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Chapter 10: Problem 55

What is the period of a pendulum consisting of a \(6.0-\mathrm{kg}\) mass oscillating on a 4.0 -m-long string?

Short Answer

Expert verified
Answer: The period of the pendulum is approximately 4.03 s.

Step by step solution

01

Identify the given values and the formula to use

We are given the mass of the pendulum (\(6.0\, \mathrm{kg}\)) and the length of the string (\(4.0\, \mathrm{m}\)). We need to find the period (T) of the pendulum. The formula to use is: \(T = 2\pi\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}\).
02

Plug in the given values

Now, substitute the given values into the formula: \(T = 2\pi\sqrt{\frac{4.0\, \mathrm{m}}{9.81\, \mathrm{m/s^2}}}\).
03

Calculate the period

Calculate the square root of the ratio and then multiply by \(2\pi\): \(T \approx 2\pi\sqrt{0.408} \approx 4.03\, \mathrm{s}\).
04

Write the answer

The period of the pendulum with a \(6.0\, \mathrm{kg}\) mass oscillating on a \(4.0\, \mathrm{m}\)-long string is approximately \(4.03\, \mathrm{s}\).

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Most popular questions from this chapter

A sphere of copper is subjected to 100 MPa of pressure. The copper has a bulk modulus of 130 GPa. By what fraction does the volume of the sphere change? By what fraction does the radius of the sphere change?
The amplitude of oscillation of a pendulum decreases by a factor of 20.0 in \(120 \mathrm{s}\). By what factor has its energy decreased in that time?
A sewing machine needle moves with a rapid vibratory motion, rather like SHM, as it sews a seam. Suppose the needle moves \(8.4 \mathrm{mm}\) from its highest to its lowest position and it makes 24 stitches in 9.0 s. What is the maximum needle speed?
A hedge trimmer has a blade that moves back and forth with a frequency of $28 \mathrm{Hz}$. The blade motion is converted from the rotation provided by the electric motor to an oscillatory motion by means of a Scotch yoke (see Conceptual Question 7 ). The blade moves \(2.4 \mathrm{cm}\) during each stroke. Assuming that the blade moves with SHM, what are the maximum speed and maximum acceleration of the blade?
Christy has a grandfather clock with a pendulum that is \(1.000 \mathrm{m}\) long. (a) If the pendulum is modeled as a simple pendulum, what would be the period? (b) Christy observes the actual period of the clock, and finds that it is \(1.00 \%\) faster than that for a simple pendulum that is \(1.000 \mathrm{m}\) long. If Christy models the pendulum as two objects, a \(1.000-\mathrm{m}\) uniform thin rod and a point mass located \(1.000 \mathrm{m}\) from the axis of rotation, what percentage of the total mass of the pendulum is in the uniform thin rod?
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