Sixth Form Entrance 2017 PHYSICS. 1 hour ANSWER ALL THE QUESTIONS ON THE PAPER

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1 Sixth Form Entrance 2017 PHYSICS 1 hour ANSWER ALL THE QUESTIONS ON THE PAPER You are advised to take note of the information and equations given at the start of each question Name (Capital Letters):... Present School:... 1

2 Q1. You may find the following information useful for this question Resistance (in Ω) = potential difference (in V) / current (in A) or in symbols R = V I Resistance is a measure of how difficult it is for the current to flow through a conductor. Note: Potential difference is another name for voltage The table below shows how the current passing through a torch bulb varies with the potential difference (voltage) across it. Potential difference /V Current/A a) Draw a circuit diagram of a circuit which could have been used to obtain these results. (3 marks) 2

3 b) On the grid below, plot a graph of potential difference on the y axis against current on the x axis. Include a suitable curve of best fit. (4 marks) ci) Use the graph to find the potential difference across the bulb when the current through it is 0.30A. ii) Calculate the resistance of the bulb filament when the current through it is 0.30A. 3

4 di) Using the graph, describe how the resistance of the bulb filament changes when the current through it is increased. ii) Suggest and explain a reason why the resistance changes in this way (think about what is causing the resistance in the filament)..... e) A component is said to obey Ohm s Law if the current is directly proportional to the potential difference. Does the bulb obey Ohm s Law? Give a reason for your answer

The following graph shows the relationship between potential difference and current for a resistor. f) Do you think that this resistor is obeying Ohm s Law? Give a reason for your answer.

5 The following graph shows the relationship between potential difference and current for a resistor. f) Do you think that this resistor is obeying Ohm s Law? Give a reason for your answer The resistance can be found by calculating the gradient of a potential difference - current graph. g) Find the resistance of this resistor using the gradient. Show your workings. h) Add a second line to show what the graph would look like for a resistor with twice the resistance of the first one (assume you have used the same measuring equipment). 5

Q2. You may find the following information useful for this question: Average velocity (in m/s) = distance (in m) / time taken (in s) or in symbols v = d t Work done (in J) = Force (in N) x distance

6 Q2. You may find the following information useful for this question: Average velocity (in m/s) = distance (in m) / time taken (in s) or in symbols v = d t Work done (in J) = Force (in N) x distance moved (in m) or in symbols w.d = F x d Power (in W) = work done (in J) / time taken (in s) or in symbols P = w.d t 1kW = 1000W ai) The motorcyclist below is accelerating. Label the forces shown by the arrows on the diagram. (3 marks) ii) What can you say about the relationship between these forces if the motorcyclist is accelerating? 6

7 b) The graph below shows the motion of the motorcycle over a 10s period. i) What is the steady velocity reached by the motorcycle during this 10s period? ii) What can you say about the forces acting when he has reached this steady velocity? ci) A force F acts on a body moving with velocity v. Starting from the definition of power and using the other equations given at the start of this question, show that Power = F v.. 7

8 ii) When the motorcycle in part (b) is travelling at the steady velocity shown in the graph, the useful power output of the engine is 40kW. Calculate the driving force required to maintain this velocity. d) At a later time the motorcycle brakes until it stops. When this happens, brake pads are forced into contact with the wheel discs. Explain what happens to the motorcycle s kinetic energy. 8

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10 Q3. Theory suggests that when a beam is loaded at the centre as in the diagram below, the deflection x is directly proportional to the cube of d, the distance between the supports, assuming that the same weight is applied to the centre of the beam. An equation to describe this relationship would be x = k d 3 where k is a constant d x You are required to design an experiment to confirm that this equation is correct using a metre rule as a beam and 2 triangular wooden blocks as supports. From initial checks you know that when a metre rule rests on edge supports 0.9m apart, its centre is deflected by about 1cm when a load of 8N is hung from the centre. a) What are the dependent and independent variables in this investigation? Dependent variable.. Independent variable 10

11 b) Describe as fully as you can how you would carry out your investigation. Remember to consider the following: o o o o What you would use to take your measurements. How you would take your measurements. The number and range of the measurements you would take How you would make this experiment as accurate as possible (5 marks) 11

12 c) Name one variable that you would need to control to make this a fair test. d) Your teacher suggests that to test the equation, you should plot a graph of x against d 3 If this relationship is correct, the graph will look like the one shown below x x = k d 3 d 3 e) What is the mathematical equation that is used to generally describe a straight line graph (using the convention that m = gradient and c= intercept)?.. f) By considering the equation x = kd 3 and the equation for a straight line graph, look at what is plotted on which axis and hence suggest which feature of the graph will enable you to determine a value for k... g) By considering the units of the other 2 quantities, suggest a suitable unit to use for k. 12

13 Q4. You may find the following information useful for this question Density (in kg/m 3 ) = mass (in kg)/ volume (in m 3 ) or in symbols D = M / V Weight (in N) = mass (in kg) x gravitational field strength (in N/kg) or W = mg On earth g = 10N/kg Archimedes Principle is used to explain buoyancy and why things float. Archimedes Principle states that an object immersed in a fluid (i.e. a liquid or a gas) experiences an upwards force called upthrust. The upthrust (U) is equal to the weight of the fluid displaced (i.e. pushed out of the way) by the object Upthrust = Weight of fluid displaced A block of a different material, which usually floats in water, is secured to the bottom of a deep pool of water by a rope. rope ai) There is now an additional force acting in the rope. What is this force called? ii) Draw an arrow on the rope to show the direction in which this force is acting 13

14 You are told the following information about the block: Length of each side = 0.2m (the block is a cube) Density of the block = 400 kg/m 3 Density of fresh water = 1000 kg/m 3 b) Calculate the mass of the block (3 marks) c) Now calculate the weight of the block.. d) Calculate the weight of the water that the block displaces (i.e. pushes out of the way) you will need to calculate the mass first as in the previous question (3 marks) 14

15 ei) Archimedes Principle tells us that this weight of water must be equal to the upthrust acting on the block. The block is not moving. Write a word equation to show the relationship between the 3 forces acting at this stage. ii) Hence deduce the size of the force acting in the rope (3 marks) END OF EXAM Total 60 Marks 15

16 Sixth Form Entrance 2015 PHYSICS 1 hour ANSWER ALL THE QUESTIONS ON THE PAPER Name (Capital Letters):... Present School:...

17 Q1a) A car engine is leaking oil. The oil drops hit the ground at regular time intervals, 2 times every second. The diagram below shows the pattern of the drops that the car leaves on part of its journey. i) What can you say about the speed of the car before it reaches the speed limit signs?.... ii) Calculate the distance between the drops on the road before it reaches the signs if the car is travelling at 10 m/s. iii) After the car passes the signs, what happens to the gaps between the drops of oil? What does this tell you about the motion of the car?

8000N 6000N F T 400N 14 000N i) What is the cause of force T?

18 b) A front-wheel drive car is travelling at constant velocity. The forces acting on the car are shown in the diagram below. 8000N 6000N F T 400N N i) What is the cause of force T? ii) What is the cause of force F?. iii). What is the size of force F? Explain your answer.....

19 iv) Force T is now increased. Describe and explain what effect this has on the speed of the car c) The acceleration of a moving object is calculated using the following equation a = acceleration in m/s 2 v = final velocity in m/s u = initial velocity in m/s t = time in s a = v u t i) A motorbike travelling at 20 m/s accelerates at a rate of 0.6 m/s 2 for 12s. Calculate its new velocity. Show all of your workings. (3 marks)

The total distance travelled by a vehicle that is accelerating can be calculated using the following equation s=u t + ½ a t 2 Where s = distance travelled (in m) and all other symbols are as defined

20 The total distance travelled by a vehicle that is accelerating can be calculated using the following equation s=u t + ½ a t 2 Where s = distance travelled (in m) and all other symbols are as defined in the previous question. ii) Calculate the distance travelled by the motorbike in the previous question over the 12s that it is accelerating. (3 marks) The motorbike now starts to go up a hill. weight iii) What effect will this have on the acceleration of the motorbike? Try to explain your answer in terms of the forces acting.

21 Q2) A pupil is carrying out an experiment using a pendulum. She is looking at the relationship between the length of the string and time period (ie the time it takes for the pendulum bob to swing from one side to the other and back again). a) Design an experiment that she could carry out to look at the relationship between length and time period. You should include the following: The variables that she would need to measure and the measuring devices she could use for this. A brief method explaining how she might carry out this experiment. A comment about how she could make this a fair test. A description of what she could do to make her experiment as accurate as possible cont..

22 (4 marks) b) The equation that relates the time period of a pendulum to the length of the string is given below T = time period in s L= length of string in m g = gravitational field strength (= 10 N/kg on Earth) π = 3.14 i) Calculate the time period of a 1.5m long pendulum.....

23 Since this is a non-linear relationship, a graph of T against L would not be a straight line and so would be difficult to analyse. A straight line graph can be obtained if the equation is squared on both sides to eliminate the square root sign. ii) Square the equation on both sides.. Now if you plot T 2 on the y axis and L on the X axis of a graph, it should give you a straight line graph. iii) In the table below are the results that the pupil collected from her experiment. Calculate the values for T 2 and quote them to 2 significant figures. L (in m) T (in s) T 2 (in s 2 ) to 2 sig figs

24 iv) Draw a graph of T 2 (on the y axis) against L (on the x axis). Choose suitable scales and include a line of best fit. (5 marks) v) Does your graph support the equation suggested? Give a reason why.

25 vi) The gradient (ie rise/run) of the graph is equal to 4π 2 g Find the gradient of your graph and use this to calculate a value for g, the gravitational field strength. (3 marks) vii) Why do you think it is better to find g from the gradient of the graph, rather than just using a pair of values from the table?

26 Q3) The graph below shows how the orbit time of an artificial satellite depends on its height above the Earth s surface Height above Earth's surface in millions of metres Orbit time in hours a) How does the orbit time change with increasing height above the Earth s surface?... b) Some satellites are in geostationary orbit. They have an orbital time of 24 hours which mean that they remain above the same point on the Earth s surface. i) Use the graph to find the height above the Earth s surface of a geostationary satellite....

27 ii) Suggest two uses of satellites that are in geostationary orbit c) The diagram shows the force that acts on a geostationary satellite. Earth i) What causes this force... ii) Eventually, a satellite in orbit around the Earth loses energy and slows down because of frictional forces acting on it. Describe what is likely to happen to the satellite over a period of time

28 The orbital velocity of a satellite can be calculated using the following equation v = 2πr T where v = orbital velocity in m/s r = radius of orbit in m (measured from the centre of the objects) T = time for one complete orbit in s (also called time period) d) A satellite is in a geostationary orbit that has a radius of km Show that the orbital velocity of this satellite is nearly 3100 m/s (3 marks) e) The speed of radio waves is m/s. Speed (in m/s) = distance (in m) / time (in s) The geostationary satellite in part d) is used for telephone communications. Estimate the time delay between a voice message being sent and received via this satellite (3 marks)

29 The table below gives some information about three satellites. satellite name Hubble space telescope NOAA-17 Intelsat-906 purpose to observe the stars to monitor the Earth s atmosphere and oceans geostationary communications satellite orbit height above Earth s surface approximate orbit time 612 km 1.5 h 833 km 1.7 h km 24 h f) NOAA-17 is in a polar orbit. This means that it travels around the earth from pole to pole as shown below i) Approximately how many orbits does NOAA-17 make in one day?... ii) Explain how this type of orbit allows NOAA-17 to monitor all the Earth s oceans

30 iii) The Hubble Space Telescope is used to study the faint light from distant stars. Suggest why it is placed in orbit just above the Earth s atmosphere g) A polar orbiting satellite has a time period of 90 minutes. Calculate its height above the Earth s surface. Take the gravitational field strength at the height of the orbit as 10 N/kg and the radius of the Earth as 6400 km. You will need to use the following equations v = 2πr T g = v2 r Note: r = total radius of the orbit of the satellite. g = gravitational field strength in N/kg END OF EXAMINATION (4 marks)

To the member of staff supervising the physics 6 th form entrance exam for The King s School, Canterbury, This paper includes a number of equations that have been formatted using Word equation writer.

31 To the member of staff supervising the physics 6 th form entrance exam for The King s School, Canterbury, This paper includes a number of equations that have been formatted using Word equation writer. Very rarely, some older versions of Word can have problems displaying these equations correctly. In the unlikely event of this happening, the equations that should be apparent are as written below. Q1 part c a= (v-u) / t and s=ut+1/2at 2 Q2 part b T = 2π (L/g) Q2 part b vi (4π 2 )/g Q3 part c ii v=(2πr)/t Q3 part g v=(2πr)/t and g=v 2 /r Apologies for any inconvenience caused.

THE KING S SCHOOL, CANTERBURY SIXTH FORM ENTRANCE EXAMINATION 2014-2015 Physics 1

32 THE KING S SCHOOL, CANTERBURY SIXTH FORM ENTRANCE EXAMINATION Physics 1 Hour ANSWER ALL THE QUESTIONS ON THE PAPER Name (Capital Letters):... Present School:... 1

Q1. When certain materials are heated, they expand ie they increase in size. a) Using ideas about particles and energy, explain why a material expands upon heating.

33 Q1. When certain materials are heated, they expand ie they increase in size. a) Using ideas about particles and energy, explain why a material expands upon heating.... The linear expansivity of a substance is the amount by which one metre length will increase for every one degree Celcius rise in temperature. Engineers can use this to work out how much their material will expand over the range of temperature in which they are to be used. b) Why is it important to know this when building a bridge? ci) The linear expansivity of steel is m per o C. What will be the length of a 500m steel bridge if the temperature rises by 50 o C? 2

ii) The linear expansivity of copper is 0.000 023m per o C and that of aluminium is 0.00003m per o C.

34 ii) The linear expansivity of copper is m per o C and that of aluminium is m per o C. Which will expand most, 50m of copper heated by 40 o C or 50m of aluminium heated by 30 o C. Justify your answers by calculations. (3 marks) iii) How was the idea of expansivity used in fitting metal tyres to wooden cart wheels as shown in the diagram below? 3

Gases exert a pressure on the container that they are in due to collisions between the particles and the walls of the container. When gases are heated they expand.

35 Gases exert a pressure on the container that they are in due to collisions between the particles and the walls of the container. When gases are heated they expand. d) The pressure of a gas is related to its temperature. How would you expect the pressure of a gas to change if the temperature was increased? Explain your answer. (3 marks) The pressure is also related to the volume of the gas. The relationship between these 2 variables is called Boyle s Law which is summarised by the following equation: where: p 1 x V 1 = p 2 x V 2 p 1 = initial pressure in Pa V 1 = initial volume in m 3 p 2 = final pressure in Pa V 2 = final volume in m 3 e) A gas at a pressure of 100 kpa is compressed from a volume of 0.3m 3 down to a volume of 0.15m 3. The temperature of the gas does not change. Calculate the new pressure of the gas. Show all of your workings. 4

36 f) A sealed container contains air. The pressure of the air is measured at different temperatures. The table shows the results. An atmosphere is a unit of pressure that gives the pressure in multiples of normal atmospheric pressure. Temperature ( 0 C) Pressure (atmospheres) i) Using the grid below, add a suitable scale to the axes and plot a line graph of pressure on the y axis and temperature on the x axis. Draw a line of best fit. (4 marks) ii) Use your graph to find the temperature of the air at which its pressure is zero.... This temperature is known as absolute zero. iii) Describe the motion of the particles at absolute zero if they are not exerting any pressure on the container. 5

37 Q2. You may find the following information useful for this question: Resistance (in Ω) = Voltage (in V) / Current (in A) The higher the resistance, the lower the current in a circuit. A student is asked to investigate how the resistance of a wire varies with its length. a) Briefly describe how she might do this experiment, giving details of any variables that she needs to measure, the equipment that she could use, any calculations she would need to do and an explanation as to how she could make this a fair test. You may include a diagram if you wish. (5 marks) 6

Here are the results of the experiment that she carried out. Length of 0.0 10 20 30 40 50 wire/cm Resistance/ Ω 0.0 4.5 9.1 13.6 18.1 22.

38 Here are the results of the experiment that she carried out. Length of wire/cm Resistance/ Ω bi) Plot a graph of length of wire against resistance. Include a line of best fit. (4 marks) ii) What can you conclude about the mathematical relationship between the resistance of the wire and its length? 7

39 A rheostat is a device that can be used to produce varying output voltages from a fixed voltage supply. It is essentially just a long coil of wire. A sliding contact can be moved along the coil of wire to vary the resistance in the circuit. This in turn varies the output voltage. Below is a circuit diagram showing the rheostat being used in a circuit. rheostat As the sliding contact is moved along the wire, the output voltage (V out) changes in proportion to the length of the coil wire between the two points of contact ie points X and Y. Assume that the wire is evenly wound along the coil. ci) What would you expect the output voltage to be at the half way point?... ii) Where would the sliding contact need to be to get an output of 4.5 V? Be as specific as you can. 8

40 The diagram below shows the fuel gauge assembly in a car. The sliding contact touches a coil of wire and moves over it. The sliding contact and the coil form a variable resistor (similar to the rheostat in the question above). The sliding contact is connected to a float via a pivot. The fuel gauge indicator is an ammeter. When the petrol level changes, the resistance of the circuit changes. This in turn affects the current (higher resistance means lower current) This causes the pointer in the fuel gauge indicator to move. d) How will the current in the circuit change as the amount of petrol in the tank falls? Explain your answer

Q3 You may find the following information useful for this question: Circumference of a circle = 2πr where r is the radius Weight (in N) = mass (in kg) x gravitational field strength (in N/kg)

41 Q3 You may find the following information useful for this question: Circumference of a circle = 2πr where r is the radius Weight (in N) = mass (in kg) x gravitational field strength (in N/kg) Gravitational field strength = 10 N/kg on the Earth s surface The height that you can jump depends inversely on the gravitational field strength. So if the field strength doubles, the height halves. ai) If the Olympic games were held on Mars (gravitational field strength= 3.8 N/kg) in a large dome to provide air to breathe, what would happen to the Olympic record for: Weight lifting circle the correct answer It would increase it would stay the same it would decrease Explain your choice ii) High jump circle the correct answer It would increase it would stay the same it would decrease Explain your choice 10

42 iii) Throwing the javelin circle the correct answer It would increase it would stay the same it would decrease Explain your choice iv) The 100m race circle the correct answer It would increase it would stay the same it would decrease Explain your choice 11

43 The diagram shows the orbits of the Earth and Mars around the Sun. Diagram not to scale Sun Mars Earth Data: Distance of Earth from the Sun: 1.49 x m Distance of Mars from the Sun: Length of one Earth year: 2.28 x m 365 days. bi) Using the data given above, and assuming that the orbit is circular, show that the orbital speed of the Earth around the Sun is approximately m/s. (3 marks) 12

44 ii) Convert this speed into km/hr.... (3 marks) In 1619 Johannes Kepler published his third law of planetary motion which stated that the square of the period of the orbit (time to go round the sun) was proportional to the cube of the radius of the orbit around the sun. Mathematically this is expressed as: T 2 = k R 3 Where T = time for one orbit in seconds R = radius of orbit in metres K = a constant c) Using the data for the Earth, calculate the value of the constant k.... d) Suggest a possible unit for k. 13

45 e) Using the same value of k, calculate the orbital period (ie T) for Mars. f) Hence, calculate the orbital velocity of Mars (in m/s) (3 marks) END OF EXAMINATION Total 60 marks 14

Sixth Form Entrance 2018 PHYSICS

Sixth Form Entrance 2018 PHYSICS 1 hour ANSWER ALL THE QUESTIONS ON THE PAPER You are advised to take note of the information and equations given at the start of each question. Use of a calculator is permitted.