Answer to Question #158497 in Physics for jillian fairchild

Question

a string is wrapped around a uniform homogeneous 3 kg solid cylinder with a 15 cm radius. The free end is attached to the ceiling from which the cylinder is then allowed to fall, starting from rest. As the string unwraps, the cylinder revolves.

a) what is the linear acceleration of the center of mass?

b) what is the linear velocity of the outer edge of the cylinder after a drop of 2m?

c) How fast is the cylinder revolving after a drop of 2m?

d) what is the tension in the chord?

Answer 1

a)

$$TR=I\alpha\\a=R\alpha\\I=\frac{1}{2}MR^2\\T=\frac{1}{2}Ma\\Ma=Mg-T\\T=\frac{1}{3}Mg$$

$$a=\frac{2}{3}g$$

b)

$$2as=v^2\\2(0.15)\frac{2}{3}(9.8)=v^2\\v=1.4\frac{m}{s}$$

c)

$$\omega=\frac{v}{R}=\frac{1.4}{0.15}=9.3\frac{rad}{s}$$

d)

$$T=\frac{1}{3}Mg=\frac{1}{3}(3)(9.8)=9.8\ N$$