PROBLEMS. Apago PDF Enhancer

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Abigail Conley
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1 PROLMS mm rod rests on a horizonta tabe. force P appied as shown produces the foowing acceerations: a m/s 2 to the right, a 5 6 rad/s 2 countercockwise as viewed from above. etermine the acceeration (a) of point, (b) of point. P 0.45 m 0.45 m Fig. P and P In Prob , determine the point of the rod that (a) has no acceeration, (b) has an acceeration of 2.4 m/s 2 to the right ft stee beam is owered by means of two cabes unwinding at the same speed from overhead cranes. s the beam approaches the ground, the crane operators appy brakes to sow down the unwinding motion. t the instant considered the deceeration of the cabe attached at is 12 ft/s 2, whie that of the cabe at is 5 ft/s 2. etermine (a) the anguar acceeration of the beam, (b) the acceeration of point. pago PF nhancer The acceeration of point is 1 ft/s 2 downward and the anguar acceeration of the beam is 0.8 rad/s 2 cockwise. Knowing that the anguar veocity of the beam is zero at the instant considered, determine the acceeration of each cabe and ar is attached to two inks and. Knowing that at the instant shown ink has zero anguar acceeration and an anguar veocity of 3 rad/s cockwise, determine the acceeration (a) of point, (b) of point. 9 ft Fig. P and P ft 240 mm 240 mm 180 mm 180 mm Fig. P Fig. P

2 966 Kinematics of Rigid odies n automobie traves to the eft at a constant speed of 48 mi/h. Knowing that the diameter of the whee is 22 in., determine the acceeration (a) of point, (b) of point, (c) of point in. Fig. P Fig. P carriage is supported by a caster and a cyinder, each of 50-mm diameter. Knowing that at the instant shown the carriage has an acceeration of 2.4 m/s 2 and a veocity of 1.5 m/s, both directed to the eft, determine (a) the anguar acceerations of the caster and of the cyinder, (b) the acceerations of the centers of the caster and of the cyinder. 75 mm Fig. P and P The motion of the 75-mm-radius cyinder is controed by the cord shown. Knowing that end of the cord has a veocity of 300 mm/s and an acceeration of 480 mm/s 2, both directed upward, determine the acceeration (a) of point, (b) of point. pago PF nhancer The motion of the 75-mm-radius cyinder is controed by the cord shown. Knowing that end of the cord has a veocity of 300 mm/s and an acceeration of 480 mm/s 2, both directed upward, determine the acceerations of points and of the cyinder and in.-radius drum is rigidy attached to a 5-in.- radius drum as shown. One of the drums ros without siding on the surface shown, and a cord is wound around the other drum. Knowing that at the instant shown end of the cord has a veocity of 8 in./s and an acceeration of 30 in./s 2, both directed to the eft, determine the acceerations of points,, and of the drums. 3 in. 5 in. 3 in. 5 in. Fig. P Fig. P15.116

3 The 150-mm-radius drum ros without sipping on a bet that moves to the eft with a constant veocity of 300 mm/s. t an instant when the veocity and acceeration of the center of the drum are as shown, determine the acceerations of points,, and of the drum. Probems mm/s 900 mm/s mm/s Fig. P in The 18-in.-radius fywhee is rigidy attached to a 1.5-in.-radius shaft that can ro aong parae rais. Knowing that at the instant shown the center of the shaft has a veocity of 1.2 in./s and an acceeration of 0.5 in./s 2, both directed down to the eft, determine the acceeration (a) of point, (b) of point. pago PF nhancer In the panetary gear system shown the radius of gears,,, and is 3 in. and the radius of the outer gear is 9 in. Knowing that gear has a constant anguar veocity of 150 rpm cockwise and that the outer gear is stationary, determine the magnitude of the acceeration of the tooth of gear that is in contact with (a) gear, (b) gear. 20 Fig. P The disk shown has a constant anguar veocity of 500 rpm countercockwise. Knowing that rod is 250 mm ong, determine the acceeration of coar when (a) u 5 90, (b) u mm Fig. P Fig. P In the two-cyinder air compressor shown the connecting rods and are each 190 mm ong and crank rotates about the fixed point with a constant anguar veocity of 1500 rpm cockwise. etermine the acceeration of each piston when u 5 0. Fig. P mm 45

4 968 Kinematics of Rigid odies rm has a constant anguar veocity of 16 rad/s countercockwise. t the instant when u 5 0, determine the acceeration (a) of coar, (b) of the midpoint of bar. 10 in. 3 in. 6 in. P Fig. P15.122, P15.123, and P rm has a constant anguar veocity of 16 rad/s countercockwise. t the instant when u 5 90, determine the acceeration (a) of coar, (b) of the midpoint of bar rm has a constant anguar veocity of 16 rad/s countercockwise. t the instant when u 5 60, determine the acceeration of coar. 50 mm Fig. P and P Knowing that crank rotates about point with a constant anguar veocity of 900 rpm cockwise, determine the acceeration of the piston P when u pago PF nhancer Knowing that crank rotates about point with a constant anguar veocity of 900 rpm cockwise, determine the acceeration of the piston P when u Knowing that at the instant shown rod has zero anguar acceeration and an anguar veocity of 15 rad/s countercockwise, determine (a) the anguar acceeration of arm, (b) the acceeration of point. 4 in. 5 in. 5 in. 4 in. 3 in. Fig. P and P mm 90 mm Knowing that at the instant shown rod has zero anguar acceeration and an anguar veocity of 15 rad/s countercockwise, determine (a) the anguar acceeration of member, (b) the acceeration of point. 90 mm Knowing that at the instant shown rod has a constant anguar veocity of 6 rad/s cockwise, determine the acceeration of point. 225 mm 225 mm Fig. P and P Knowing that at the instant shown rod has a constant anguar veocity of 6 rad/s cockwise, determine (a) the anguar acceeration of member, (b) the acceeration of point.

5 Knowing that at the instant shown rod has zero anguar acceeration and an anguar veocity v 0 cockwise, determine (a) the anguar acceeration of arm, (b) the acceeration of point. Probems t the instant shown rod has zero anguar acceeration and an anguar veocity of 8 rad/s cockwise. Knowing that m, determine the acceeration of the midpoint of member and Knowing that at the instant shown bar has a constant anguar veocity of 4 rad/s cockwise, determine the anguar acceeration (a) of bar, (b) of bar. Fig. P and P mm 7 in. 4 in. 500 mm 8 in. pago PF nhancer 3 in. 400 mm 400 mm Fig. P and P Fig. P and P and Knowing that at the instant shown bar has an anguar veocity of 4 rad/s and an anguar acceeration of 2 rad/s 2, both cockwise, determine the anguar acceeration (a) of bar, (b) of bar by using the vector approach as is done in Sampe Prob enoting by r the position vector of a point of a rigid sab that is in pane motion, show that (a) the position vector r of the instantaneous center of rotation is r 5 r 1 V 3 v v 2 v Where V is the anguar veocity of the sab and v is the veocity of point, (b) the acceeration of the instantaneous center of rotation is zero if, and ony if, r w a 5 a v v 1 V 3 v O r a where 5 ak is the anguar acceeration of the sab. Fig. P15.137

6 970 Kinematics of Rigid odies * The whees attached to the ends of rod ro aong the surfaces shown. Using the method of Sec. 15.9, derive an expression for the anguar veocity of the rod in terms of v, u,, and b. b d v Fig. P and P * The whees attached to the ends of rod ro aong the surfaces shown. Using the method of Sec and knowing that the acceeration of whee is zero, derive an expression for the anguar acceeration of the rod in terms of v, u,, and b. Fig. P b * The drive disk of the Scotch crosshead mechanism shown has an anguar veocity V and an anguar acceeration, both directed countercockwise. Using the method of Sec. 15.9, derive expressions for the veocity and acceeration of point. pago PF nhancer * Rod moves over a sma whee at whie end moves to the right with a constant veocity v. Using the method of Sec. 15.9, derive expressions for the anguar veocity and anguar acceeration of the rod. b x Fig. P and P * Rod moves over a sma whee at whie end moves to the right with a constant veocity v. Using the method of Sec. 15.9, derive expressions for the horizonta and vertica components of the veocity of point. * disk of radius r ros to the right with a constant veocity v. enoting by P the point of the rim in contact with the ground at t 5 0, derive expressions for the horizonta and vertica components of the veocity of P at any time t.

*15.144 t the instant shown, rod rotates with an anguar veocity V and an anguar acceeration, both cockwise. Using the method of Sec. 15.9, derive expressions for the veocity and acceeration of point.

7 * t the instant shown, rod rotates with an anguar veocity V and an anguar acceeration, both cockwise. Using the method of Sec. 15.9, derive expressions for the veocity and acceeration of point Rate of hange of a Vector with Respect to a Rotating Frame 971 Fig. P and P r * t the instant shown, rod rotates with an anguar veocity V and an anguar acceeration, both cockwise. Using the method of Sec. 15.9, derive expressions for the horizonta and vertica components of the veocity and acceeration of point. * The position of rod is controed by a disk of radius r which is attached to yoke. Knowing that the yoke moves verticay upward with a constant veocity v 0, derive an expression for the anguar acceeration of rod. Fig. P * In Prob , derive an expression for the anguar acceeration of rod. pago PF nhancer * whee of radius r ros without sipping aong the inside of a fixed cyinder of radius R with a constant anguar veocity V. enoting by P the point of the whee in contact with the cyinder at t 5 0, derive expressions for the horizonta and vertica components of the veocity of P at any time t. (The curve described by point P is a hypocycoid.) * In Prob , show that the path of P is a vertica straight ine when r 5 R/2. erive expressions for the corresponding veocity and acceeration of P at any time t. R r y Fig. P w P x RT OF HN OF VTOR WITH RSPT TO ROTTIN FRM We saw in Sec that the rate of change of a vector is the same with respect to a fixed frame and with respect to a frame in transation. In this section, the rates of change of a vector Q with respect to a fixed frame and with respect to a rotating frame of reference wi be considered. You wi earn to determine the rate of change of Q with respect to one frame of reference when Q is defined by its components in another frame. It is recaed that the seection of a fixed frame of reference is arbitrary. ny frame may be designated as fixed ; a others wi then be considered as moving. Photo 15.7 geneva mechanism is used to convert rotary motion into intermittent motion.

1) For a block of mass m to slide without friction up a rise of height h, the minimum initial speed of the block must be

1) For a block of mass m to slide without friction up a rise of height h, the minimum initial speed of the block must be v m 1) For a bock of mass m to side without friction up a rise of height h, the minimum initia speed of the bock must be a ) gh b ) gh d ) gh e ) gh c ) gh P h b 3 15 ft 3) A man pus a pound crate up a