Please answer and explain questions 2-3. A small metal ball is suspended from th

Question

Please answer and explain questions 2-3.

A small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread's trajectory describes a cone. The acceleration of gravity is 9.8 m/s2. What is the speed of the ball when it is in circular motion? Answer in terms of g,l and theta How long does it take Tperiod for the ball to rotate once around axis? In order to slide a heavy desk across the floor at constant speed in a straight line, you have to exert a horizontal force of 300 Newtons. Compare the 300-Newton horizontal pushing force F to the frictional force f between the desk and the ground. It depends on the direction the desk moves. F f; the frictional force is always less than any other force acting on the object.

Explanation / Answer

1) sum forcesin the y
T cos theta - mg = 0
T = mg/cos theta

sum forces in the x
T sin theta = mv^2/r

mg tan theta = mv^2/r

r = l sin theta

so v = sqrt( g l tan theta sin theta)

so 1)

2) T = 2 pi r/v = 2 pi l sin theta/sqrt(g l tan theta sin theta)

= 2 pi sqrt( l sin theta/(g tan theta))
= 2 pi sqrt( l co shteta/g)

so 5)

3)
since constant speed a = 0
so F = f from first law

so 4)

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