A conical pendulum is a weight or bob fixed on the end of a string suspended fro
ID: 1351727 • Letter: A
Question
A conical pendulum is a weight or bob fixed on the end of a string suspended from a pivot. It moves in a horizontal circular path, as shown in the diagram below.
What is the magnitude of the centripetal force acting on the pendulum bob in terms of the tension T and angle ?
Fc = ?
Suppose the bob has a mass of 0.29 kg, the length of the pendulum is 0.85 m and the angle that it swings at is 14°.
What is the magnitude of the centripetal acceleration?
What is the radius of the horizontal circular path?
What is the speed of the mass?
Explanation / Answer
a)
Here The bob is in equilibrium in y-direction.
so, Fnety = 0
T*cos(theta) - m*g = 0
T = m*g/cos(theta)
Fc = T*sin(theta)
= m*g*sin(theta)/cos(theta)
= m*g*tan(theta)
b) Fc = 0.29*9.8*tan(14)
= 0.7086 N
c) a = Fc/m
= 0.7086/0.29
= 2.44 m/s^2
d) from figure, r = L*sin(14)
= 0.85*sin(14)
= 0.206 m
e) a = v^2/r
==> v = sqrt(a*r)
= sqrt(2.44*0.206)
= 0.708 m/s
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