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HW6Problems

# HW6Problems - cords as 15.30 A pulley and two loads are...

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15.30 A pulley and two loads are connected by inextensible cords as shown. Load A has a constant acceleration of 300 mm/s 2 and an initial velocity of 240 mm/s, both directed upward. Determine (a) the number of revolutions executed by the pulley in 3 s, (b) the velocity and position of load B after 3 s, ( c) the acceleration of point D on the rim of the pulley at t = 0. 15.31 A pulley and two loads are connected by inextensible cords as shown. The pulley starts from rest at t = 0 and is accelerated at the uniform rate of 2.4 rad/s 2 clockwise. At t = 4 s, determine the velocity and position (a) of load A, (b) of load B. 15.32 Disk B is at rest when it is brought into contact with disk A which is rotating freely at 450 rpm clockwise. After 6 s of slippage, during which each disk has a constant angular acceleration, disk A reaches a final angular velocity of 140 rpm clockwise. Determine the angu- lar acceleration of each disk during the period of slippage. Fig. P15.32 and P15.33 15.33 and 15.34 A simple friction drive consists of two disks A and B. Initially, disk A has a clockwise angular ve locity of 500 rpm and disk B is at rest. It is known that disk A will coast to rest in 60 s. However, rather than waiting until both disks ar e at rest to bring them together, disk B is given a constant angular acceleration of 2.5 rad/s 2 counterclockwise. Determine (a) at what time the disks can be brought together if they are not to slip, (b) the angular veloc- ity of each disk as contact is made. 15.35 Two friction disks A and B are both rotating freely at 240 rpm counterclockwise when they are brought into contact. After 8 s of slippage, during which each disk has a constant angular accelera- tion, disk A reaches a final angular velocity of 60 rpm counter- clockwise. Determine ( a) the angular acceleration of each disk during the period of slippage, (b) the time at which the angular D Fig . P15.30 and P15.31 velocity of disk B is equal to zero. Fig. P15.34 and P15.35

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15.48 In the planetary gear system shown, the radius of gears A, B, C, and D is 3 in. and the radius of the outer gear E is 9 in. Knowing that gear E has an angular velocity of 120 rpm clockwise and that the central gear has an angular velocity of 150 rpm clockwise, determine (a) the angular velocity of each planetary gear, (b) the angular veloc- ity of the spider connecting the planetary gears. Fig. P15.48 and P15.49 15.49 In the planetary gear system shown the radius of the central gear A is a, the radius of each of the planetary gears is b, and the radius of the outer gear E is a + 2b. The angular velocity of gear A is wA clockwise, and the outer gear is stationary. If the angular velocity of the spider BCD is to be wA/5 clockwise, determine (a) the required value of the ratio b!a , (b) the corresponding angu- lar velocity of each planetary gear. 15.50 Gear A rotates with an angular velocity of 120 rpm clockwise.
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