If the 250-lb block is released from rest when the spring is unstretched, determine the velocity of the block after it has descended 5 ft. The drum has a weight of 40 Ib and a radius of gyration of k, = 0.5 ft about its center of mass 0. 0 375 6
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- A drum is used to drag a [ma]-kg block A up the slope (0 = [0]°). The coefficients of static and kinetic friction between the block and slope are 0.5 and 0.3 respectively. The [mp]-kg drum has a radius of 0.6 m and a radius of gyration of [k] mm. A constant torque of [t] Nm (CCW) is supplied to the drum. Assume the drum pivot is frictionless. „Lightweight cable A 0 T (a) Draw clear free body diagrams of block A and the drum. Values (b) Calculate the acceleration of block A and the tension in the cable. 24.1 MA 13.6 8.4 나나8 mp = k = 149Find the magnitude of the torque exerted by F on the bolt at P if PQ = 4 in. and F = 36 Ib. %3D 450 The magnitude of the torque exerted by F on the bolt at P is ..... ft-lb.The center of gravity of a simple pendulum of mass m and length L is located at the pendulum bob, a distance L from the pivot point. The center of gravity of a uniform rod of the same mass m and length 2L pivoted at one end is also a distance L from the pivot point. Compared to the period of the simple pendulum, is the period of this uniform rod (i) longer; (ii) shorter; or (iii) the same?
- Two masses, m1 and m2, are attached to a 1.95-m-long steel wire which runs over a light, frictionless pulley as shown. Assume the cross section of the wire is circular with a diameter of d = 4.00 mm, m1 = 3.30 kg, and m2 = 4.90 kg. The masses are released from rest and allowed to move freely. Compared with its length before the masses were attached, by how much has the wire stretched (in mm) while the masses are in\100 In Fig. 15-59, a solid cylinder attached to a horizontal spring (k = 3.00 N/m) rolls without slipping along a horizontal surface. If the sys- tem is released from rest when the м oo000d 00000 Figure 15-59 Problem 100. spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these condi- tions the cylinder's center of mass executes simple harmonic mo- tion with period ЗМ T = 27 2k where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.)