PROBLEM = Knowing that P = 50 N, determine (a) the acceleration of block B, (b) the tension in the cord.
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1 PROLEM 1.16 lock ha a ma of 40 k, and block ha a ma of 8 k. The coefficient of friction between all urface of contact are 0.0 m k = Knowin that P = 50 N, determine (a) the acceleration of block, (b) the tenion in the cord. P 5 ontraint of cable: x x x x x contant. a a 0, or a a ume that block move down and block move up. lock : F 0: N W co 0 y W Fx ma : T N W in a x Eliminate N and a. a a T Win co W W lock : F 0: N N W co Pin 0 y N N W co Pin W W co Pin F m a : T W in F F Pco W a x a Win co W Win Wco a W Wco Pin Pco W a W W in W 3W co P in co W W heck the condition of impendin motion. 0.0, a a 0, 5 W W W W P in 3 co in co 0
2 PROLEM 1.16 ONTINUED P W W W W 3 co in in co = ( 0. 0)( 64)( 9. 81)co 5 ( 3)( 9. 81) 00. in 5 co5 = N < 50 N lock will move with P 50 N. alculate a uin 0.15, 5, and P 50 N. k a = ( W - W )in q - mk ( W 3 W ) co q P ( mk inq co q) W W ( 3)( 9. 81)in 5 ( 0. 15)( 64)( 9. 81)co 5 ( 50)( in 5 co 5 ) = ( 48)( 9. 81) = a = ( ) (9.81) = m/ (a) a = m/ (b) a T = W (inq mcoq) W a m/ = (8) (9.81) (in co 5 ) (8) (9.81) ( ) 5 T 59.8 N
3 5 m 0.9 m a 1 D 65 PROLEM 1. To tranport a erie of bundle of hinle to a roof, a contractor ue a motor-driven lift conitin of a horizontal platform which ride on rail attached to the ide of a ladder. The lift tart from ret and initially move with a contant acceleration a 1 a hown. The lift then decelerate at a contant rate a and come to ret at D, near the top of the ladder. Knowin that the coefficient of tatic friction between the bundle of hinle and the horizontal platform i 0.30, determine the laret allowable acceleration a 1 and the laret allowable deceleration a if the bundle i not to lide on the platform. cceleration a 1 : Impendin lip. F1 N N1 F m a : N W m a in65 y y 1 1 N W m a in m a in 65 1 F m a : F m a co65 x x 1 1 F N or ma co m a in a1 co in m/ a m/ 65 Deceleration a : Impendin lip. F N 0.30 N F ma : N W m a in65 y y 1 N1 W m ain 65 S F ma : F m a co65 x x F N or maco650.30m aco65 S 0.30 a co in m/ a 4.4 m/ 65
4 PROLEM 1.9 P The coefficient of friction between the three block and the horizontal urface are 0.5 and k 0.0. The mae of the block are m m 10 k, and m 5 k. Knowin that the block are initially at ret and that move to the riht throuh 0.8 m in 0.4, determine (a) the acceleration of each block, (b) the tenion in the cable, (c) the force P. Nelect axle friction and the mae of the pulley. Let the poitive direction for poition coordinate, velocitie, and acceleration be to the riht. Let the oriin lie at the fixed anchor. ontraint of cable: x x x x x 3 contant 4a a 3a 0 (1) lock : F 0: N m 0 y N m, F N m k k F m a : 3T F m a x x a 3T km 3T 0.0 () m 10 lock : N m, F m k F m a : T F m a x a T km T 0.0 (3) m 5 lock : N m, F m k F m a : P 4T m a (4) x 1 1 Kinematic: x x v at 0 at o o a x o 0.4 x m/ (5) t Subtitute (), (3) and (5) into (1). T 3T T
5 PROLEM 1.9 ONTINUED T ( )( ) = = = N From (4), P T m a ( )( ) ( )( ) = 4 = = N From (), From (3), ( 3)( 9.94) ( 0.0)( 9.81) 6.86 m/ a = = 10 ( )( 9.94) ( 0.0)( 9.81) m/ a = = 5 (a) cceleration vector. a 6.83 m/ = a 9.76 m/ = a 10 m/ = Since a, a, and a are to the riht, the friction force F, F, and F are to the left a aumed. (b) Tenion in the cable. (c) Force P. T = 9.3 N P = 37 N
6 PROLEM N 5 7 k 15 k The 15 k block i upported by the 7 k block and i attached to a cord to which a 50 N horizontal force i applied a hown. Nelectin friction, determine (a) the acceleration of block, (b) the acceleration of block relative to. a a a/, where a / i directed alon the inclined contact urface. lock : F x max : T W in 5 m a co5 m a / (15 co 5 ) a 15 a / = 50 (15) (9.81) in a 15 a / = (1) F m a : N W co5 m a in5 y y (15 in 5 ) a N = (15) (9.81) co 5 or a N = () lock : F ma : T Tco5 N in5 m a x x 7 a (in 5 ) N = 50 (1 co 5 ) Uin () and (3) to eliminate 7 a 0.46 N 3.43 (3) N and olve for a, (a) cceleration of block. a.7m/ Subtitutin for a into (1) and olvin for a /, (b) cceleration of relative to. a / 10 m/ 5
7 0 PROLEM k block ret on an inclined urface, and a 15-k counterweiht i attached to a cable a hown. Nelectin friction, determine the acceleration of and the tenion in the cable immediately after the ytem i releaed from ret. Let the poitive direction of x and y be thoe hown in the ketch, and let the oriin lie at the cable anchor. ontraint of cable: x y/ contant or a a/ 0, where the poitive direction of a and a / are repectively the x and the y direction. Then a / a (1) Firt note that a a a a a / / 0 0 lock : : in0 F m a m N m a x x ma N m in 0 15 a N () F m a : m co0 T m a y y / ma / T mco 0 15 a T (3) / lock : F m a : m in0 N T m a x ma N T min 0 5 a N T (4) / Eliminate a / uin Eq. (1), then add Eq. (4) to Eq. () and ubtract Eq. (3). a a 55 a or m/, m/ From Eq. (1), a / m/ From Eq. (3), T 137. N T 137. N
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