Question

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 describes a cone. The acceleration of gravity is 9.8 m/s2, 2.7 m, 6 kg, 31C. What is the speed of the ball when it is in circular motion? Answer in units of m/s.

Answer 1

Answer:

a) -2.1731 m⁻s

Explanation:

L= length of thread, H= height of ball from ceiling,

N/B h= l cosФ, Ф=31°, l=2.7m,  g=9.8m⁻s, m= 6kg

Required to find speed v, of the ball in m⁻s

ω=√g/h, =√g/lcosФ

⇒ ω=√9.8/2.7×cos31°

= 1.992rad⁻s

Now, speed in m/s, v= r.ω

where tanФ= r/h ⇒

r= h×cos 31°

r= 2.7 × cos(31) × tan(31) =-1.0909m

v= 1.992× -1.0909 =  -2.1731 m/s