CfE. Higher. Higher Physics Homework (Unit 1, 2 & 3)

Transcription

1 CfE Higher Higher Physics Homework (Unit 1, 2 & 3)

2 Relationships Required for Higher Physics 2

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4 Homework 1 - Significant Figures, Prefixes & Scientific Notation 1. In each of the following cases, the stated value has too many significant figures. The appropriate number of significant figures is stated in brackets after the quantity. Round each quantity to the correct number of significant figures. a) V (3 significant figures) b) Hz (2 significant figures) c) m (3 significant figures) d) x 10 8 ms -1 (2 significant figures) (2) 2. Calculate the following quantities from the information given, and report your answer to an appropriate number of significant figures. Remember to give your answer in scientific notation! a) Calculate the frequency of microwaves that have a wavelength of 3.1 x 10-2 m, and are travelling at 3.0 x 10 8 ms -1. b) Calculate the energy used if a 1.2 kw kettle takes 2 minutes to boil. 3. Copy the table below, and fill in all the blanks. QUANTITY VALUE SCIENTIFIC NOTATION Speed of light 3 x 10 8 ms -1 Charge on an electron Wavelength of red light Voltage used in the Super Grid C V (to 3 sig figs) 7 x 10-7 m 4. Re-write the following quantities using the most appropriate prefix. a) m b) Hz c) 3200 W d) g e) 2.7 x 10 6 J f) 7.42 x 10-7 m (2) Total marks: 11 4

5 Homework 2 - Uncertainties 1. a) The circuit shown is set up to determine the resistance of a resistor. In one repetition of the experiment, the readings are as shown on the meters. The experiment is repeated several times to allow mean values for both current and voltage to be found V A a) (i) Give the ammeter and voltmeter readings and state the absolute scale reading uncertainty in each case. (2) (ii) Give the percentage uncertainty for the ammeter and voltmeter readings. (2) b) Using Ohm s Law (V = IR), calculate a value for the resistor. Estimate the absolute uncertainty in the calculated value of the resistance and explain how you arrived at your estimate. c) The experiment is repeated 5 times, and the values recorded for the current are as follows: 0.44 A; 0.43 A; 0.45 A; 0.42 A; 0.44 A Calculate the mean current, and the random uncertainty in the mean. 2. A current is measured with an analogue meter which has scale divisions of 0.1 A, and is found to be 5.4 A. The reading is double-checked with a digital meter, and again is found to be 5.4 A. Using which instrument gives the larger scale reading uncertainty? Explain your answer. (2) Total marks: 12 5

6 Homework 3 - Vectors 1. Explain the difference between a vector and a scalar quantity and give 2 examples of each. (2) 2. A ferry crosses a river that is flowing at 5 ms -1. If the ferry is travelling at 12 ms -1, calculate its resultant velocity. 5 ms ms An aircraft pilot wishes to fly north at 800 km h -1. A wind is blowing at 80 km h -1 from west to east. What speed and course must he select in order to fly the desired course? 4. A footballer runs around a football pitch as part of his training. He starts at the halfway line (point X), and runs around the pitch to point D as shown. This run takes him 50 seconds. 100 m C B N 70 m 70 m W E S D X 50 m A a) Calculate the total distance travelled by the footballer. (1) b) What is his final displacement at point D? (1) c) Calculate the footballer s average velocity for the run. Total marks: 13 6

7 Homework 3B - Vectors 1. Competitors are racing remote control cars. The cars have to be driven over a precise route between checkpoints. Each car is to travel from checkpoint A to checkpoint B by following these instructions. Drive 150m due North, then drive 250m on a bearing of 60 East of North (060). Car X takes 1 minute 6 seconds to follow these instructions exactly. (a) By scale drawing or otherwise, find the displacement of checkpoint B from checkpoint A. (b) Calculate the average velocity of car X from checkpoint A to checkpoint B. (c) Car Y leaves A at the same time as car X. Car Y follows exactly the same route at an average speed of 6.5ms 1. Which car arrives first at checkpoint B? Justify your answer with a calculation. (d) State the displacement of checkpoint A from checkpoint B. (1) Total marks: (10) PTO for Homework 3B Q2

8 2. (1) (1) (4) Total marks: (11)

9 Homework 4 - Equations Of Motion 1. A workman on scaffolding outside one of the physics classrooms drops a wrench. A student times it as it falls past the 2m tall classroom window and found that it took 0.6s to fall. Calculate the wrench s initial velocity as it appears at the top of the window. 2. A train decelerates from 12.0 ms -1 to 5.0 ms -1 while travelling a distance of m along a straight track. Calculate the deceleration of the train. 3. A skier sets off from rest and accelerates uniformly down a straight ski run. After 4 50 seconds she reaches a speed of 23 0 m s-1. After this time the skier no longer accelerates but continues to travel at 23 0 m s-1 for a further 11 0 s. Calculate: a) the acceleration of the skier during the first 4 50 s of her run. b) the total distance travelled by the skier. (4) 4. In a handicap sprint race, sprinters P and Q both start the race at the same time but from different starting positions on the track. The handicapping is such that both sprinters reach XY, as shown below, at the same time. Sprinter P has a constant acceleration of 1.6 ms - 2 from the start line to the line XY. Sprinter Q has a constant acceleration of 1.2 ms -2 from the start line to XY. a) Calculate the time taken by the sprinters to reach line XY. b) Find the speed of each sprinter at this line. (4) c) What is the distance, in metres, between the starting lines for sprinters P and Q? Total marks: 23 7

10 Homework 5 - Forces 1. A train made up of 3 carriages is pulled along a level track by a force of N. Each of the carriages has a mass of kg, and each experiences 1500 N of resistive forces. Force applied by the engine A B a) Calculate the acceleration of the train. b) Work out the tension in link B. (4) 2. A rocket of mass 200 kg accelerates vertically upwards from the surface of a planet at 2ms -2. The gravitational field strength on the planet is 4 Nkg -1. What is the size of the force being supplied by the rocket s engines? (4) 3. The lift in a department store has a mass of 1100kg. The lift is descending with a uniform downwards acceleration of 2ms -2. The acceleration due to gravity can be taken as 10ms -2. What is the force applied to the lift by the lift cable? (4) 4. A pupil pushes two blocks A and B with a 30 N force. 4kg 2kg Ignoring friction, a) calculate the acceleration of the blocks. b) find the force A exerts on B. Total marks: 21 8

11 Homework 6 Force as a Vector 1. In the diagram below, calculate the component of the weight acting down the slope. The mass of the trolley is 24 kg A 2 kg trolley is placed on a 35 o slope. The trolley accelerates down the slope and a frictional force of 1.5 N acts up the slope. 1.5 N 35 a) Calculate the acceleration of the trolley. (4) b) What effect does increasing the angle of slope have on acceleration? (1) 3. Two ropes are used to pull a boat at constant speed along a canal. Each rope exerts a force of 150 N at 20 o to the direction of travel of the boat as shown. a) Calculate the magnitude of the resultant force exerted by the ropes. (4) b) What is the magnitude of the frictional forces acting on the boat? (1) Total marks: 13 9

12 Homework 7 Conservation of Energy 1. A block of mass 3 0 kg is held at rest on a frictionless slope. The front edge of the block is 0 80 m above the ground as shown in Figure 2. a) Calculate the gravitational potential energy of the block when it is in the position shown in Figure 2. b) The block is released. Use conservation of energy to find the speed of the block at the foot of the slope. 2. In an experiment to calculate the power developed, a 70 kg man runs up the stairs as fast as he can. The flight of stairs is 4.30 m tall. If it took the man 5.0 s to run up the stairs, calculate his power. (4) 3. A pendulum swings as shown in the diagram. Points A and C are the extremities of the swing of the pendulum. The mass of the bob is 0.5 kg. Calculate: 20 cm a) the maximum potential energy of the bob. b) the maximum kinetic energy of the bob. (1) c) the maximum speed of the bob. Total marks: 17 10

13 Homework 8 Momentum and impulse 1. In a rugby match, a 110 kg forward in one team tackles an 85 kg back in the other team. The forward is travelling at 5 ms -1 and the back at 7 ms -1 in the opposite direction when they collide and stick together. Take the direction of the forward as the positive direction. a) Calculate the velocity of the pair immediately after the collision. b) Show by calculation whether this collision is elastic or inelastic. 2. Explain, in terms of forces on the driver, why a seatbelt offers a far less damaging alternative to a steering wheel when a car stops suddenly during a collision. (2) 3. In a game of squash, a ball of mass 0.1 kg is moving towards the player with a velocity of 20 ms -1. She strikes it with the racquet and it returns towards the wall at 40 ms -1. If the time of contact between racquet and ball is 50 ms, calculate the force applied on the ball by the racquet. 4. A golfer strikes a stationary golf ball, and the force applied by the club on the ball varies as shown in the graph below. Use this graph to determine the final speed of the golf ball. The ball s mass is 0.1 kg. (4) Average Force (N) Total marks: Time of Contact (ms)

14 Homework 9 - Gravitation 1. During a visit to the moon, the astronaut fires a small experimental projectile across a level surface. The projectile is launched, from point P, at a speed of 24.0 ms -1 and at an angle of 60 to the horizontal. The projectile lands 26.0 s later at point X. a) Calculate the horizontal speed of the projectile at point P. (1) b) Calculate the horizontal distance from P to X. 2. A model rocket enthusiast launches a rocket from the edge of a cliff on a calm day (no air resistance). The flight of the rocket from launch at point O to splashdown in the sea, at B, takes 7 seconds. a) The rocket is launched at an angle of 30 to the ground with velocity 40ms -1. Show that the time it takes to go from point O to point A, which is level with the cliff, is 4 1s. b) Find the height of the cliff. 3. Calculate the gravitational force between two cars parked 0.50 m apart. The mass of each car is 1000 kg. Total marks: 13 12

15 Homework 10 Special Relativity 1. A scientist in the laboratory measures the time taken for a nuclear reaction to occur in an atom. When the atom is travelling at ms 1 the reaction takes s. Calculate the time for the reaction to occur when the atom is at rest. 2. The light beam from a lighthouse sweeps its beam of light around in a circle once every 10 s. To an astronaut on a spacecraft moving towards the Earth, the beam of light completes one complete circle every 14 s. Calculate the speed of the spacecraft relative to the Earth. 3. A pi meson is moving at 0 90 c relative to a magnet. The magnet has a length of 2 00 m when at rest to the Earth. Calculate the length of the magnet in the reference frame of the pi meson. 4. In the year 2050 a spacecraft flies over a base station on the Earth. The spacecraft has a speed of 0 8 c. The length of the moving spacecraft is measured as 160 m by a person on the Earth. The spacecraft later lands and the same person measures the length of the now stationary spacecraft. Calculate the length of the stationary spacecraft. 5. The star Alpha Centauri is 4 2 light years away from the Earth. A spacecraft is sent from the Earth to Alpha Centauri. The distance travelled, as measured by the spacecraft, is 3 6 light years. a) Calculate the speed of the spacecraft relative to the Earth. b) Calculate the time taken, in seconds, for the spacecraft to reach Alpha Centauri as measured by an observer on the Earth. c) Calculate the time taken, in seconds, for the spacecraft to reach Alpha Centauri as measured by a clock on the spacecraft. Total marks: 21 13

16 Homework 11 Doppler Effect 1. In the following sentences the words represented by the letters A, B, C and D are missing: A moving source emits a sound with frequency f s. When the source is moving towards a stationary observer, the observer hears a A frequency f o. When the source is moving away from a stationary observer, the observer hears a B frequency f o. This is known as the C D. Match each letter with the correct word from the list below: Doppler effect higher louder lower quieter softer (2) 2. A student is standing on a station platform. A train approaching the station sounds its horn as it passes through the station. The train is travelling at a speed of 25 m s 1. The horn has a frequency of 200 Hz. a) Calculate the frequency heard as the train is approaching the student. b) Calculate the frequency heard as the train is moving away from the student. 3. A man standing at the side of the road hears the horn of an approaching car. He hears a frequency of 470 Hz. The horn on the car has a frequency of 450 Hz. Calculate the speed of the car. 4. A source of sound emits a signal at 600 Hz. This is observed as 640 Hz by a stationary observer as the source approaches. Calculate the speed of the moving source. 5. A battery-operated siren emits a constant note of 2200 Hz. It is rotated in a circle of radius 0 8 m at 3 0 revolutions per second. A stationary observer, standing some distance away, listens to the note made by the siren. a) Show that the siren has a constant speed of 15 1 m s 1. b) Calculate the minimum frequency heard by the observer. c) Calculate the maximum frequency heard by the observer. Total marks: 23 14

17 Homework 12 Redshift and Hubble s Law 1. Light from a distant galaxy is found to contain the spectral lines of hydrogen. The light causing one of these lines has a measured wavelength of 466 nm. When the same line is observed from a hydrogen source on Earth it has a wavelength of 434 nm. a) Calculate the Doppler shift, z, for this galaxy. b) Calculate the speed at which the galaxy is moving relative to the Earth. c) In which direction, towards or away from the Earth, is the galaxy moving? (1) 2. The galaxy Corona Borealis is approximately million light years away from the Earth. Calculate the speed at which Corona Borealis is moving away from the Earth. 3. A galaxy is moving away from the Earth at a speed of m s 1. The frequency of an emission line coming from the galaxy is measured. The light forming the same emission line, from a source on Earth, is observed to have a frequency of Hz. a) Show that the wavelength of the light corresponding to the emission line from the source on the Earth is m. b) Calculate the frequency of the light forming the emission line coming from the galaxy. 4. A distant quasar is moving away from the Earth. Hydrogen lines are observed coming from this quasar. One of these lines is measured to be 20 nm longer than the same line, of wavelength 486 nm from a source on Earth. a) Calculate the speed at which the quasar is moving away from the Earth. b) Calculate the approximate distance, in millions of light years, that the quasar is from the Earth. Total marks: 22 15

18 Homework 13 AC Signals 1. The oscilloscope below shows the potential difference over a bulb attached to an AC power supply. The y-gain is set at 5V / div. The time base is set at 5ms / div. a) State the peak potential difference of the trace. (1) b) Calculate the frequency of the supply. c) Calculate the rms value of the potential difference. 2. The root mean square voltage produced by a low voltage power supply is 10 V. a) Calculate the peak voltage of the supply. b) An oscilloscope, with its time-base switched off, is connected across the supply. The Y-gain of the oscilloscope is set to 5 V cm 1. Describe the trace seen on the oscilloscope screen. (2) 3. An a.c. signal of frequency 20 Hz is connected to an oscilloscope. The time-base switch on the oscilloscope is set at 0.01 s cm 1. Calculate the distance between the neighbouring peaks of this waveform when viewed on the screen. Total marks: 15 16

19 Homework 14 Emf & Internal Resistance 1. In the circuit below, the reading on the voltmeter is 5 V when switch S is open and 3 V when it is closed. a) What is the Emf of the cell? (1) b) Calculate the current flowing in the circuit when the switch is closed. c) What is the internal resistance of the cell? 2. The graph shows how the voltage across the terminals of a battery changes as the current from the battery is varied. a) Calculate the internal resistance of the battery. b) What is the value of the current from the battery when it is shortcircuited? Total marks: 13 17

20 Homework 15 - Capacitors 1. The circuit below is set up with the capacitor initially discharged. The switch is put to position A, and the capacitor allowed to fully charge. This process takes 60 seconds. a) Calculate the initial charging current in the circuit. b) State the current once the capacitor is fully charged. (1) c) Draw a graph of charging current Vs time. You should have values on both axes. d) What is the potential difference over the capacitor when it is fully charged? (1) The switch is thrown to position B, and the capacitor is allowed to fully discharge. e) Calculate the initial discharge current. f) How would the discharge time compare to the charge time? Explain your answer. (2) 2. The charge stored by a 2 F capacitor is 4 x 10-4 C. a) How much energy was required to charge the capacitor? b) What is the voltage across the capacitor? Total marks: 19 18

21 Homework 16 Conductors, Semiconductors and Insulators 1. Give examples of two conductors, two insulators and two semiconductors. 2. The conductivity of a semiconductor material can be increased by doping. a) Explain what is meant by the conductivity of a material. (1) b) Explain, giving an example, what is meant by doping a semiconductor. (2) c) Why does doping decrease the resistance of a semiconductor material? (1) 3. A sample of pure germanium (four electrons in the outer shell) is doped with phosphorus (five electrons in the outer shell). What kind of semiconductor is formed? 4. Why does a sample of n-type semiconductor still have a neutral overall charge? (1) (1) 5. Describe the movement of the majority charge carriers when a current flows in: i. an n-type semiconductor material (1) ii. a p-type semiconductor material. (1) Total marks: 11 19

22 Homework 17 p-n Junctions 1. A p-n junction diode is connected across a d.c. supply as shown. a) Is the diode connected in forward or reverse bias mode? (1) b) Describe the movement of the majority charge carriers across the p-n junction. (2) c) What kind of charge is the only one that actually moves across the junction? (1) 2. When positive and negative charge carriers recombine at the junction of ordinary diodes and LEDs, quanta of radiation are emitted from the junction. a) Does the junction have to be forward biased or reverse biased for radiation to be emitted? (1) b) What form does this emitted energy take when emitted by: (i) an LED (1) (ii) an ordinary junction diode? (1) 3. a) State two advantages of an LED over an ordinary filament lamp. (1) b) An LED is rated as follows: operating p.d. 1 8 V, forward current 20 ma The LED is to be operated from a 6 V d.c. power supply. (i) Draw a diagram of the circuit, including a protective resistor, which allows the LED to operate at its rated voltage. (1) (ii) Calculate the resistance of the protective resistor that allows the LED to operate at its rated voltage. Total marks: 12 20

23 Homework 18 The Standard Model 1. Copy and complete the table by placing the fermions in the list below in the correct column of the table. bottom charm down electron strange electron neutrino muon muon neutrino tau tau neutrino top up Quarks Leptons 2. a) State the difference between a hadron and a lepton in terms of the type of force experienced by each particle. (2) b) Give one example of a hadron and one example of a lepton. (2) 3. Information on the sign and charge relative to proton charge of six types of quarks (and their corresponding antiquarks) is shown in the table. Quark name Charge relative Antiquark name Charge relative to size of proton to size of proton charge charge up +2/3 antiup 2/3 charm +2/3 anticharm 2/3 top +2/3 antitop 2/3 down 1/3 antidown +1/3 strange 1/3 antistrange +1/3 bottom 1/3 antibottom +1/3 a) Calculate the charge of the following combinations of quarks: i. two up quarks and one down quark ii. one up quark and two down quarks iii. two antiup quarks and one antidown quark iv. one antiup quark and two antidown quarks. (4) b) Name the force which holds the quarks together in protons and neutrons. (1) (2) Total marks: 11 21

24 Homework 19 Forces on Charged Particles 1. Draw the electric field around the following charges. You must show the direction of the field clearly. (a) + (b) 2. What is the definition of a volt? (1) 3. Look at the following diagram. a) What is the potential difference between the two plates? (1) b) Calculate the work done in moving the charged particle across the electric field. 4. The diagram shows an arrangement which is used to accelerate electrons. The potential difference between the cathode and anode is 2.5 kv. Assuming the electrons start from rest, calculate the speed of the electron as it reaches the anode. (5) Total marks: 13 22

25 Homework 20 Particle Accelerators In the following questions, when required, use the following data: Charge on electron = C Charge on proton = C Mass of electron = kg Mass of proton = kg 1. In an evacuated tube, an electron initially at rest is accelerated through a p.d. of 500 V. a) Calculate, in joules, the amount of work done in accelerating the electron. b) How much kinetic energy has the electron gained? (1) c) Calculate the final speed of the electron. 2. In an electron gun, electrons in an evacuated tube are accelerated from rest through a potential difference of 250 V. a) Calculate the energy gained by an electron. b) Calculate the final speed of the electron 3. The power output of an oscilloscope (cathode-ray tube) is estimated to be 30W. The potential difference between the cathode and the anode in the evacuated tube is 15 kv. a) Calculate the number of electrons striking the screen per second. (5) b) Calculate the speed of an electron just before it strikes the screen, assuming that it starts from rest and that its mass remains constant. (4) Total marks: 22 23

26 Homework 21 Fission and Fusion 1. There are three isotopes of hydrogen: a) How many protons does each nucleus have? (1) b) How many neutrons does each nucleus have? (1) 2. Energy is produced within the Sun by fusion reactions. a) State what is meant by a fusion reaction. (1) b) Explain briefly why a fusion reaction releases energy. (1) 3. A nuclear reaction is described by the equation below: a) What type of reaction is this? (1) b) Calculate the missing numbers X and Y. (2) c) Using information from the table below, calculate the energy released in this reaction. NUCLEUS/PARTICLE MASS (kg) 239 Pu Te Y Mo n (4) Total marks: 11 24

27 Homework 22 Photoelectric Effect 1. When introducing the photoelectric effect a Physics teacher writes: One of the important factors affecting photoelectric emission from a metal is the threshold frequency for the metal. Explain the meaning of the terms: a) photoelectric emission; (1) b) threshold frequency. (1) 2. Red light has a wavelength of m. Calculate the energy of one photon of this light. 3. For a certain metal, the energy required to eject an electron from an atom is 3 x J. a) What is the minimum frequency of electromagnetic radiation required to produce the photoelectric effect with this metal? b) The metal is illuminated with blue light that has a wavelength of 400 nm. Show by calculation that this will cause the photoelectric effect to occur. c) Calculate the kinetic energy that the ejected electrons will have when the metal is illuminated with this light. Total marks: 14 25

28 Homework 23 Interference 1. An experiment is set up to investigate interference effects and a pattern of dark and bright fringes is produced. Explain, in terms of waves, how the pattern of bright and dark fringes are produced. (2) 2. Microwaves are passed through two slits, A and B, in a metal plate as shown in the diagram below. A microwave detector is moved along a straight line from X to Y. The first minimum of microwave intensity is detected at point P. The distance AP is 41cm and BP is 43cm. Find the wavelength of the microwaves. 3. A grating with 300 lines/mm is used with a spectrometer and a source of monochromatic light to view an interference pattern as shown below. The second maximum of interference is observed when the telescope is at an angle of 24.5 o. Calculate the wavelength of the light. 4. A grating or a prism can be used to produce spectra from a source of white light. Give two differences between the spectra obtained using the grating and the prism. Diagrams may be used to illustrate your answer. (2) Total marks: 10 26

29 Homework 24 Refraction 1. A ray of red light has a wavelength of 700 nm in air. It is incident on a block of plastic, and is refracted as shown below: a) Calculate the refractive index of the block of plastic. b) What is the wavelength of the red light in the block of plastic? c) A blue light now replaces the red light. What happens to the angle of refraction? (1) 2. A physics student decides to propose to his girlfriend. Just as he is presenting the diamond engagement ring to her, he notices the sparkling is caused by total internal reflection. He is so taken by this observation, he rushes off to find out the refractive index of diamond so that he can calculate the critical angle for the diamond. His girlfriend immediately dumped him. a) If the refractive index of diamond is 2.42, calculate the critical angle. b) What is meant by critical angle? (1) 3. White light is shone onto a triangular glass prism. A spectrum is viewed on the other side of the prism. a) Why is a spectrum produced? (1) b) List the colours in order from most deflected to least deflected. (1) Total marks: 12 27

30 Homework 25 Spectra 1. (a) A light meter is used to measure the irradiance of light from a small lamp At a distance of 1.5 m from the lamp, the irradiance of the light is 0.60 Wm -2. What is the irradiance at a distance of 4.5 m from the lamp? (b) At a distance of 1.5m from a laser, the irradiance of the laser light is 400 Wm -2. What is the irradiance at a distance of 4.5 m from the laser? (1) 2. The following diagram represents the energy levels of a particular metal s atoms. -5 x J -9 x J -16 x J -25 x J a) How many possible transitions are there for this atom? (1) b) Calculate the maximum frequency of light absorbed by this atom. c) Which part of the spectrum would this absorption line be found in? Explain your answer. 3. Explain why the absorption spectrum of an atom has dark lines corresponding to frequencies present in the emission spectrum of the atom. (2) 4. A laser used in a CD player emits monochromatic light of wavelength 840 nm. a) When the light passes through a grating only one bright line is seen in the spectrum. Explain why only one line appears in the emission spectrum of the laser. (1) b) Calculate the difference in energy between the two energy levels that produce photons with this wavelength. Total marks: 17 28