thermodynamics

MECH 292 – P.S. 13 Fall, 2015

Problem Set 13 (5 points)

Note: Problems labeled with an asterisk (*) are bonus problems worth 1 point each. These problems are due with your homework on Tuesday if you wish to complete them for credit. 1. Gear A on the drive shaft of an outboard motor has a radius rA = 0.6 in, while the meshed pinion gear B on the propeller shaft has a radius of rB = 1.1 in. Find the angular velocity of the propeller at t = 1.7 s, if the drive shaft rotates with an angular acceleration a = (400t3) rad/s2, where t is in seconds. The propeller is originally at rest, and the frame of the motor does not move. 2. Next, find the magnitude of the velocity and acceleration of point P, which is located on the tip of the propeller (above), at the instant t = 0.5 s. 3. The wheel below rolls without slipping with an angular velocity of w = 8 rad/s. Determine the magnitude of the velocity of B at the instant shown. *4. Find the angular velocity of the spool shown below, knowing that the cable is wrapped around its inner core. Assume that no slipping occurs between the spool and the platform.

MECH 292 – P.S. 13 Fall, 2015

5. The crank arm OA rotates with an angular velocity of 12 rad/s. Find the velocity of piston B and the angular velocity of rod AB for the instant shown. 6. Pinion gear A rolls on two gear racks as shown. If gear rack B is moving to the right at 4 ft/s and C is moving to the left at 2 ft/s, find the angular velocity of the pinion gear and the velocity of its center A. *7. A bowling ball is cast with a backspin of w = 10 rad/s. Its center O has a forward velocity v0 = 8 m/s. Find the velocity of point A when it is contact with the bowling alley floor.