Which of the following are two vector quantities?
D.
A graph shows how the velocity of an object varies with time. What does the gradient of the graph represent?
B.
Newton’s second law of motion states that:
D.
A car of mass m is traveling along a horizontal road at constant speed. The total resistive force acting on the car is F and the power of the car’s engine is P. What is the speed of the car?
D.
It takes an object two seconds to move from point A to point B along the path shown in the diagram.
What is the average speed and the magnitude of the average velocity of the object?
| Average speed | Magnitude of average velocity | |
| A. | 4 + 2 \pi m s^{-1} | 6 m s^{-1} |
| B. | 4 + 2 \pi m s^{-1} | 4 + \pi m s^{-1} |
| C. | 4 + \pi m s^{-1} | 6 m s^{-1} |
| D. | 4 + \pi m s^{-1} | 4 + \pi m s^{-1} |
C.
A firework rocket is launched vertically upwards and it explodes when it reaches a height of 50 m. What is true about the kinetic energy and the momentum of the system when compared right before and right after the explosion?
| Kinetic energy | Momentum | |
| A. | Conserved | Conserved |
| B. | Increased | Increased |
| C. | Increased | Conserved |
| D. | Conserved | Increased |
C.
Boxes A and B are pushed along a surface by a 20 N force. The mass of box A is 1.5 kg and the mass of box B is 0.50 kg. The boxes travel at constant speed.
What is the resultant force that acts on box B?
D.
A temperature of 58 ^{o}C is equal to:
D.
A monatomic real gas can behave very similarly to an ideal gas under certain conditions. Which of the following is one of these conditions?
A.
When a transverse wave travels through a medium, which of the following is true about the direction of propagation and the energy transfer of the wave in relation to the displacement of the medium?
| Direction of propagation | Direction of energy transfer | |
| A. | Perpendicular | Parallel |
| B. | Parallel | Parallel |
| C. | Parallel | Perpendicular |
| D. | Perpendicular | Perpendicular |
D.
Two pulses travel towards each other as shown on the diagram.
Which one of the following diagrams shows a possible configuration when the two pulses meet?
C.
What is true about the magnitude of the acceleration of an object that is moving with simple harmonic motion (SHM)?
A.
Which of the following lists electromagnetic waves in increasing order of frequency?
D.
One electronvolt is equivalent to:
D.
The power supplied by a battery per unit current from the battery is a definition of:
B.
A student wants to connect an ammeter and a voltmeter to measure the current through and the potential difference across a resistor. How should the ammeter and the voltmeter be connected to the resistor?
| Ammeter | Voltmeter | |
| A. | Series | Parallel |
| B. | Parallel | Series |
| C. | Series | Series |
| D. | Parallel | Parallel |
A.
What is true about a secondary cell’s ability to be recharged and the energy conversion when the cell is discharging?
| Ability to be recharged | Energy conversion during discharge | |
| A. | Can be recharged | Electrical energy to chemical energy |
| B. | Cannot be recharged | Electrical energy to chemical energy |
| C. | Can be recharged | Chemical energy to electrical energy |
| D. | Cannot be recharged | Chemical energy to electrical energy |
C.
Phobos is one of the moons that orbits Mars. Newton’s universal law of gravitation can be applied to calculate the force between Phobos and Mars. Which one of the following conditions enables this calculation?
A.
Which of the following properties is affected when a nucleus decays through gamma-decay?
D.
On the graph that shows how average binding energy per nucleon varies with nucleon number, the most stable elements can be found:
B.
Which of the following statements is true about the Higgs boson?
C.
The SI unit combination of energy density is:
B.
What part of the nuclear power plant conveys energy from the reactors to the turbines?
C.
An object on a spring oscillates with simple harmonic motion (SHM) on Earth. Which of the following statements is true about the period of this system?
B.
The Doppler effect:
C.
At infinity:
D.
Which of the following quantities is needed in order to calculate the orbital speed of a satellite about a planet?
B.
The direction of the current induced in a conductor is such as to oppose the change that created the current. This statement is:
C.
What is definitely true about an ideal transformer?
D.
An electron and an antineutrino are emitted in:
B.
The initial number of nuclides in a pure sample of radioactive isotope is N_{0}. Which graph correctly shows how N, the number of undecayed nuclides in the sample varies with time?
B.
A helicopter is lifting a skydiver vertically upwards at constant speed.
a. State the net force that acts on the skydiver.
[1 mark]
When the helicopter reaches a certain distance above the ground, the skydiver drops from the helicopter vertically downwards.
b. Draw a free body diagram
i. for the skydiver the moment after she has dropped from the helicopter.
[1 mark]
ii. for the helicopter the moment after the skydiver has dropped from it.
[2 marks]
While the helicopter pilot is waiting for the skydiver to reach the ground, the helicopter is hovering motionless above the ground.
c. Outline how the lift force on the helicopter is achieved. In your answer, refer to Newton’s third law of motion.
[2 marks]
Zero
The rotating helicopter blades exert a downward force on the air.
The air exerts an upward force on the blades that has the same magnitude as the downward force exerted by the blades.
An expandable balloon is filled with a fixed mass of argon-40 gas. The pressure of the gas is maintained at 1.3 kPa. The graph shows how the volume of the gas varies with temperature.
a. State two assumptions of the kinetic model of an ideal gas.
[2 marks]
b. Explain why argon-40 behaves as an ideal gas for temperatures between 20 \: ^{\circ}C and 70 \: ^{\circ}C.
[2 marks]
c. Find the mass of the argon-40 gas in the balloon.
[2 marks]
Any two of the following:
Gas molecules are considered tiny, point-like particles that have the same mass.
The volume of each molecule is negligible compared to the total volume of the gas.
Intermolecular forces between the particles are negligible.
The gas molecules only have kinetic energy.
All collisions that take place are elastic.
The duration of collisions is negligible compared to the time between collisions.
At any moment, the number of molecules moving in one direction is the same as the number of molecules moving in any other direction.
The effects of gravity are ignored.
If argon behaves as an ideal gas, then the ideal gas equation should work for this gas on the given temperature range. This means that at constant pressure \frac{V}{T} should be constant.
Let’s pick two points from the graph to show this:
\frac{15}{300} = 0.05
\frac{25}{500} = 0.05
This means that argon behaves as an ideal gas on the given temperature range.
n = \frac{(1.3 \times 10^{3})(15)}{(8.31)(300)} \approx 7.82 moles
The molar mass of argon-40 is 40 grams, so the mass of the gas in the container is (7.82)(40) \approx 313 \approx 310 grams
A pulse is travelling on a string that has one end fixed to a wall.
When the pulse reaches the wall, it is reflected.
a. Sketch the pulse after it has been reflected at the wall.
[1 mark]
The end of the string is vibrated vertically so that a transverse wave travels through the string. The time period of the vibrations is 1.62 s. The length of the string is 1.95 m.
b. Distinguish between a transverse and a longitudinal travelling wave.
[2 marks]
c. Calculate the speed of the wave. Give your answer to an appropriate number of significant figures.
[3 marks]
In a transverse wave the displacement of the medium is perpendicular to the direction of wave propagation/energy transfer.
In a longitudinal wave the displacement of the medium is parallel to the direction of wave propagation/energy transfer.
Wavelength of the wave: \lambda = \frac{1.95}{2.5} = 0.780 m
v = f \lambda = \frac{\lambda}{T} = \frac{0.780}{1.62} \approx 0.481 m s^{-1}
Answer must be given to 3 significant figures in order to earn final mark.
A variable resistor is connected to a cell of internal resistance r. An ideal voltmeter is also connected to the circuit as shown.
The graph shows how the voltmeter reading varies with the current in the cell as the resistance of the variable resistor is adjusted.
a. State what is meant by the emf of a cell.
[2marks]
b. State the emf of the cell.
[1 mark]
c. Find r.
[2 marks]
The work done per unit charge by the cell to move charge all the way around the circuit.
The vertical axis intercept of the graph, so 16 V
The internal resistance of the cell is given by the magnitude of the gradient of the graph.
Picking two points from the graph we get:
\frac{5 - 16}{2.25 - 0} \approx -4.9
So the internal resistance is 4.9 \: \Omega
An object of mass 2.3 kg is moving in a vertical circle of radius 5.1 m at constant speed in an anticlockwise direction.
a. When the object is at the position shown on the diagram, state the direction of:
i. the object’s velocity.
ii. the net force on the object.
[2 marks]
The magnitude of the net force that acts on the object is 37 N.
b. Calculate the angular velocity of the object. Include an appropriate SI unit with your answer.
[2 marks]
c. Determine the kinetic energy of the object.
[2 marks]
d. Explain why the kinetic energy of the object is constant.
[2 marks]
Downwards
To the right/towards the centre of the circle.
\omega = \sqrt{\frac{37}{\left ( 2.3 \right )\left ( 5.1 \right )}} \approx 1.8 rad s^{-1}
v = (1.78)(5.1) \approx 9.1 m s^{-1}
E_{k} = \frac{1}{2}\left ( 2.3 \right )\left ( 9.1 \right )^{2} \approx 95 J
The acceleration and the velocity of the object are perpendicular to each other, so the speed of the object is unchanged.
We can assume that the mass of the object is also unchanged and since kinetic energy depends on mass and speed, kinetic energy is constant.
The graph shows how binding energy per nucleon E_{B} varies with nucleon number A.
a. Use the letter S to label the region of most stable elements on the graph.
[1 mark]
The following equation shows the fission of plutonium-239.
_{\, \, \, 94}^{239}\textrm{Pu} + X\rightarrow _{\, \, \, 54}^{134}\textrm{Xe} + _{\, \, \, 40}^{103}\textrm{Zr} + 3X
b. Write down the name of particle X.
[1 mark]
c. Use the graph to calculate the energy released in this fission reaction. Give your answer in pJ.
[3 marks]
Region around the peak of the graph is labeled S.
Neutron
Reading values from the graph (accept a range of values here)
(134 \times 8.35 + 103 \times 8.55) - 239 \times 7.55 \approx 195 MeV
Converting into joules:
(195 \times 10^{6})(1.6 \times 10^{-19}) \approx 3.12 \times 10^{-11} J = 31.2 pJ
The diameter of the area swept out by the blades of a wind turbine is 126 m. The average wind speed at the location of the turbine is 6.7 m s^{-1} and air density is 1.22 kg m^{-3}.
a. Calculate, in MW, the maximum power output of the wind turbine. Give your answer to an appropriate number of significant figures.
[3 marks]
b. State one reason why the result is question part (a) is a maximum.
[1 mark]
c. Outline, without a calculation, what happens to the maximum power output of the turbine when the length of its blades are halved and wind speed is doubled.
[2 marks]
P = \frac{1}{2}(\pi \times 63^{2})(1.22)(6.7^{3}) \approx 2.288 \times 10^{6} W \approx 2.3 MW
Final answer must be given to 2 significant figures.
Some energy is lost as heat due to friction between the moving parts of the turbine.
Not all the air that enters the turbine hits the blades.
The speed of the wind that leaves the blades is not zero.
Considering the formula P = \frac{1}{2}A \rho v^{3}:
Halving the diameter means that the area swept out by the blades decreases fourfold, so power output decreases fourfold.
Doubling the wind speed means that power output increases eightfold.
The combined effect of these changes means that the maximum power output of the turbine is doubled.
Monochromatic light is incident on two slits and forms an interference pattern on a screen. The diagram shows the intensity of the pattern on the screen.
The separation of the slits is 0.83 mm and the distance between the slits and the screen is 5.7 m.
a. Explain why intensity is zero at P.
[2 marks]
The distance between the central maximum and P is 13.3 mm.
b. Calculate the wavelength of the incident light.
[2 marks]
c. State two changes to the intensity pattern when two slits are replaced by ten slits.
[2 marks]
The diagram shows the combined effects of the double-slit and single-slit patterns.
The single-slit pattern has a minimum at P.
Destructive interference at P results in zero intensity.
Distance between bright fringes on the screen:
\frac{13.3 \times 10^{-3}}{4} = 3.325 \times 10^{-3} m
\lambda = \frac{(3.325 \times 10^{-3})(0.83 \times 10^{-3})}{5.7} \approx 4.8 \times 10^{-7} m or 480 nm
The fringes on the screen become more narrow.
The intensity of the bright fringes increases.
A particle of mass 7.2 \times 10^{-18} kg and charge Q is moved from point A to point B.
a. Outline what is meant by gravitational potential at a point.
[2 marks]
The following data are provided:
Gravitational potential at A: 38M J kg^{-1}
Gravitational potential at B: -45 MJ kg^{-1}
Electric potential at A: 21 mV
Electric potential at B: 8.7 mV
Work done when moving the particle: 480 pJ
b. Outline why the work done by the gravitational field on the particle is positive.
[1 mark]
c. Determine, in nC, the charge of the particle.
[3 marks]
The work done per unit mass when moving a test mass from infinity to the point.
The particle moves from a higher to a lower gravitational potential, so the work done by the field is positive.
Since work is done (energy is supplied to the system) to move the particle from A to B, the total work done by the two fields is negative.
W_{total} = -(m \Delta V_{g} + q \Delta V_{e})
480 \times 10^{-12} = -((7.2 \times 10^{-18})(-83 \times 10^{6}) + (Q)(-12.3 \times 10^{-3}))
Q \approx -9.56 \times 10^{-9} C \approx -9.6 nC