The following information applies to the next two questions (18 and 19). Generic

Question

The following information applies to the next two questions (18 and 19). Generic man swings a rock attached to a massless rope in a horizontal circle around his head with constant speed as shown in the figure to the right. The rope has a length L = 0.850 meters. The rope makes an angle theta = 60.0degree with respect to vertical. 18. As viewed from the side, at the position shown in the Side View, what is the direction of the net force acting on the rock? 19. What is the speed of the rock? (A) 2.75 m/s (B) 3.53 m/s (C) 4.68 m/s (D) 5.17 m/s (E) 6.06 m/s

Explanation / Answer

18) B

because, the ball is in uniform circular motion.

so, accelereation is towards center. so, net force must be tpwards center.

19) B) 3.53 m/s

radius of orbit, r = L*sin(60)

= 0.85*sin(60)

= 0.736 m

Let T is the tension in the string.

Apply, Fnety = 0

T*cos(theta) - m*g = 0

T*cos(theta) = m*g ---(1)

Fnetx = T*sin(theta)

m*a_rad = T*sin(theta)

T*sin(theta) = m*v^2/r ---(2)

from the equations 1 and 2

tan(theta) = (m*v^2/r)/(m*g)

m*g*tan(theta) = m*v^2/r

v = sqrt(r*g*tan(theta))

= sqrt(0.736*9.8*tan(60))

= 3.53 m/s

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