Body Rotation about a Moving Axis. A uniform cylinder rolls up an incline without slipping. As it rolls uphill, its speed decreases. The surface of the incline and the cylinder are both perfectly rigid. Which of the forces on the cylinder exert(s) a torque about the center of the cylinder? Answer: the friction force. Since the surface and incline are perfectly rigid, the normal force exerted by the incline on the cylinder is directed toward the cylinder's center. Hence, this force exerts zero torque about the center. The weight of the cylinder acts at its center (because the cylinder is uniform), so this force also exerts zero torque around the center. The friction force acts tangential to the circumference of the cylinder, so it does exert a torque around the center. Torque Magnitude Ranking Task. The wrench in the figure has six forces of equal magnitude. Rank these forces (A through F) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt. Rank from largest to smallest. To rank items as equivalent, overlap them. We assume that all the forces are of the same magnitude. The moment arm values (ranked from largest to smallest): D, B and E, F, A, C. The moment arm that corresponds to F is greater than that for A because the angle between the wrench axis and horizontal direction is less than 45 0 . Net Torque on a Pulley. The figure below shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord's weight can be ignored.
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The statement that correctly describes the system shown in the figure: the angular acceleration of the pulley is nonzero. Indeed, block B moves with acceleration down, block A moves with acceleration up. Since the cord moves on the pulley without slipping, the linear speed of the pulley surface, v , increases, and this means that the angular acceleration is nonzero: dd v dt dt r ω α ⎛⎞ == ⎜⎟ ⎝⎠ , where r is the radius of the pulley. On the other hand, this also means that the net torque on the pulley is nonzero: I τ = where τ is the net torque on the pulley, I is the pulley’s moment of inertia.
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phys124s11-hw01 - HW 1 Solutions Equilibrium of a Mobile...

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