The 480lb cylinder at A is hoisted using the motor and the p

The 480-lb cylinder at A is hoisted using the motor and the pulley system shown. The speed of point B on the cable is increased at a constant rate from zero to vB = 30 ft/s int = 9 s . (Figure 1)

Part A

Determine the tension in the cable at B to cause the motion.

Express your answer to three significant figures and include the appropriate units.

lb

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Figure 1 of 1

Solution

From the figure it is evident,

velocity of point B, vB = 2*velocity of mass A = 2*vA

Now, using the equation of motion,

v = u + at

So, 30 = 0 +a*9

So, a = 30/9 = 3.33 ft/s2 <-----accelection of point B

So, acceleration of point A, aA = 3.33/2 = 1.67 m/s2

Now, 2T - mA*g = mA*aA

So, T = (480*1.67 + 480*32)/2 = 8080.8 lb