Two mass are connected by a rope/pulley system as shown in the above diagram, wh

Question

Two mass are connected by a rope/pulley system as shown in the above diagram, where m1 = 22.5kg and the length of rope from the center of mass of m2 to the nearest pulley is 4.98m. (a) If we know m2 = 11.5kg, then what maximum initial angle from the pulley can m2 be released from so that m1 never leaves the ground? (b) If we, however, do not yet know the mass of m2 but want to release it from an angle, ? = 28.5o, then how big can m2 be before causing m1 to leave the ground? http://i.imgur.com/Hrl8bF3.jpg

Explanation / Answer

T = m1g = 22.5 * 9.8 = 220.5 N

now on m2

T - mg = mV^2/r

220.5 - 112.7 = mv^2/r

v = 6.83 m/s

mgh(1-cos?) = 1/2mV^2

2gh(1-cos?) = 46.65

? = cos inverse ( 1 -0.477 ) = 58.5 deg

b)for m1 to leave ground

T = m1g = 220.5 N

mgh(1-cos28.5) = 1/2mv^2

v = 3.44 m/s

T - mg = mv^2/r

220.5- 9.8m = 2.37m

m = 18.17 kg

therfore m2 should be greater than 18.17 kg

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