Question Part Points Submissions Used A simple pendulum consists of circular bob

Question

Question Part Points Submissions Used A simple pendulum consists of circular bob that is attached to the end of a massless straight rod. The mass of the bob is m = 2.05 kg . The length of the massless rod is 3.65 m. The pendulum has a speed of 1.20 m/s at its equilibrium position. (a) What is the period of this pendulum? s (b) What is the total energy of the pendulum? J (c) What is the maximum angular displacement of the pendulum from its equilibrium position? (Find the angular displacement from the vertical.) °

Explanation / Answer

part a:

time period of the pendulum=2*pi*sqrt(l/g)

where l=length of the rod

time period=2*pi*sqrt(3.65/9.8)=3.8345 seconds

part b:

total energy of the pendulum=total kinetic energy at equilibrium position (as at this position, potential energy is zero)

=0.5*mass*speed^2

=0.5*2.05*1.2^2

=1.476 J

part c:

maximum angular displacement will occur when speed becomes zero and all the total energy is converted to potential energy.

if angle with vertical is theta, then height above equilibrium position=length of the rod*(1-cos(theta))

equating potential energy at this height to total enery,

mass*g*height=total energy

==>2.05*9.8*3.65*(1-cos(theta))=1.476

==>1-cos(theta)=1.476/(2.05*9.8*3.65)

==>theta=11.515 degrees

hence maximum displacement from vertical is 11.515 degrees

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