The block on the frictionless incline is moving up with a constant acceleration of 2.00 m/s2. (a) Determine T1 and T2, the tensions in the two parts of the string. (b) Find the moment of inertia of the pulley.
72.A common demonstration, illustrated in Figure P10.72, consists of a ball resting at one end of a uniform board of length , hinged at the other end, and elevated at an angle . A light cup is attached to the board at rc so that it will catch the ball when the support stick is suddenly removed. (a) Show that the ball will lag behind the falling board when is less than 35.3. (b) If the board is 1.00 m long and is supported at this limiting angle, show that the cup must be 18.4 cm from the moving end.
73.As a result of friction, the angular speed of a wheel changes with time according to
d/dt = 0e– t
where 0 and are constants. The angular speed changes from 3.50 rad/s at t = 0 to 2.00 rad/s at t = 9.30 s. Use this information to determine and 0. Then determine (a) the magnitude of the angular acceleration at t = 3.00 s, (b) the number of revolutions the wheel makes in the first 2.50 s, and (c) the number of revolutions it makes before coming to rest.
74.The hour hand and the minute hand of Big Ben, the Parliament tower clock in London, are 2.70 m and 4.50 m long and have masses of 60.0 kg and 100 kg, respectively. (a) Determine the total torque due to the weight of these hands about the axis of rotation when the time reads (i) 3:00, (ii) 5:15, (iii) 6:00, (iv) 8:20, (v) 9:45. (You may model the hands as long thin uniform rods.) (b) Determine all times when the total torque about the axis of rotation is zero. Determine the times to the nearest second, solving a transcendental equation numerically.
75.(a) Without the wheels, a bicycle frame has a mass of 8.44 kg. Each of the wheels can be roughly modeled as a uniform solid disk with a mass of 0.820 kg and a radius of 0.343 m. Find the kinetic energy of the whole bicycle when it is moving forward at 3.35 m/s. (b) Before the invention of a wheel turning on an axle, ancient people moved heavy loads by placing rollers under them. (Modern people use rollers too. Any hardware store will sell you a roller bearing for a lazy susan.) A stone block of mass 844 kg