1st yr ann 09 LAST

SIR MA REFALO CENTRE FOR FURTHER STUDIES ANNUAL EXAM 2009A LEVEL - PHYSICS 1st year TIME ALLOWED: 3 HRS

Whenever required take the acceleration due to gravity to be 9.8 m/s2.

Section A. Attempt all questions.

1. A particle of mass m strikes a rigid wall perpendicularly from the left with velocity v.

If the collision is perfectly elastic, find the change in momentum of the particle which occurs as aresult of the collision.

2. a) What are the units of momentum? b) A force, F, varies with time, t, as shown by the graph and is applied to a body initially at reston a smooth surface. i) What are the units of a small square of the area under the graph? ii) Calculate the momentum of the body after 5.0 s?

3. A body moves with simple harmonic motion of amplitude 0.50 m and period 4π seconds.Calculate the speed of the body when the displacement of the body from the equilibriumposition is 0.30 m?

A solid wooden cylinder rolls without slipping down two different inclined planes ofthe same height but with different angles of inclination.(a) Sketch the two planes.(b) Will the cylinder reach the bottom with the same speed in each case?(c) Will it take longer to roll down one inclined plane than the other?Provide explanations for your answers in (b) and (c).

(a) Three resistors, each of resistance 4 , are connected in series. What is the resistance of thisseries combination? (b) If a 2 Volt power supply is connected across the series combination of resistors in (a), find (i)the current drawn from the supply, (ii) the current in each resistor, and (iii) the power generated ineach resistor. (c) Three capacitors, each of capacitance 2 µF, are connected in parallel. What is the capacitanceof the parallel combination? (d) A 2 Volt dc power supply is connected across the parallel capacitor combination in part (c). Find

the charge on each of the three capacitors (when fully charged).

4. Flywheels store energy very efficiently and are being considered as an alternative to batterypower.The energy storage capacity of the flywheel can be improved by adding solid discs tothe flywheel as shown in cross-section A in the figure, or by adding a hoop or tyre to therim of the flywheel as shown in B in the figure. The same mass of material is added ineach case.

State, with reasons, which arrangement stores the more energy when rotating at a given angular speed.

Give definitions for the terms electric potential and electric field strength.

a) A square box shed of side 8m and wall thickness 400 mm is situated in cold climate. The outside temperature is a constant -20°C on all of its surfaces. Calculate the power output required from an internal heater to keep the inside temperature at a steady 15°C.( thermal conductivity of shed walls = 0.12 Wm-1 K-1 )b) The shed in the previous question is coated with an additional layer of material of thickness 100 mm. What power output from the heater is needed in this case? Assume that the dimensions of the shed remain the same. ( thermal conductivity of coating material = 0.06 Wm-1 K-1 )

Show that in a stretched wire, the energy stored per unit volume = ½ x Stress x Strain. Is this equation valid for all extensions of the wire or is there some limiting factor? Briefly explain your answer.One end of a steel wire, diameter 0.05 mm and length 1.5 m, is fixed firmly to a solid roof beam. If a mass of 500 g is attached to the free end of wire, calculate by how much the wire will increase in length if the Young’s Modulus of steel is 2x1012 Pa

Two parallel wires are separated by a distance of 0.75 m. Wire X is 3.0 m long and carries a current of 2.0 A. Wire Y can be considered to be infinitely long and carries a current of 5.0 A. Both currents flow in the same direction along the wires.(a) What is the direction of the force that exists between the two wires?(b) Sketch a graph that shows how the force between the two wires would vary if the length of Wire X was increased.

A mass is attached to a spring and caused to oscillate.

Wire X

Wire Y

0.75 m

a) Is there an instance in time when both velocity and acceleration are zero? If so, when does this occur? b) Is there an instant when velocity is zero and acceleration is negative? If so, when does this occur? Sketch the position and velocity as functions of time for two cycles.

A turntable of mass 20kg and radius 0.5m is spinning at an initial angular speed of 20 rad/sec. A torque of 2 Nm is applied to slow the turntable.i) Find the angular deceleration .ii) Find the number of revolutions necessary to stop the turntable.( moment of inertia of the turntable about an axis through its centre is (1/2)mr2 )

The pressure p of an ideal gas is given by both of the following equations.

(i) Use the equations to show that the average translational kinetic energy of a molecule = (1/2) k T. .(ii) Calculate the average kinetic energy of a molecule of an ideal gas at a temperature of27 °C. (iii) Explain why the answer to (ii) is independent of the mass of the gas molecules. (iv) A laboratory contains 2600 mol of air at a temperature of 27 °C. Calculate the totalkinetic energy of all the molecules of air in the laboratory.

State one similarity and one difference between evaporation and boiling. (a) Define specific heat capacity. (b) In a physics lab experiment a student immersed 200 one-cent coins, each with a mass of 3.0 g, in boiling water. After they reached thermal equilibrium, she took them out and immediately dropped them into 0.240 kg of water at the room temperature of 20°C in an insulated container of negligible mass. She measured the final temperature of the water and coins to be 35°C. What is the specific heat capacity of the metal from which the coins are made?[Specific heat capacity of water = 4190 J/kg.K]

The temperature difference between the inside and outside surface of a skylight of 12 K.(a) Calculate the energy per second transmitted through the skylight if the U-valuefor the glass used is 1.2 W m−2 K−1.(b) State and explain the effect on the U-value for the skylight if the single pane ofglass in part (a) were replaced with two panes of glass of half the original thicknessseparated by a layer of air.

A long rod, insulated to prevent heat loss along its sides, is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an ice-water mixture at the other (see figure below). The rod consists of a 1.00 m section of copper (one end in boiling water) joined end-to-end to a length L2 of steel (one end in ice). Both sections of the rod have cross-sectional areas of 4.00 cm2. The temperature of the copper-steel junction is 65.0°C after a steady state has been set up.i) How much heat per second flows from the boiling water to the ice-water mixture? ii) What is the length L2 of the steel section?

The relationship pV = constant applies to a sample of a gas provided that two othervariables are constant. Name the two other variables.An air bubble released from a diver’s breathing apparatus at a depth of 40 m has adiameter of 2.0 cm. When it reaches the surface of the water it has a diameter of 3.4 cm.Show that the volume of the air bubble has increased by a factor of approximately 5.Hence calculate the increase in pressure experienced by the diver when descending to adepth of 40 m, assuming that the temperature is constant.(Atmospheric pressure = 101 kPa)

a) Define electric field strength Eb) A charged sphere of mass 2.1 × 10-4 kg, suspended from a thread of insulating material,was placed between two vertical parallel plates 60 mm apart. When a potential difference of4200 V was applied to the plates, the sphere moved until the thread made an angle of 6.0º tothe vertical, as shown in the figure.

(i) Draw a free body force diagram for the sphere. (ii) Show that the electrostatic force F on the sphere is given by F = mg tan 6.0º, where m is the mass of the sphere. (iii) Calculate the charge on the sphere.

In a construction project various materials are being considered. Figure 4 shows the stress–strain relationship for four different materials through to the point of failure, marked by the symbol.

Which of the four materials is the most brittle?Which of the four materials is the most ductile, and may most readily be drawn into a wire?

In an experiment to measure the temperature of the flame of a Bunsen burner, a lump ofcopper of mass 0.12 kg is heated in the flame for several minutes. The copper is thentransferred quickly to a beaker, of negligible heat capacity, containing 0.45 kg of water, andthe temperature rise of the water measured.Specific heat capacity of water = 4200 J kg-1 K-1Specific heat capacity of copper = 390 J kg-1 K-1(a) (i) The temperature of the water rises from 15ºC to 35ºC. Calculate the thermalenergy gained by the water.thermal energy gained = ....................................(ii) Calculate the temperature reached by the copper in the flame. Assume no heat islost when the copper is transferred.

(b) When the lump of copper entered the water, some of the water was turned to steam.(i) The specific latent heat of vaporisation of steam is 2.25 MJ kg-1. What furthermeasurement would need to be made to calculate the energy used to produce thissteam? (ii) Without further calculation, describe how this further measurement should beused to obtain a more accurate value of the flame temperature.

(a) (i) Define the capacitance of a capacitor. (ii) Calculate the charge, in C, stored on a 470 ìF capacitor which has apotential difference of 2.3 × 102 V across it. (b) A 470 ìF capacitor is connected in a circuit which enables it to charged when theswitch is in position S1 and discharged when the switch is in position S2. Thearrangement is shown in the figure.

(i) Calculate the time constant of the discharge circuit when the switch is inposition S2. (ii) The capacitor is fully charged and then discharged. Sketch a graph to show the variation of thepotential difference across the capacitor with time for the discharge of thecapacitor.(c) The figure shows the variation of charge with time for the charging of the capacitor.

Explain why the charge across the capacitor changes in the way shown by thegraph.

A satellite is placed in orbit around the Earth at an orbital radius of 4.2 . 107 m. Thegravitational field strength at 4.3 . 107m from the centre of the Earth is 0.23 N m-1.(a) (i) Show that the orbital period of this satellite is about 24 hours.(ii) The satellite is to be placed in a geostationary orbit. Explain what thismeans and give one use for such a satellite. (b) The speed of the satellite in orbit needs to be changed by 2.3 m s−1 as part of themanoeuvre to make the orbit geostationary. Fuel is ejected from the satellite at95 m s−1 to accomplish this.If the final mass of the satellite after the gas ejection is 1800 kg, show that about44 kg of gas needs to be ejected.(c) (i) Dust particles collide with the satellite. A dust particle has a mass of

1.2 . 10−4 kg and a speed, relative to the satellite, of 58 km s−1. Thecollision takes 1.4 ms. Calculate the resistive force acting on the satellite as a result of thiscollision. Assume that the dust particle was initially travelling in theopposite direction to the satellite and after the collision is imbedded in thesatellite. (ii) Suggest what effect these dust particle collisions will have on the motion ofthe satellite. (a) The moment of inertia I of a body can be defined using the equation. I = T/α State the meaning of the symbols T and α .(b) A fairground ride spins the passengers around a circle of radius 5.0 m. The maximum centripetal acceleration allowed for a human on the ride is 50 m s−2.(i) Show that the maximum safe angular speed of the ride is about 3 rad s−1.(ii) The ride starts to rotate from rest and the maximum angular accelerationallowed during this start-up phase is 0.6 rad s−2.Calculate the minimum safe time to reach this speed. (iii) The moment of inertia of the ride when it is fully loaded is 4.3 . 105 kg m−2.Calculate the torque required to accelerate the ride.

In 1774, Nevil Maskelyne carried out an experiment near the mountain ofSchiehallion in Scotland to determine the density of the Earth.The figure shows two positions of a pendulum hung near to, but on opposite sides of,the mountain. The centre of mass of the mountain is at the same height as thependulum.

(b) (i) Explain why the pendulums do not point towards the centre of the Earth.(c) The next figure shows measurements made with the left-hand pendulum in the previous figure.

(i) The mountain is in the appropriate shape of a cone 0.50 km high and 1.3 kmbase radius; it rises from a locally flat plain.Show that the mass of the mountain is about 2 . 1012 kg.volume of a cone = 1/3 π r2 hdensity of rock = 2.5 . 103 kg m−3(ii) Figure 2 shows the left-hand pendulum bob lying on a horizontal line thatalso passes through the centre of mass of the mountain. The bob is 1.4 kmfrom the centre of the mountain and it hangs at an angle of 0.0011° to thevertical.Calculate the mass of the Earth.

b) The figure shows an electrical circuit.

The battery has e.m.f. 4.5 V and has negligible internal resistance. The resistance wire has resistance 4.0 Ω, length 15 cm and cross-sectional area 2.3 × 10–8 m2.(i) Suggest how you can arrange switches S1 and S2 (e.g. opened or closed) so that thecircuit has a total resistance of 12 Ω.(ii) Calculate the resistivity of the material of the resistance wire.(iii) When both switches are closed, calculate the total resistance of the circuit, the total electrical power delivered by the battery and the ratio (current in the 12 Ω resistor)/(current in the resistance wire).

An ideal gas system, with an initial volume of 1.0 m3 at standard temperature and pressure, undergoes the following three stage cycle.Stage 1 - an isothermal expansion to twice its original volumeStage 2 - a process by which its volume remains constant, its pressure returns to its original value and 104J of heat is added to the systemStage 3 - an isobaric compression to its original volume, with 3x104 J of heat being removed from the system.i) How many moles of gas are present in the system?ii) Calculate the work done on the system during each of the three stages.iii) What is the resultant change in the internal energy over the whole three stage cycle?(At STP, temperature = 0°C = 273.15K and pressure = 1atm = 1.01 x 105 Pa, R=8.31 J K-1 mol-1 )

The International Space Station (ISS) is in orbit around the Earth at an altitude 380 km . (Radius of Earth = 6.4 × 106 m, Mass of Earth = 6.0 × 1024 kg, Total mass of ISS = 5 × 105 kg, Universal gravitational constant G = 6.7 × 10–11 N m2 kg–2What is the period of the ISS in seconds?

(a) (i) Draw a p -V diagram showing adiabatic, isothermal and isobaric compressionfrom an initial volume V1 to final volume V2 . Indicate the direction of thesethermodynamic processes with an arrow on each curve.(ii) With the aid of your p -V diagram, rank in increasing order the work done inadiabatic, isothermal and isobaric compression.(b) In a diesel engine, air in the cylinders is adiabatically compressed to 1/15 of its initialvolume. The high temperature of air attained as a result of this compression causes theinjected fuel to ignite spontaneously without the need for spark plugs.Let the initial temperature and pressure of the air in the cylinders be T1= 27.0 °C andp1= 1.01 x 10 5 Pa respectively. Assume that air is mostly a mixture of diatomic oxygenand nitrogen and can be treated as an ideal gas with g = 1.40.(i) Find the final temperature and pressure after the adiabatic compression.(ii) Calculate how much work the air does during the compression if the initialvolume is V1 = 1.00 10-3 m3 (Hint: A diatomic gas has CV =52 R).

(a) (i) Explain what is meant by the spring constant k of a spring. (ii) Give the unit of k. (b) The figure shows the stages in a bungee jump.

In bungee jumping, the participant jumps from a high point attached to an elasticcord (step 1). After a period of free fall, the cord slows the fall of the jumper(step 2) with the system eventually undergoing oscillation (step 3).A bungee jump is to be set up from a suspension bridge with the jumper of weight700 N falling towards the river below. The roadway of the bridge is 76 m abovethe river surface. The bungee cord is adjusted so that the jumper just reaches theriver surface at the bottom of the first oscillation.The unstretched length of the elastic cord is to be 12 m. (i) Calculate the time taken in free fall, that is before the cord begins to stretch. (ii) Show that, when jumping from the bridge to the river, the jumper losesabout 53 kJ of gravitational potential energy.(iii) Calculate the extension of the cord when the jumper is momentarily at the bottom of thefirst oscillation.(iv) Calculate the spring constant of the cord. (v) Calculate the time period of oscillation of the jumper.(c) Calculate the tension in the cord when the jumper comes momentarily to rest for the firsttime.

You are asked to design a circuit to detect a customer as they enter and leave a shop by walking through a light beam. The light source is a light-emitting diode (LED), and the light sensor is a light-dependent resistor (LDR). The circuit is shown in Figure 3.

In order to test this design you first consider the LED circuit by itself; this is shown in Figure 4 along with the LED current-voltage characteristics.

What is the current in the circuit of Figure 4? Show your working and express your answer in mA.Having established that this works correctly you now consider the complete circuit, including the LDR. The characteristics of this device are shown in Figure 5.

When the light beam is not broken the incident light intensity at the LDR is 100 lux. Calculate the current in the LDR circuit, ILDR. Show your working and express your answer in mA.

When the light beam is broken as a customer walks through the door, the voltage measured across the 900 Ω resistor in series with the LDR is measured as 0.01 V. What is the incident light intensity at the LDR? Show your working.

readily be drawn into a wire?