PHY009/PHY010 PHYSICS – Oscillations & Waves, Atomic and Nuclear Spring Semester 2020-2021

1.

Daylight passes through a fixed polarising filter. An observer views the light after it subsequently passes through a second polarising filter which may be rotated in  the plane normal to the direction of the light. The two polarisers are initially  orientated in the same direction.

the second polariser is slowly rotated through 0– 180 degrees inclusive. Ensure that

you include details of the polarisation of the light before and after the polarisers in

your diagrams.                                                                                                        

An oscillator of variable frequency f is used to vibrate a horizontal wire that is     stretched between a fixed point A and passes over a pulley B . The wire has a mass m suspended to it after it passes over the pulley. The length of the wire L between the fixed point and the pulley is 2.0 m.

When f  =  882 Hz a well-defined pattern of nodes and antinodes is seen. As f is gradually reduced the pattern disappears but the next well-defined pattern is seen when f  =  784 Hz. The total mass of the length of wire is 1.2 × 10−3 kg.

(i)      Calculate the speed of sound along the wire.

(ii)     Calculate the value of the mass m being suspended.

‘angular frequency’ for a resonant system with light damping.  On the same axes

sketch two more annotated plots to show different amounts of applied damping for

the same system.

[Note numerical values on the axes are not required.]                                     

A damped oscillator has a general solution of the form

X = Ae−t cos(仙 ′ t + p)

Where

仙 ′ = √( − )

Assume we have a damped mass/spring system with a mass m of 1.00 kg. The phase angle of this system p = 0.

is critically damped. Explain why this is the case?                                              

This particular system is critically damped and it is found that it will return to e −1 of its initial amplitude in 0.10 s

(iii)    Use this information and the general solution to calculate the damping value b.      

(iv)    Determine the spring constant k of the system, hence calculate the natural

undamped oscillation frequency 仙0 of the mass/spring system.     

2.

(a)

A plane mirror is placed at the bottom of a long dish containing water. The mirror makes an angle of 15.0 degrees to the horizontal. The index of refraction of the    water is 4/3.

A beam of monochromatic light falls onto the surface of the water at an angle of incidence e .

Hint: It may be useful to carefully draw out the geometry for this question. If so, please include this in your scanned answers. Feel free to use a separate sheet of paper.

the mirror with respect to the plane of the mirror. (i.e., Not with respect to the normal.)

(ii)     Therefore calculate, in terms of e, the angle of incidence of the light just before it leaves the water.

(iii)    Therefore, calculate the maximum angle of incidence e for which light would be able to be refracted from the water surface and explain why this is so.                  from 450nm to 600nm.  When this filtered light is normally incident upon a diffraction grating, the 450nm light in one order of the spectrum is diffracted at the same angle 45 degrees as the 600nm light in the adjacent order. Find the spacing between the lines in the grating, explaining any reasoning that you use.     

A clock pendulum has a period of 3.00 s. A simple pendulum is set and it is found that it is slightly faster than the clock pendulum and the two oscillate in phase      every 35.0 s. Calculate the frequency of the simple pendulum

3.

In the following you should use these neutral atomic masses:

Am: 241.056828 u

Np: 237.048167 u

2(4)He: 4.002603 u

(i)   Evaluate whether the alpha decay of 241Am is energetically allowed, explaining your reasoning.

(ii)   Calculate the kinetic energies of the decay products, assuming that the parent

nucleus was at rest.

(iii)   241Am has a half-life of 432 years. Knowing that there are about 0.3 μg of 241Am in a smoke detector at the time the detector is manufactured, calculate how many 241Am atoms would be left in the smoke detector 100 years after it has been    installed.

(iv)   Sketch an annotated graph showing how the abundance of the decay product from the 241Am decay changes over time.

b)             An atom has two energy levels above the ground state: at 2.0 eV and 6.0 eV.

(i)   Draw a ladder diagram showing all possible electron transitions that would lead to the release of a photon.

(ii)   If an electron in this atom is initially in its ground state, what are the possible single photon energies that it can absorb?

An X-ray diffraction experiment is set up to study the crystal structure of a       material. To produce the X-ray, a tube is used to accelerate electrons through a potential difference of 20.0 kV. Assume each electron produces one photon per impact with the target material.

(i)   Calculate the minimum possible wavelength of the resulting X-rays.

(ii)   How would the minimum wavelength change if the target material was changed

for one with a higher density?