The figure below shows, at left, a solid disk of radius R = 0.600 m and mass 75.0 kg. Tu Mounted directly to it and coaxial with it is a pulley with a much smaller mass and a radius of r = 0.230 m. The disk and pulley assembly are on a frictionless axle. A belt is wrapped around the pulley and connected to an electric motor as shown on the right. The turning motor gives the disk and pulley a clockwise angular acceleration of 1.67 rad/s². The tension T in the upper (taut) segment of the belt is 145 N. (a) What is the tension (in N) in the lower (slack) segment of the belt? N (b) What If? You replace the belt with a different one (one slightly longer and looser, but still tight enough that it does not sag). You again turn on the motor so that the disk accelerates clockwise. The upper segment of the belt once again has a tension of 145 N, but now the tension in the lower belt is exactly zero. What is the magnitude of the angular acceleration (in rad/s²)? rad/s²

A bridge truss extends x = 217 m across a river (shown in the figure below) where 0 = 40°. The structure is free to slide horizontally to permit thermal expansion. The structural components are connected by pin joints, and the masses of the bars are small compared with the mass of a 1300 kg car at the center. Calculate the force of tension or compression in each structural component (in N). B D T T T T T 22820 AB AC BC ||| || || || BD N ---Select--- N ---Select--- N ---Select--- N ---Select--- DE N ---Select--- T DC= N ---Select--- TEC N ---Select--- с ✓ E

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A block of mass m₁ = 1.85 kg and a block of mass m₂ is 0.360 for both blocks. 5.90 kg are connected by a massless string over a pulley in the shape of a solid disk having a mass of M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction m M, R m2 Ꮎ (a) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (b) Determine the tensions in the string on both sides of the pulley. left of the pulley right of the pulley N N

Consider as a system the Sun with Venus in a circular orbit around it. Find the magnitude of the change in the velocity of the Sun relative to the center of mass of the system during the time Venus completes half an orbit. Assume the mass of the Sun is 5.68 x 1029 kg, the mass of Venus is 4.87 × 1024 kg, its period is 1.94 × 107 s, and the radius of its orbit is 1.08 × 1011 m. Ignore the influence of other celestial objects. m/s

Your physics instructor loves to put on physics magic shows for elementary school children. He is working on a new trick and has asked you, his star physics student, for assistance. The figure below shows the apparatus he is designing. Cup Hinged end - Support stick A small ball rests on a support so that the center of the ball is at the same height as the upper lip of a cup of negligible mass that is attached to a uniform board of length = 1.89 m. When the support stick is snatched away, the ball will fall and the board will rotate around the hinged end. As the board hits the table, your instructor wants the ball to fall into the cup. The larger the angle 0, the more time the elementary school children will have to watch the progress of the trick. But if the angle is too large, the cup may not pull ahead of the ball. For example, in the limiting case of 90°, the board would not fall at all! (a) Your instructor wishes to know the minimum angle 0 (in degrees) at which the support would…

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= Consider the schematic of the molecule shown, with two hydrogen atoms, H, bonded to an oxygen atom, O. The angle between the two bonds is 106°. If the bond length r 0.106 nm long, locate the center of mass of the molecule. The mass mH of the hydrogen atom is 1.008 u, and the mass mo of the oxygen atom is 15.9999 u. (Use a coordinate system centered in the oxygen atom, with the x-axis to the right and the y-axis upward. Give the coordinates of the center of mass in nm.) XCM YOM = = H 53° 53° nm nm r H

An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk's center, as in the figure below. The disk has mass 2.60 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.700 m long. HINT (a) Find the ceiling fan's moment of inertia about a vertical axis through the disk's center. (Enter your answer in kg • m².) kg. m² (b) Friction exerts a constant torque of magnitude 0.113 N m on the fan as it rotates. Find the magnitude of the constant torque provided by the fan's motor if the fan starts from rest and takes 15.0 s and 17.5 full revolutions to reach its maximum speed. (Enter your answer in N. m.) N.m