# chapter 5 answers - 5.3 a The two sides of the rope each...

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5.3: a) The two sides of the rope each exert a force with vertical component T θ sin , and the sum of these components is the hero’s weight. Solving for the tension T , . N 10 54 . 2 0.0 1 sin 2 ) s m (9.80 kg) 0 . 90 ( sin 2 3 2 × = ° = θ = w T b) When the tension is at its maximum value, solving the above equation for the angle θ gives . 01 . 1 N) 10 50 . 2 ( 2 s m (9.80 kg) (90.0 arcsin 2 arcsin 4 2 ° = × = = T w θ 5.8: a) . 0 45 cos 30 cos and , 45 sin 30 sin , = ° - ° = = ° + ° = B A C B A C T T w T T T w T Since , 45 cos 45 sin ° = ° adding the last two equations gives , ) 30 sin 30 (cos w T A = ° + ° and so . 732 . 0 366 . 1 w T w A = = Then, . 897 . 0 45 cos 30 cos w T T A B = = ° ° b) Similar to part (a), , 45 sin 60 cos , w T T w T B A C = ° + ° - = and . 0 45 cos 60 sin = ° - ° B A T T Again adding the last two, , 73 . 2 ) 60 cos 60 (sin w T w A = = ° - ° and . 35 . 3 45 cos 60 sin w T T B B = = ° ° 5.13: a) In the absence of friction, the force that the rope between the blocks exerts on block B will be the component of the weight along the direction of the incline, α w T sin = . b) The tension in the upper rope will be the sum of the tension in the lower rope and the component of block A ’s weight along the incline, . sin 2 sin sin α = α + α w w w c) In each case, the normal force is . cos α w d) When , , 0 w n = = α when . 0 , 90 = ° = α n 5.15: a) The tension is related to the masses and accelerations by . 2 2 2 1 1 1 a m g m T a m g m T = - = - b) For the bricks accelerating upward, let a a a = - = 2 1 (the counterweight will accelerate down). Then, subtracting the two equations to eliminate the tension gives . s m 96 . 2 kg 0 . 15 kg 0 . 28 kg 0 . 15 kg 0 . 28 s m 80 . 9 or , ) ( ) ( 2 2 1 2 1 2 2 1 1 2 = + - = + - = + = - m m m m g a a m m g m m c) The result of part (b) may be substituted into either of the above expressions to find the tension N. 191 = T As an alternative, the expressions may be manipulated to eliminate

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## This note was uploaded on 03/25/2008 for the course PHYS 218 taught by Professor Safonov during the Spring '06 term at Texas A&M.

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chapter 5 answers - 5.3 a The two sides of the rope each...

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