Year 12 Physics
Unit Analysis: Motion in one and two dimensions
MECHANICS
1.1
1.2
1.3
1.4
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Vectors & Scalars
Displacement, Velocity, Acceleration (includes graphs)
Equations of motion (for constant acceleration)
Relative motion
Newton’s Laws of motion
Normal Force and Inclined Planes
Projectile motion
Includes graphs of displacement & velocity.
Includes Vertical motion as an application of
the equations of motion.
Includes effect of air resistance.
ENERGY & COLLISIONS
2.1
2.2
2.3
2.4
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Momentum, Impulse
Conservation of momentum
Work, energy & power
Work done by a force at an angle to the displacement
Conservation of energy
Elastic & inelastic collisions
Hooke’s law & elastic potential energy
Includes F-t graphs & crumple zones.
Rockets
Kinetic & Gravitational potential.
Force-extension graphs, elastic limit
CIRCULAR MOTION
2.5
2.6
2.7
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Uniform circular motion
Centripetal acceleration & force
Ball on a string
Banked corners
Leaning into corners
Circular motion in a vertical plane
Apparent weight
Includes questions where speed is found from
gravitational potential energy
GRAVITY & SATELLITES
3.1
3.2
3.3
3.4
3.5
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Newton’s law of universal gravitation
Gravitational fields
Satellites in circular orbits
Energy changes in gravitational fields
Weightlessness
Ratio problems, 4 fundamental forces
Freely falling objects
Includes Fg and g vs distance graphs.
and more on apparent weight
Summary of question types
Type of question
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3.
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5.
6.
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10.
Simple motion/relative motion problems
Newton’s laws/work problems
Inclined planes
Projectile motion
Collisions (conservation of momentum)
Hooke’s law (elastic potential energy)
Horizontal circular motion
Circular motion in a vertical plane
Gravitational force and field strength
Satellite motion
2007
VCAA Exam
2008
2009
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Other questions
Here are some types of questions you may encounter that are not dealt with in the following pages.
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Simple vector addition and subtraction. May involve the use of Pythagoras or Trigonometry for the vector sum. May also
involve dividing (or combining) vectors into components such as vertical and horizontal. (Heinemann 12: 1.1 q6, 10).
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Often questions ask you to state a ratio rather than an actual value. These require students to use their algebra skills to
simplify, but not solve the problem. Practice is recommended. Examples are shown on pages 80 & 88 in Heinemann 12.
Heinemann 12: Chapter 1 Review q20. 2.4 q4. 3.1 q4,7. 3.2 q6. 3.3 q10. Chapter 3 Review q4,11. VCAA Exams: 2007-1 q12
Simple Motion Problems
In these questions you are given basic information about the motion of one, two or more objects and are asked to determine
other information such as the time where one object catches up to another, or the velocity required for objects to meet at a
certain point.
Tips
 Always list the quantities you have been given.
 Look for extra information in the question such as objects starting from rest or travelling with constant velocities (so a
= 0).
 Do not confuse scalar and vector quantities.
 When finding vector quantities always state the direction.
See Heinemann Physics 12 page 3-11
Types of questions
Simple questions involve applying the formulas for displacement, speed, velocity, and
acceleration. These questions are often designed to test that you understand the difference
between vector and scalar quantities (such as distance and displacement).
Examples
Heinemann 12: 1.1 q4. Ch1
Review q1
Others involve reading from graphs of displacement and velocity versus time in order to test
your understanding of these graphs, particularly the use of areas under graphs and the gradient
of a line.
Some questions involve vertical motion and require you to use a value for acceleration due to
gravity near the surface of the Earth (usually 9.8ms-1).
Some questions may also involve the use of the equations of motion (for constant acceleration).
Heinemann 12: 1.1 q3. Exam
Style Questions q5-8
Heinemann 12: 1.1 q5*, 8*.
Ch1 Review q3*
Heinemann 12: 1.1 q5*, 7,
8*, 9. Ch1 Review q3*, 4
Questions marked with an * apply to more than one category.
Relative Motion Problems
In these questions we use the velocities of some objects relative to each other or the ground in order to find other relative
velocities. The questions that are asked do not vary a lot but the descriptions can be confusing and must be read carefully.
Tips
Remember that the velocity of A relative to B is the same as B relative to A, but in the opposite direction.
There are a number of ways to approach these problems...
 Use the formula. (This is easy use incorrectly. Always use this in addition to another method).
 Try to visualize the situation described in order to determine the answer.
 Draw the velocity vectors and add them.
 Consider the distance travelled by each object in a given time (eg: 1 second).
See Heinemann Physics 12 page 10-11
Types of questions
There are not a lot of specific variations on these questions. Some questions will require further
logic, such as an understanding that water flows downstream.
Examples
Heinemann 12: Ch1 Review
q5
Newton’s Laws
Questions involving Newton’s laws often involve labelling forces on a diagram applying the concept of inertia (which most
students do without thinking at this year level) and using the formula of Newton’s Second law (F=ma). These questions usually
involve a range of forces, the net force, mass and velocity.
There is a lot of variations in the questions that can be asked here so a good understanding of the concepts is essential.
Tips
 Remember if there is no acceleration (or a constant velocity) then the net force is zero.
 On force diagrams weight acts from the centre of mass and the normal force acts from the surface. Friction forces can
be drawn at the point of contact (ex. for tyres on a road).
 The action and reaction forces (Newton’s third law) act on different objects and should never be added together.
 Don’t forget to supply a direction unless you are asked to find only the magnitude of a force.
See Heinemann Physics 12 pages 13-15
Types of questions
Using mass, acceleration and force in F=ma. These questions may also test that you understand
that constant velocity implies a zero net force and that you understand balancing forces (eg: if
resistance = 100N and net force is zero then the driving force must be 100N in the opposite
direction). In many cases resistance or other forces are provided on a graph and work may be
found from the area under a force-distance graph.
Labelling forces on a diagram. From simple action-reaction forces to specific situations. In some
cases you may be expected to draw the length of the vectors to scale. This is often also required
in inclined plane problems.
More complex questions involve two objects joined (for example by a rope).
Other questions require the use of the equations of motion. An example of this involves finding
an acceleration from u, v and t. Then using the acceleration to find mass or force in F=ma.
Examples
Heinemann 12: 1.2 q3, 5. Ch1
Review q4c
Some questions involve a force that is in a different direction to the motion. In these cases you
must use trigonometry to find the vector component of the force that is parallel to the motion.
Heinemann 12: 1.2 q7.
Some questions involve apparent weight for object moving vertically. The apparent weight is
given by the normal reaction force on an object from a surface pushing on it. This can often be
found by subtracting the weight force from the net force.
VCAA Exams: 2009-1 q7,8,9
VCAA Exams: 2007-1 q6,7,8*
Heinemann 12: 1.2 q10.
Exam style questions q49,50
VCAA Exams: 2008-1 q1,2
Heinemann 12: 1.2 q6
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Inclined Plane Problems
These questions are an application of Newton’s third law, as they involve the normal reaction force from an inclined plane. This
results in a component of the weight force acting down the slope causing an object to accelerate or requiring a friction force to
remain stationary. These questions require trigonometry to find the component of the weight force acting down a slope. An
angle must be provided, or in some cases you may be asked to find the angle.
Tips
 A good way to think of these is to consider that the weight force can be divided into two components...
 A component that acts down the slope causing acceleration.
 A force perpendicular to the surface (this pushes the object against the surface and is equal and opposite to the
normal reaction force)
 Draw a diagram. Practice is essential when trying to put the angle in the right place. But you may want to memorize
or write down where it goes as it always works the same way.
 Don’t get fooled if the angle is stated as an angle to the vertical instead of to the horizontal.
 Only ignore friction if you have been told to do so.
 Remember a constant velocity means a zero net force.
 Also remember that on a slop a friction force must be present to produce zero acceleration (so either a zero velocity
or constant velocity).
See Heinemann Physics 12 pages 18-21
Types of questions
Most questions are variations on the following...
 Using mass and an angle to calculate the force down the slope.
 Using mass, angle and known forces (such as friction) to calculate acceleration down
the slope.
 Using acceleration and know forces to calculate mass.
 Using mass, acceleration down the slope and/or forces to find the angle.
These may also involve labelling force diagrams.
Other questions may require you to use the constant acceleration down the slope in the
equations of motion to find time, displacement, initial velocity or final velocity.
Examples
Heinemann 12: 1.3 q1-5,6-8.
Heinemann 12: 1.3 q7,9
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Projectile Motion Problems
These questions are an application of the equations of motion involving dividing the motion into two components; horizontal
and vertical. You may need to divide the initial velocity into these components using an angle and trigonometry.
The vertical component involves acceleration due to gravity (9.8ms-1 near the surface of the Earth). The horizontal component
involves a constant horizontal velocity (zero acceleration) when air friction is ignored. The two components are joined because
they both occur over the same time. So you may need to use the vertical component to find time, then use the time to find a
value in the horizontal component.
You may also be asked questions about the effect of air friction on the motion of a projectile. For these remember that air
resistance acts in the opposite direction to the motion (a diagram may help) and the only other force acting is weight. Also note
that the maximum friction will occur at the point where the velocity is highest (that is the vector sum of the horizontal and
vertical velocities). This usually occurs at the start or the end of the motion (as the vertical velocity is zero in the middle).
There is not much variation in the questions that are asked for projectile motion.
Tips
 Often it helps to draw a diagram especially if you are asked to comment on the effect of air friction. (Remember that
air friction acts in the opposite direction to the motion, and will add to the weight force to produce a net force)
 Choose whether up is positive or negative and use this consistently throughout the question.
 Remember that the vertical velocity is zero at the maximum height.
 Don’t confuse vertical and horizontal values. For example don’t use the horizontal displacement with the vertical
acceleration (-9.8ms-1).
 Because the horizontal acceleration is zero, usually you can use v=x/t for the horizontal component. (so the equations
of motion are only needed for the vertical component)
 Do not rely on special formulas for range. These are no substitute for a good understanding of the concepts and you
will find questions where they cannot be used, or where using them may be incorrect.
 A projectile launching from and landing on a horizontal surface follows a symmetrical parabolic path. So the velocity
and angle to the horizontal is equal at the start and the finish. This also means the total time spent in the air will be
twice the time taken to reach the maximum height).
See Heinemann Physics 12 pages 23-28
Types of questions
Some questions involve an object being launched horizontally (so the initial vertical velocity is
zero).
Examples
Heinemann 12: 1.4 q1,2. Ch1
Review q6
VCAA Exams: 2007-1 q1-2
Many problems involve an object being launched in the air from a horizontal surface. They often
provide an initial velocity at an angle (from horizontal or vertical). You then use trigonometry to
divide this into horizontal and vertical components before calculating things like the time in the
air, the maximum height and the total horizontal displacement.
You may also be asked to do this in reverse finding the initial velocity and/or the angle.
One question (A) has a variation that may confuse some students. The projectile hits a wall after
a certain distance and you are asked to determine the height. This is actually not very different
to most other questions. Simply remember that the time (Δt) is the link between the vertical
component and the horizontal component.
In some questions kinetic energy and/or gravitational potential energy formulas must be used
to calculate energy, velocity or height.
A more difficult problem (A) involves a projectile which is launched from a height 1.5m off the
ground. T solve this find the time taken for the vertical displacement to reach -1.5m.
Heinemann 12: 1.4 q3-8,10.
Ch1 Review q7-10. Exam
style questions q17-20
VCAA Exams: 2008-1 q5-7A.
2007-1 q14-17
Heinemann 12: 1.4 q9. Ch1
Review q11A,12-15, 16-18
VCAA Exams: 2009-1 q10A,
11A
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Collision Problems
In these questions you apply the law of conservation of momentum to describe the motion of objects before and/or after a
collision. At year 12 students are also expected to be able to explain whether a collision is elastic or inelastic. Questions will
often involve impulse and/or force-time graphs as a variation on just mass, velocity or momentum. You may also be asked about
rockets and how the conservation of momentum allows a rocket to move through space when there appears to be nothing for
them to push against.
Tips
 Remember that momentum is a vector quantity.
 Remember that the law only applies in a closed system.
 The complete formula for conservation of momentum can be confusing. Consider just finding the momentum of each
object separately then add them together.
 You need to be able to explain how momentum may appear to be lost in a collision with the Earth. Remember... it’s
not lost, but the huge mass of the Earth means that any change in its velocity is insignificant.
 Remember to consider direction. Choose one direction to be given positive values and apply this consistently.
 In a two-body collision the momentum lost by one object must be gained by the other.
 Some questions ask you what will happen when joined objects travelling with some velocity separate. The answer is
that nothing will happen. Each object retains its own velocity and momentum.
 Don’t confuse conservation of momentum with conservation of energy.
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Note that in a collision kinetic energy in the system is not always conserved (some is transferred out of the
system in forms such as sound or heat). This is the distinction between elastic and inelastic.
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Sometimes it may appear that momentum has not been conserved. This does not necessarily mean energy has
been lost (as sound, heat etc) but may involve momentum transferred into the Earth (producing an extremely
small change in its velocity).
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Remember that the distinction between elastic and inelastic collisions depends on whether kinetic energy is
conserved. This is separate from the conservation of momentum, and different to the law of conservation of energy.
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In an elastic collision kinetic energy is conserved.
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In an inelastic collision some kinetic energy is transformed into heat and sound.
 Note that collisions are usually inelastic. The only truly elastic collisions occur at the atomic level. All other collisions
involve energy loss to heat and sound and are thus inelastic.
See Heinemann Physics 12 pages 33-42. Note that elastic and inelastic collisions are discussed on pages 48-49.
Types of questions
Simple problems involve two objects with known masses and velocities. You will be told
something about their motion after the collision such as that they move off together or one of
them has a certain velocity. You will then work out remaining information such as final
velocities or changes in momentum.
Variations on this require you to work backwards to find information about the system before
the collision.
Some questions involve a discussion of elastic and inelastic collisions.
As an expansion on the discussion of elastic and inelastic collisions some questions discuss the
energy efficiency of the collision.
Examples
Heinemann 12: 2.2 q1-9. Ch2
Review q1, 7-10, 11A. Exam
style questions q21-24
VCAA Exams: 2009-1 q1.
2008-1 q8,9,11. 2007-1 q3,5
Heinemann 12: 2.3 q6,10.
Exam style questions q43-46
VCAA Exams: 2009-1 q2.
2008-1 q10. 2007-1 q4
Ch2 Review q11A,12-14B,
15C,16
A simple example (A)specifies that the collision is 95% energy efficient. This problem does not
require calculations of momentum. Just find the total initial kinetic energy. This final kinetic
energy will be 95% of this.
A more complex example (B) requires you to find the final momentum of a system then
calculate the kinetic energy before and after the collision in order to determine the energy
efficiency.
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Work Problems
These questions involve a force used to move an object over some distance. When work is done by a force that is at an angle to
the displacement, the component of the force that is parallel to the motion must be found using trigonometry. If the force is not
constant formulas cannot be used and work must be found by the area under a force-displacement graph (not to be confused
with a force-time graph). Some questions look at when work is done opposing gravity (with no apparent displacement). Often a
further step is required to calculate power.
Tips
 Energy and work are scalar quantities.
 Remember that a force at 90° to the direction of motion does no work.
 Work is only done when an unbalanced force causes an energy change. If the energy of an object has not changed
then no work has been done on it.
 Mechanical energy is the sum of an objects kinetic and potential energies.
See Heinemann Physics 12 pages 44-49
Types of questions
Simple questions involve a force and a displacement that are in the same direction. In some
questions you are not given the force but you need to calculate. Sometimes you will need to
factor in Friction or other forces to find the net force. Remember a zero net force in these
questions does not always mean that there is no work done. We may be interested in the work
done by one force that is opposing another (see below).
When work is done opposing friction or gravity it can appear that no work has been done...
 An object may move with a constant speed suggesting a zero net force. In this case the
size of the force being opposed is used to determine the applied force. For example to
maintain a constant upwards velocity the applied force equals the weight force.
 If a force is applied in order to maintain equilibrium, but no displacement occurs then
no work is done. For example a force applied against gravity that holds an object in the
same position does not do any work.
Most questions at year 12 will involve a force that is at an angle to the displacement. You will
need to find the component of the force that is in the same direction as the motion using
trigonometry.
Examples
Exam style questions q2829.
Often questions approach work indirectly by having you calculate changes in kinetic or potential
energy. Other questions ask you to calculate the work and then express it in terms of an change
in energy.
Heinemann 12: 2.3 q9*.
Exam style questions q30-33
Questions where the force changes over time may involve a graph of force-distance. Usually
work is found by the area under the graph. For problems involving elastic potential energy if the
gradient is constant then it can be used to find k and the formula for elastic potential energy
can then be used.
Heinemann 12: 2.3 q7-8. Ch2
Review q4-6
VCAA Exams: 2009-1 q6
Heinemann 12: 2.3 q1,9*.
Heinemann 12: 2.3 q2-5*.
Ch2 Review q2,3
VCAA Exams: 2007-1 q8*
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Hooke’s law and elastic potential energy problems
These questions involve considering energy stored in an object as a result of a reversible change in shape. When the object is a n
ideal spring (it obeys Hooke’s law) the formula can be used. When it is not ideal, the gradient of the Force vs compression (or
extension) graph is not constant and so the area under graph the graph is used to find the elastic potential energy. When an
object is ideal up to a certain point (after which the gradient of the force-compression graph changes) then this point is called
the elastic limit of the object. Changes in elastic potential energy are often discussed in terms of work done.
Tips
 The gradient of the force-compression graph is equal to k (the spring constant) in the formula and tells us the stiffness
of the spring.
 The elastic potential energy can also be called strain energy.
 Sometimes the formula is stated as –k. This can be confusing if k is already a negative value. The negative value
indicates that the force is in the opposite direction to the compression or extension. So make sure your answer agrees
with this. (so if you compress the spring to the right, it applies a force to the left).
See Heinemann Physics 12 pages ?-?
Types of questions
Simple problems use ideal springs where k is known or can be found by finding the gradient of a
force-compression graph. A more complex question involves finding a ratio of the compression
of one spring to another.
Some questions involve finding a force on the spring in order to find the displacement
(extension or compression) using F=mg=-kx. You can then use the displacement in the formula
for elastic potential energy.
Some problems involve converting the energy in the spring to other forms such as kinetic and
gravitational potential.
Other problems involve non-ideal springs where k is not constant. Here a force-compression
graph is provided and the elastic potential energy is given by the area under the graph.
Examples
Heinemann 12: 2.4 q2,3,4^.
Exam style questions q34,
38-42
VCAA Exams: 2008-1 q12.
2007-1 q9-11
Heinemann 12: 2.4 q5,6
Heinemann 12: 2.4 q7,8.
VCAA Exams: 2009-1 q5.
2008-1 q13,14
Heinemann 12: 2.4 q9,10.
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Horizontal circular motion problems
These questions involve objects travelling in a horizontal circular path. Usually we look at objects moving at a constant speed but
with a constantly changing direction. Because velocity is a vector quantity this means that velocity is changing and therefore
there is a centripetal acceleration and centripetal force. This centripetal force must be supplied by a real force such as friction in
order for the object to stay on the circular path.
See Heinemann Physics 12 pages 57-60
More complex questions consider a ball on a string that is travelling in a horizontal circle while under the influence of gravity. If
the speed of the ball is increased the string will approach but not reach horizontal. Remember the length of the string is not the
radius of the path (but it can be used to find the radius if the angle of the string to the horizontal is known.
On banked corners the normal force and the weight of an object are at an angle to each other. This produces a net force down
the slope which can supply the centripetal force without the need for any friction. The speed at which the object can travel
without friction is called the design speed of the corner and is found by setting the centripetal force equal to the vector sum of
the weight and normal forces.
See Heinemann Physics 12 pages 62-66
Tips
 The centripetal acceleration formula only applies where the speed at which the object is moving around the circular
path is constant.
 It’s important to understand that the centripetal force is not real, but is supplied by a real force. If the real force is not
enough to supply the centripetal force then the object cannot stay on the circular path.
 These formulas involve squared values. If finding the velocity or period you may need to take the square root as a
final step. Don’t forget.
 The formula includes π2 don’t get confused and do r2 by accident.
 Also remember that no work is done on the object by the centripetal force. This can be seen because the kinetic
energy of the object does not change and the centripetal force acts at 90° to the movement.
Types of questions
Simple questions provide all but one of the values in the centripetal acceleration or force
formulas and require students to find the remaining value. This may involve using a mass,
velocity and radius. Some questions do not require calculation but test your understanding of
the concepts.
Ball on a string problems describe a ball travelling on a horizontal circular path. It is connected
to a string, but the path of the string is not horizontal. You may be given the angle and the
length of the string in order to calculate the radius of the path using trigonometry. It then
becomes a normal circular motion problem as above.
Banked corner problems often involve finding the design speed or comparing the actual speed
to the design speed to see if a vehicle will stay on the track without friction (or with a limited
amount of friction). This involves finding the net force using a given angle between the weight
and normal forces. It may also involve working backwards from the net force to find the angle.
Examples
Heinemann 12: 2.5 q1-10.
Ch2 Review q17-20. Exam
style questions q9-13
VCAA Exams: 2009-1 q3,4.
2008-1 q3,4
Heinemann 12: 2.6 q1-8
Heinemann 12: 2.6 q9,10.
Ch2 Review q21,22
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Circular motion on a vertical plane problems
In vertical circular motion the transformation between gravitational potential and kinetic energy means that a vehicle will speed
up towards the bottom of a dip and slow down towards the top of a hump. This acceleration produces a net force that is in a
different direction to the centripetal force. To get around this we only analyse the motion at the top of a hump or the bottom of
a rise because here the other acceleration becomes zero and the centripetal force can be calculated.
A car travelling over a hump with enough speed will leave the road. This occurs because the weight force of the car is not
enough to supply the centripetal force. The point at which this begins to happen is when the weight force is equal to the
centripetal force. At this point the normal force and thus the apparent weight is zero.
Tips
 Problems are solved using the formula for centripetal force but must take into account the kinetic energy lost or
gained from/to gravitational potential energy as a result of the change in height.
 The centripetal force is equal to the net force found by adding the weight and normal forces.
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At the top of a hump the sum of a smaller normal force and the weight produces a net/centripetal force down.
This involves a lower apparent weight for the vehicle.
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At the bottom of a dip the sum of a larger normal force and the weight produces a net/centripetal force up.
This involves a larger apparent weight for the vehicle.
 At the point of lift-off the normal force is zero and the acceleration is equal to gravity (g).
See Heinemann Physics 12 pages 68-73
Types of questions
The simplest problems state a constant speed when travelling through the circular path, or they
state the speed at the top of the hump or the bottom of the loop so that we do not have to
work it out before finding the centripetal force.
Examples
Heinemann 12: 2.7 q1-3,6-8.
Ch2 Review q23. Exam style
questions q47,48
Other problems give an initial velocity and the radius of the circular path. This radius is also the
change in height used to calculate the gravitational potential energy that adds to the kinetic
energy reaching the bottom of the dip, or subtracts from the kinetic energy when going to the
top of a hump.
Heinemann 12: 2.7 q9-10
One variation that is sometimes used in questions is to have a vehicle travelling upside-down
around a loop. Here the normal force and the weight are in the same direction. If the
net/centripetal force is less than the weight then the vehicle will fall of the track.
More complex problems require a vehicle to be released from some height before reaching the
circular path. These will ask things like “what height does the vehicle need to be released at in
order to reach the point of lift off going over the hump?” These questions are not as complex as
they seem. Find the required speed, convert this to energy in the kinetic energy formula then
convert it to height using the gravitational potential energy formula.
Heinemann 12: 2.7 q4,5.
VCAA Exams: 2009-1 q12
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Gravitational force & field strength
Newton’s law of universal gravitation can be used to find the gravitational force of attraction between two bodies. We can also
use the mass of one object to find its gravitational field strength (g) in N kg -1. We know that near the surface of the Earth, g is 9.8
N kg-1 although in the past we’ve seen this expressed as acceleration due to gravity in ms-2. To find the gravitational force of
attraction between two bodies when g is known for one body we simply multiply g by the mass of the second body (W=mg).
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Tips
Gravitational field strength (g) decreases with distance, so the one value for g can only be used over short distances.
Don’t forget to square R.
You may want to store the value for G in your calculator.
Make sure you only use the centripetal acceleration formula for objects travelling on a circular path. For other objects
use ΣF=ma.
 The acceleration of a freely falling object is given by the gravitational field strength (g).
See Heinemann Physics 12 pages ?-?
Types of questions
Gravitational Force
Many questions involve applying the formula for Newton’s law of universal gravitation.
Some questions (A) ask you to find acceleration. For these you simply use ΣF=ma. Make sure you
only use the centripetal acceleration formula for objects travelling on a circular path.
Examples
Heinemann 12: 3.1
q1,3B,4^,5A,6B,7^,8B. Ch3
Review q1,2^,4^
VCAA Exams: 2007-1 q12^,13
Other questions (B) require you to apply the inverse square law (F∝1/R2). This means that if R
increases by a factor of x, then F will be multiplied by a factor of 1/x 2. So if R is multiplied by 4, F
is divided by 16 and if F is multiplied by 2 then R is divided by 4.
More complex problems (^) involve using the formulas to find ratios.
Gravitational Field Strength
When only one mass is being considered we cannot find the gravitational force. Instead we find
the gravitational field strength (g) which is the force that will be applied to each unit of mass in
an object (N kg-1).
Heinemann 12: 3.2 q1-9,11
Ch3 Review q5. Exam style
questions q25-27
Energy changes in gravitational fields
Some problems discuss objects that are moving through gravitational fields. Objects moving
towards a planet will gain kinetic energy while losing gravitational potential energy. Objects
moving away from a planet will gain gravitational potential energy. This occurs for objects that
are not in orbit, and for objects that are in non-circular orbits. Note that the circular motion
formulas are of limited use for objects travelling in non-circular orbits.
Heinemann 12: 3.4 q5-10.
Ch3 Review q10,13-16. Exam
Style Questions q1-4
VCAA Exams: 2008-1 q15
When objects change their height we cannot use a single value for g in our calculations because
g is changing. In these cases we read the energy changes from graphs.


On gravitational force – distance graph (F-x), the area under the graph tells us the work
done (energy change).
On a gravitational field strength – distance graph (g-x) the area under the graph
multiplied by the mass of the object that is moving through the field gives the work
done (energy change).
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Satellite motion problems
Satellite motion is a combination of circular motion and gravity. The formulas for both of these can be used because for a
satellite in a circular orbit, the centripetal acceleration is equal to the gravitational field strength (a=g). Because the formulas for
satellites include all of the formulas for centripetal acceleration and for gravitational field strength they are quite long and there
are many different combinations that can be used to answer questions. It may help to record some of the forms that you use the
most.
Some questions involve satellites in non-circular orbits. In these cases the circular motion formulas cannot be used. These often
involve using Newton’s law of universal gravitation or reading from a graph of gravitational force or gravitational field strength
versus time.
Tips
 Objects in orbit have an acceleration equal to g. This means their normal force is zero and they experience apparent
weightlessness.
 Remember that the gravitational force is perpendicular to the motion of a satellite and so does no work.
 A satellite in a geosynchronous orbit around a planet stays above the same point of the planet all the time. It does
this by orbiting at the same rate at which the planet is spinning (so a geosynchronous satellite orbiting the Earth has a
period (T) of 24 hours.
 Remember that the centre of a satellites orbit must be the centre of mass of the planet being orbited.
See Heinemann Physics 12 pages ?-?
Types of questions
Most questions are an application of the formulas, although the formulas in this case allow for a
lot of different combinations so it is important to list the values required and carefully look
through the formulas for a combination that will work.
Examples
Heinemann 12: 3.3 q5,6,7,12.
Ch3 Review q6,7,12,20.
Exam style questions q14,15.
VCAA Exams: 2009-1 q13,14.
2008-1 q16,17
Some problems require calculation of ratios.
Heinemann 12: 3.3 q9*. Ch3
Review q11. Exam style
questions q35-37
Other problems require the use of Kepler’s third law which states that R3/T2 is a constant for
Heinemann 12: 3.3 q9*. Ch3
different objects in orbit around the same object.
Review q18,19. Exam style
questions q16
Some questions require an understanding of satellites in synchronous orbits.
Heinemann 12: 3.3 q8. Ch3
Review q,8, 9
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.
Title Problems
Description.
Tips
 Tip.
See Heinemann Physics 12 pages ?-?
Types of questions
Description.
Description.
Description.
Description.
Examples
Heinemann 12: 1.? q?. Ch1
Review q?
Heinemann 12: 1.? q?
Heinemann 12: 1.? q?. Ch1
Review q?
Heinemann 12: 1.? q?. Ch1
Review q?
Questions marked with an * apply to more than one category. An ^ indicates more complex questions.