A simple pendulum with mass m = 1.4 kg and length L = 2.39 m hangs from the ceil

Question

A simple pendulum with mass m = 1.4 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of ݸ = 9.1ݰ from the vertical and released at t = 0.

1) What is the period of oscillation?

2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0?

3) What is the maximum speed of the pendulum?

4) What is the angular displacement at t = 3.57 s? (give the answer as a negative angle if the angle is to the left of the vertical)

6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position?

Explanation / Answer

a)

Period

T=2pi*sqrt[L/g] =2pi*sqrt[2.39/9.8]

T=3.1 s

b)

F=mgsin(o)=1.4*9.8*sin9.1

F=2.17 N

c)

By conservation of enery

mgL(1-cos(o))=(1/2)mV2

9.8*2.39*(1-cos9.1)=(1/2)*V2

V=0.7678 m/s

d)

O=OoCos(2pit/T) =9.1*Cos(2pi*3.57/3.1)

O=5.274 degrees

e)

W=2pi/T=2pi/3.1

W=2.03 rad/s

at=OoW2=(9.1*pi./180)*2.032

at=0.65 rad/s2

f)

ar=V2/L =0.592/2.39

ar=0.2467 m/s2

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