Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Q39P (page 463)

(a) What is the period of small-angle oscillations of a simple pendulum with a mass of 0.1kgat the end of a string of length1m?(b) What is the period of small-angle oscillations of a meter stick suspended from one end, whose mass is0.1kg?

Short Answer

Expert verified

The period of small angle oscillations of a sample pendulum is 2.01 s.

The period of small angle oscillation of a meter stick suspended from one end is 1.64 s.

Step by step solution

01

Define oscillations of a simple pendulum.

A pendulum completes one oscillation when it begins at one extreme position A, goes to the opposite extreme point B, and then returns to A. The time period is the amount of time it takes to complete one oscillation. The oscillation's time period remains constant.

02

Find the period of small angle oscillations of a simple pendulum.

  1. The period of small angle oscillations of a sample pendulum is,

T=2πlg

Here, lis length of the pendulum and gis acceleration due to gravity.

Substitute 1mfor land 9.8m/s2for g.

T=2π1m9.8m/s2=2.01s

Therefore, the period of small angle oscillations of a simple pendulum is2.01s.

03

Find the period of small angle oscillation of a meter stick suspended from one end.

b. The period of small angle oscillation of a meter stick suspended from one end is,


T=2πImgl'


Here,l'is length of stick from its center to the one end,mis mass of the scale and lis moment of inertia of the scale relative to one end.

The moment of inertia of the scale is,

I=13ml2


Substitute 13ml2for Iand l2for l'in equation T=2πImgl'


T=2π13ml2mgl2=2π2l3g


Substitute 1mfor land 9.8m/s2for g.


T=2π21m39.8m/s2=1.64s

Therefore, the period of small angle oscillation of a meter stick suspended from one end is1.64s.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A sick of length Land mass Mhangs from a low-friction axle (Figure 11.90). A bullet of mass mtravelling at a high speedstrikes vnear the bottom of the stick and quickly buries itself in the stick.

(a) During the brief impact, is the linear momentum of the stick + bullet system constant? Explain why or why not. Include in your explanation a sketch of how the stick shifts on the axle during the impact. (b) During the brief impact, around what point does the angular momentum of the stick + bullet system remain constant? (c) Just after the impact, what is the angular speed ωof the stick (with the bullet embedded in it) ? (Note that the center of mass of the stick has a speed ωL/2.The moment of inertia of a uniform rod about its center of mass is112ML2.(d) Calculate the change in kinetic energy from just before to just after the impact. Where has this energy gone? (e) The stick (with the bullet embedded in it) swings through a maximum angleθmaxafter the impact, then swing back. Calculate θmax.

The axis of gyroscope is tilted at an angle of 30∘to the vertical (figure 11.110). The rotor has a radius of 15cm , mass 3kg , moment of inertia is 0.06Kg/m2and spins on its axis at 30rad/s. It is supported in a cage (not shown) in such a way that without an added weigh it does not process. Then a mass of 0.2 kg is hung from the axis at a distance of 18 cm from the center of the rotor.

a. Viewed from above, does the gyroscope process in a (1) clockwise or a (2) counterclockwise direction? That is, does the top end of the axis move (1) out of the page or (2) into the page in the next instant? Explain your reasoning

b. How long does it take for the gyroscope to make one complete procession?

Two balls of equal radius and mass, free to roll on a horizontal plane, are separated by a distance L large compared to their radius. One ball is solid, the other hollow with a thickness small compared to its radius. They are attracted by an electric force. How far will the solid ball roll before it collides with the hollow ball?

A board of length 2d=6mrests on a cylinder (the “pivot”). A ball of mass 5kgis placed on the end of the board. Figure 11.104 shows the objects at a particular instant. (a) On a free-body diagram, show the forces acting on the ball + board system, in their correct locations. (b) Take the point at which the board touches the cylinder as location A. What is the magnitude of the torque on the system of (ball + board) about locationA?(c) Which of the following statements are correct? (1) Because there is a torque, the angular momentum of the system will change in the next tenth of a second. (2) The forces balances, so the angular momentum of the system about location Awill not change. (3) The forces by the cylinder on the board contributes nothing to the torque about the location A.

Review with derivation of the Bohr model of the hydrogen atom and apply this reasoning to predict the energy levels of ionized helium He+ (a helium atom with only one electron, and a nucleus containing two protons and two neutrons). What are the energies in of the ground state and the first excited state? What is the energy of a photon emitted in a transition from the first excited state to the ground state? How do these results differ from those for a hydrogen atom?
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Astrophysics

Read Explanation

Magnetism

Read Explanation

Force

Read Explanation

Linear Momentum

Read Explanation

Modern Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free