I am getting 6.548 m/s and the Quest home work service is saying that im incorre

Question

I am getting 6.548 m/s and the Quest home work service is saying that im incorrect. Please Help!

I am getting 6.548 m/s and the Quest home work service is saying that im incorrect. Please Help! Two masses of 23 kg and 15 kg are suspended by a pulley that bas a radius of 11 cm and a mass of 6 kg. The cord has a negligible mass and causes the pulley to rotate without slipping. The pulley rotates without friction. The masses start from rest 3.9 m apart. Determine the speeds of the two masses as they pass each other. Treat the pulley as a uniform disk. The acceleration of gravity is 9.8m/s^2. Answer in units of m/s.

Explanation / Answer

When both the masses pass each other they will travel a distance of

                   h = 3.9/ 2 = 1.95 m

change in PE for 23 kg = +23*9.8*1.95 we will take downward as +ve

change in PE of 15 kg   = -15*9.8*1.95

Total change of PE = 8*9.8*1.95 = 152.88 J

Let v be the speed at that instant

KE of 23kg = 0.5*23*v^2 = 11.5v^2

KE of 15kg = 0.5*15*v^2 = 7.5v^2

KE (rotational) of the pulley = 0.5 I^2

For a circular disc I = MR^2 /2

The rope is not slipping and hence any point on the rim of the pulley will have the same speed as that of the two masses and the rope

Hence angular speed of the pulley   = v/R

KE of the pulley = 0.5*MR^2/2*(v/R)^2 = 0.5*(6v^2)/2 = 1.5v^2

Total KE = (11.5+7.5+1.5)v^2 = 152.88 J (net change in PE)

V= 2.73 m/s

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