A 100-kg barrel with a radius of 31.5 cm has two ropes wrapped around it, as sho
ID: 1264878 • Letter: A
Question
A 100-kg barrel with a radius of 31.5 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 = 11.9 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 31.5 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 = 11.9 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.Explanation / Answer
Let the center of the cylinder falls with an acceleration a.
The angular acceleration @ of the cylinder about its axis is
@ = a / r ( a = @*r), ( a= linear acceleration)
The equation of motion for the center of mass of the cylinder is
mg - 2T = ma ---------------------1 ( T = tension in the rope)
equation for motion about the center of mass is;
2 T r = ( 1/2* m r2 *@) ( from torque= F*r -------------------A
By putting the value of @ ( also torque = I* @ ( I = moment of interia = 1/2 * m r2) -------------B
2T = 1/2 *m*a -------------------2 ( from eq A and B, F*r = I*@, 2 T*r = 1/2 m r2 *@ )
From equations 1 and 2:
a = 2/3 *g , T = mg / 6
(b) tension in the rope T= mg / 6
T = 100* 9.8/ 6 = 163.3 N
(a) Since center of cylinder starts moving from rest, initial velocity u = 0
Velocity after it has fallen through a distance h is
v = (4gh/3)1/2 (from v2 - u2 = 2as , v = (2as)1/2 = (2* 2/3*g*h)1/2 )
v = 12.46 m/s
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.