Question

Two blocks are connected by a lightweight string passing over a pulley, as shown in the figure below. The block with mass m = 16.5 kg on the incline plane accelerates up the plane with negligible friction. The block's acceleration is a = 1.80 m/s2, and the tension in the segment of string attached to this block is T,. The hanging block has a mass of m, = 23.5 kg, and the tension in the string attached to it is T,. The radius of the pulley is r 0.270 m and its moment of inertia is I. The incline plane makes an angle of e 37.0° with the horizontal. Ti T2 mo ө (a) What is the tension force T,? (Give your answer, in N, to at least three significant figures.) Enter a number.bck on the plane as the system and apply Newton's second law to relate the forces to its acceleration. What forces act on the block? What are their directions? N (b) What is the tension force 7T,? (Give your answer, in N, to at least three significant figures.) (c) Find a symbolic expression for the moment of inertia of the pulley in terms of the tensions T, and T, the pulley radius r, and the acceleration a. (Do not substitute numerical values; use variables only.) (d) What is the numerical value of the moment of inertia of the pulley? (Give your answer in kg .m2.) kg m2

Answer 1

nd laus By Nautar's en mi AT Tm at mia Sn 2 atgsine) TE 16.5(1.8 (4.8.xSin 22)). 16.s C.8t S.89) N m, (at 127 yNeuten's d g-Te mg-ma =m T23.59.8-1) law on mga- = 23.SX 8 TN 88 Fron tiguae Taque in pully r T-1 Mle tegue T-T- (T-T) a puctting valus .2218-127) I = 9.15 1 1.8

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