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 = 9.1° 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)

5)

What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position?

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=0.59 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=0.1456 m/s2

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