http://s17.postimg.org/7gk898zwf/994.png A 100-kg barrel with a radius of 42.3 c

Question

http://s17.postimg.org/7gk898zwf/994.png

A 100-kg barrel with a radius of 42.3 cm has two ropes wrapped around it, as shown in the figure. The barrel is released from rest, causing the ropes to unwind and the barrel to fall spinning toward the ground.

a) What is the speed of the barrel after it has fallen a distance of h = 14.1 m?

b) What is the tension in each rope? Assume that the barrel's mass is uniformly distributed and that the barrel rotates as a solid cylinder.

A 100-kg barrel with a radius of 42.3 cm has two ropes wrapped around it, as shown in the figure. The barrel is released from rest, causing the ropes to unwind and the barrel to fall spinning toward the ground. What is the speed of the barrel after it has fallen a distance of h = 14.1 m? What is the tension in each rope? Assume that the barrel's mass is uniformly distributed and that the barrel rotates as a solid cylinder.

Explanation / Answer

equation of motion,

mg - 2T = ma

for the motion of centre of mass

2*T*r = (1/2*mr^2* alpha) = 1/2 *m*r * alpha

2T = m*a/2

solving these two equations

T = mg/6 and a = 2*g/3

Tension = 163.33 N

acc = 6.53 m/s2

v^2 = 2as

v^2 = 2 *6.53*14.1

speed of barrel, v = 13.57 m/s

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