OCR A Level Physics A Unified Physics June 2018 question paper H556/03

This question is about a resistance wire made of nichrome.

A student is investigating a 230 V, 1.0 kW heating element. The heating element is shown in Fig. 1.2.

A length of nichrome wire is wound in a spiral groove along 18 cm of a ceramic cylinder of diameter 1.4 cm. The distance between the centres of adjacent turns of the wire is 1.5 mm.

The numbers labelling the reels of loose wire on the laboratory shelf are the imperial standard wire gauge (swg). The student wishes to find out which reel holds the same wire as that wound on the heating element of Fig. 1.2.

The book of data gives the following information:

resistivity of nichrome at operating temperature = 1.1 × 10⁻⁶ m

Show that the resistance of the nichrome wire wound on the ceramic cylinder is 53

Show that the length of wire wound on the heating element is 5.3 m.

Use the information given in (i) and (ii) to determine the swg number of the wire used as the heating element.

The 500 m tall Taipei 101 tower is shown in Fig. 2.1. The tower has a massive sphere suspended across five floors near the top of the building to dampen down movement of the tower in high winds and earthquakes. The sphere is connected to pistons (not shown) which drive oil through small holes providing damping. The vibration energy of the sphere is converted to thermal energy.

Fig. 2.2 models the damper system as the sphere held between two springs. The movement of the walls of the tower forces the sphere to oscillate in simple harmonic motion.

In the strongest wind, the natural frequency of the oscillations of the tower is 0.15 Hz and the maximum acceleration of the sphere is 0.050 m s⁻².

Calculate the maximum displacement of the sphere in the strongest wind.

Explain why the natural frequency of the damper system must be about 0.15 Hz.

The acceleration a of the sphere is given by the equation

where k is the force constant of the spring combination, x is the displacement of the sphere and m is the mass of the sphere.

The mass of the sphere is 6.6 × 10⁵ kg. The natural frequency of the oscillations of the sphere is 0.15 Hz.

The S-wave of an earthquake causes a sudden movement of the building displacing the sphere 0.71 m from its equilibrium position relative to the building.

Use your answer in (i) to calculate the energy transferred to the springs of the damper system.

A binary star is a pair of stars which move in circular orbits around their common centre of mass.

In this question consider the stars to be point masses situated at their centres.

Fig. 3.1 shows a binary star where the mass of each star is m. The stars move in the same circular orbit.

Explain why the stars of equal mass must always be diametrically opposite as they travel in the circular orbit.

The stars are viewed from Earth in the plane of rotation. The stars are observed using light that has wavelength of 656 nm in the laboratory. The observed light from the stars is Doppler shifted.

Calculate the maximum change in the observed wavelength of this light from the orbiting stars. Give your answer in nm.

The centre of mass of the binary star lies at the surface of the star of mass 4 m. Draw on

Fig. 3.2 two circles to represent the orbits of both stars.

Explain why the smaller mass star travels faster in its orbit than the larger mass star.

Fig. 4.1 shows an arrangement used by a student to determine the acceleration of free fall.

A trolley is attached to a variable mass m by a string which passes over a pulley.

The mass m is released from rest and falls through a fixed height of 0.600 m accelerating the trolley of mass 0.800 kg. When the mass m hits the floor, the trolley then continues to move at a constant velocity v.

This constant velocity v is determined by measuring the time t for the card of length 0.200 m to pass fully through a light gate connected to a timer.

Frictional forces on the trolley and the falling mass m are negligible.

Show that the relationship between v and m is

where g is the acceleration of free fall.

The student records the information from the experiment in a table. The column headings and just the last row for m = 0.600 kg from this table are shown below.

It is suspected that the card on the trolley did not pass at right angles through the light beam.

Discuss, without doing any calculations, the effect this may have on the experimental value for the acceleration of free fall g.

Explain the shape of the graph in terms of the magnetic flux linking the coil.

The coil shown in Fig. 5.1 has 150 turns. The maximum induced e.m.f. V₀ across the coil is 1.2 V when the magnet is rotating at 24 revolutions per second.

Calculate the maximum magnetic flux through the coil using the equation

V₀ = 2π × (frequency) × (maximum magnetic flux linkage)

Give a unit with your answer.

* A student is given a transformer with coils X and Y, as shown in Fig. 5.4.

The student is intending to investigate how the maximum induced e.m.f. V₀ in coil Y depends on the frequency f of the alternating current in coil X.

The changing magnetic flux density in coil X induces an e.m.f. in coil Y. Faraday’s law indicates that the maximum induced e.m.f. V₀ should be directly proportional to f.

Describe how you would investigate the suggested relationship between V₀ and f in the laboratory using these coils. In your description include all of the equipment used and how you would analyse the data collected.

Use the space below to draw a suitable diagram.

Fig. 6.1 shows a single photomultiplier tube and its internal components. The tube can detect gamma photons in high-energy physics experiments. A single gamma photon incident on the scintillator crystal generates many photons of blue light. These visible light photons travel to the photocathode where they are converted into photoelectrons. The number of electrons is then multiplied in the photomultiplier tube with the help of electrodes called dynodes. A short pulse of electric current is produced at the output end of the photomultiplier tube.

Fig. 6.2 shows a section through the scintillator crystal in air.

The refractive index of the scintillator crystal for visible light is 1.69. The refractive index of air is 1.00. Calculate the critical angle C for this crystal.

Explain why the visible light inside the scintillator crystal follows the path shown in Fig. 6.2.

A high energy gamma photon passing through the scintillator crystal converts some of its energy into visible light photons of mean wavelength 450 nm.

Show that the energy of a single photon of wavelength 450 nm is less than 3 eV.

The photocathode is coated with potassium which has a work function of 2.3 eV. Each emitted photoelectron is accelerated by a potential difference of 100 V between the photocathode and a metal plate, called the first dynode.

Show that the maximum kinetic energy of an emitted electron at the photocathode is very small compared to its kinetic energy of 100 eV at the first dynode.

2000 photoelectrons are released from the photocathode. Each photoelectron has enough energy to release four electrons from the first dynode at the collision. These four electrons are then accelerated to the next dynode where the process is repeated. There are 9 dynodes in the photomultiplier tube. The total number of electrons collected at the anode for each photoelectron is 4⁹.

The pulse of electrons at the anode lasts for a time of 2.5 × 10⁻⁹ s.

Calculate the average current due to this pulse.