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The grandfather clock in the opening storyline depends on the period of a pendulum to keep correct time. (i) Suppose the clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow, (b) fast, or (c) correctly?

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SadhaLv10
11 Jan 2021
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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A grandfather clock uses a physical pendulum to keep time. Thependulum consists of a uniform thin rod of mass M and length L thatis pivoted freely about one end, with a solid sphere of the samemass, M, and a radius of L/2 centered about the free end of therod.
(a) Obtain an expression for the moment of inertia of the pendulumabout its pivot point as a function of M and L. (Use any variableor symbol stated above along with the following as necessary:g.)
I =

(b) Obtain an expression for the period of the pendulum for smalloscillations. (Use any variable or symbol stated above along withthe following as necessary: g.)
T =

(c) Determine the length L that gives a period of T = 2.5 s.

The Michelson-Morley experiment is known as a second orderexperiment because the observed effect depends on (v/c)^2. Considerthe following first order experiment:
At time t = 0, observer a sends a signal to observer b at adistance L away. b records the arrival time. Assume that the systemis moving through the ether with speed v in the direction shown(left). Suppose the laboratory is then rotated 180 degrees withrespect to the velocity, reversing the positions of a and b. Attime t = T, a sends a second signal to b.

a. Show that the interval b observes between the arrival of thesignals is T + (delta)T, where
(delta)T = (2Lv)/(c^2)
to order (v/c)^3.

b. Assume that the experiment is done between the clock on theground and one on the satellite overhead. For an orbit with a 24hour period, l = 5.6R (radius of Earth). Present atomic clocksapproach a stability of 1 part in 10^14. What is the smallest valueof v that this experiment could detect using such clocks?

Good Vibes: Introduction to Oscillations

Ā 

The conditions that lead to simple harmonic motion are as follows:

There must be a position ofĀ stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring forceĀ Fāƒ—Ā Ā is given by āƒ—, where is the displacement from equilibrium and kĀ is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of massĀ mĀ attached to a spring with force constantĀ k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located atĀ x=0. If the block is pulled to the right a distanceĀ AĀ and then released,Ā AĀ will be theĀ amplitudeĀ of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released fromĀ x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.Ā 

(c) move to the left until it reaches x= ā€“A and stop there.Ā 

(d)Ā move to the left until it reachesĀ x=āˆ’A and then begin to move to the right.

Ā 

Ā 

Ā 

The time it takes the block to complete one cycle is called theĀ period. Usually, the period is denotedĀ TĀ and is measured in seconds.

TheĀ frequency, denotedĀ f, is the number of cycles that are completed per unit of time:Ā f=1/T. In SI units,Ā fĀ is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchangedĀ 

(b) doubledĀ 

(c) halved

Ā 

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequencyĀ f?

Express your answer in hertz.

Ā 

Part D

If the frequency is 40 Hz, what is the periodĀ T?

Express your answer in seconds.

Ā 


The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents theĀ x-coordinate of the oscillating object, and the horizontal axis represents time.

Ā 

Part E

Which points on theĀ x-axis are located at a distance AĀ from the equilibrium position?

(a) R only

(b) Q only

(c) both R and Q

Ā 

Part F

Suppose that the period isĀ T. Which of the following points on theĀ t-axis are separated by the time intervalĀ T?

(a) K and L

(b) K and MĀ 

(c) K and P

(d) L and NĀ 

(e) M and PĀ 

Ā 

Ā 

Now assume for the remaining Parts G - J, that theĀ xĀ coordinate of point R is 0.12 m and theĀ tĀ coordinate of point K is 0.0050 s.

Part G

What is the periodĀ T?

Express your answer in seconds.

Ā 

Part H

How much timeĀ tĀ does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Ā 

Part I

What distanceĀ dĀ does the object cover during one period of oscillation?

Express your answer in meters.

Ā 

Part J

What distanceĀ dĀ does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

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