A parallel plate capacitor filled with air is connected to a battery. A dielectric material of dielectrical constant is K=4 is added between the two plates while the capacitor remains connected to the battery. Determine how the following five quantities are affected by the insertion of the dielectric
a) capacitance
b) voltage across the capacitor's plates
c) charge on the plates of the capacitor
d) energy stored in the capacitor.
If a quantity changes specifiy whether it increases or decreases and bby what factor. Justify and show all work. Thank you.
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Show that the moment of inertia of a spherical shell of radius R
and mass M about an axis through
its centre is 2/3 MR2. Show also that the moment of inertia of a
uniform solid sphere of radius R and
mass M is 2/5MR2. The spheres are allowed to roll (from rest),
without slipping a distance L down
a plane inclined at a angle θ to the horizontal. Find expressions
for the speeds of the spheres at the
bottom of the incline and show that ∆v/〈v〉 = 8.7% where ∆v is the
difference in the speeds and 〈v〉 is
the mean of the two speeds. Which sphere has the larger speed?
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Explain the control loops using current amplifier for the robot joint motions mentioning the response equations involved
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Calculate the following centripetal accelerations as fractions or multiples of g and comment on the results: (a) The acceleration to- wards the Earth’s axis of an object resting on the Earth’s surface at 45◦ latitude. The Earth’s radius is 6378 km. (b) The acceleration of the Moon towards the Earth. The radius of the Moon’s orbit is 384399 km and its period is 27.3 days. (c) The acceleration of an electron moving around a proton at a speed of 0.007c where c is the speed of light in an orbit of radius 0.05 nm (the first Bohr orbit of the H atom)
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do you have answer of exercise 3.4 (chapter 3) of book Sakurai (Modern Quantum Mechanic 2nd ) ?
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Q1: Liquid drop model of nuclei: Describe how one
views a nucleus in this model. What is the nucleus made
of?
What is the relationship between the atomic number, A,
and the nuclear radius?
According to this model, how does nuclear density
scale with A?
Q2: What are the indications that the "nucleus is made
of alpha particles" model might work?
Discuss why protons and neutrons could be considered
as the basic constituents of a nucleus?
Why could alpha particles be considered as the basic
constituents of a nucleus?
Where does the "nucleus is made of alpha particles"
model work better, for high A or for low A?
Q3: How many stable nuclei are there? How many
unstable, approximately? What is the highest Z of all stable
nuclei?
What is the reason that there are no stable nuclei
above that Z? Why do high-A stable nuclei have more neutrons
than
protons?
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A stepladder consists of two sides of equal mass and a length of 3.7 m, and the two sides are connected by a rope fixed 1.2 m from the bottom of the ladder. When opened, the angle between the two sides of the ladder is 61°. The ladder stands on a frictionless horizontal floor.
Determine the tension in the rope T and the reaction force at the top hinge if the total mass of the ladder is 17 kg. (Hint: draw free body diagram for one side of the ladder)
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When a car corners at speed one is relying on the friction between the tyres and the road to counter the centrifugal force tending to throw the car outwards. One way to reduce the dependence on friction is to ‘bank’ the corner. For a car travelling with a speed v entering a corner of radius r, show that the angle of the bank, θ, (measured from the horizontal) should satisfy tanθ = v2/(gr) if there is to be no reliance on friction. In the light of this result discuss the design of the ‘Wall of Death’ fairground attraction in which a motorbike is ridden at speed around the inner surface of a large vertical cylinder, with the bike and rider at a small angle to the horizontal plane. What role does friction play and why is a small angle necessary?
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The H-R diagram is the most important graph in astronomy. One of the reasons that this graph is so powerful is the number of different kinds of data it shows. Most graphs show two types of data. The H-R diagram shows at least 5. Can you name these 5 types of information about stars that appear on the H-R diagram?
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A question about the amplitude graph of the pendulum:
Should I say; Period does not depend on Amplitude and just make a
zero slope graph just like the mass graph.
OR
Should I say; The time period of a pendulum changes as the
amplitude changes, but change is negligible if the amplitude is
very small. Period only depends on amplitude, if the amplitude
isn't very small and make a positive slope graph that represents a
slight change as the amplitude of pendulum increases.
Q2: What's the maximum amplitude of a 0.71m pendulum is it 90° or
180°?
Q3: As a negative test charge moves farther from a negative charge in an electric field, the potential energy?
a.decreases.
b. increases.
c. doubles.
d. remains the same.
Q4: If a magnetic field points upward and the current is to your left, the force is.
a. toward you
b. to your right
c. away from you
d. to your left
Q5: A device used to measure both magnitude AND direction of an electric current is a(n)
a. ammeter.
b. galvanometer.
c. voltmeter.
d. ohmmeter.
Q6: The current is least in a rotating loop when the loop’s motion is __________ the magnetic field.
a. slow and perpendicular to
b. slow and parallel to
c. fast and perpendicular to
d. fast and parallel to
Q7: The force on a test charge in an electric field is __________ the magnitude of the field.
a. inversely proportional to
b. directly proportional to
c. inversely proportional to the square of
d. unrelated to
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A diffraction grating has a chromatic resolving power of 20,000 in first order (m = 1). (i) What is the number of slits in the grating? (ii) This grating is used to analyze the spectrum of light coming from stars, in the third order (m = 3). The analysis involves resolving wavelengths that are close the spectral wavelength of some element (500.0 nm). What is the range of wavelengths you cannot distinguish from the said spectral wavelength?
Hint: Chromatic resolving power is: Nm=λΔλ.
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a) An ice cube initially at zero degrees C has mass 37g. It is used to cool a hot cup of water at 184 which has mass 200g. What is the final temperature in degrees Celcius? Use as specific heat of water 4.18 kJ/(kg K) and the heat of fusion 334 kJ/kg.
b) A mass of 1kg is attached to a spring with spring constant 10N/m. How many meters down does its equilibrium position fall when it is used to hang the mass vertically?
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How dense was the universe when it was 1 million years old?
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The G-string on a guitar is 64.8 cm long and is properly tuned to 196 Hz (fundamental) frequency.
a. Sketch the first harmonic on this guitar string at two different times.
b. What is the frequency of the G note one octave above this frequency? One octave below?
c. What is the frequency of the note a perfect fifth above this frequency?
d. What is the wavelength of the first harmonic of this guitar string?
e. What is the speed of waves on this guitar string? f. If a tuning fork is played at 194 Hz, will there be a beat? At what frequency?
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