A simple pendulum has a mass of 0.650 kg and a length of 7.00 m. It is displaced

Question

A simple pendulum has a mass of 0.650 kg and a length of 7.00 m. It is displaced through an angle of 6.0 ^ degree and then released. Using the analysis model of a particle in simple harmonic motion, calculate the following. (Give your answer to the thousandths place.) (a) What is the maximum speed of the bob? m/s (b) What is the maximum angular acceleration of the bob? rad/s^2 (c) What is the maximum restoring force of the bob? N (d) Solve parts (a)through (c) by using other analysis models. (Hint: you may need to use separate analysis models for each part.) maximum speed m/s maximum angular acceleration rad/s^2 maximum restoring force N

Explanation / Answer

a)

Here , ampiltude , A = 6 degree

A = 0.1047 radians

Now, w = sqrt(g/L)

w = sqrt(9.80/7)

w = 1.183 rad/s

as maximum speed = A * w * L

maximum speed = 1.183 * 0.1047 * 7

maximum speed = 0.867 m/s

the maximum speed of bob is 0.867 m/s

b)

maximum angular acceleration = A* w^2 * L

maximum angular acceleration = 1.183^2 * 0.1047

maximum angular acceleration = 0.147 rad/s^2

the maximum angular acceleration of the bob is 0.147 rad/s^2

c)

maximum resisting force = m * a

maximum resisting force = 1.03 * 0.650

maximum resisting force = 0.67 N

the maximum resisting force is 0.67 N

d)

Now, for ,maximum speed , using conservation of energy

0.5 * m * v^2 = m * g * L * (1 - cos(theta))

v^2 = 2 * 9.8 * 7 * (1 - cos(6))

solving for v

v = 0.867 m/s

the maximum speed is 0.867 m/s

---------------------------

maximum restoring force = mg * sin(theta)

maximum restoring force = 0.650 * 9.8 * sin(6)

maximum restoring force = 0.67 N

the maximum restoring force is 0.67 N

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