General comment: Given that we measure things slightly differently from each other and that our measuring instruments might not be totally accurate, consider all numerical answers derived through measurement as correct if they lie within +1 or –1 of the given answers.
For example, if the given answer is 58, then accept 57, 58 and 59 as correct.
1.1.1 Car may slow down (reaches a corner, up a hill, speed bump, pedestrian crossing etc) or speed up (down hill, moving away from stop lights, as it starts etc). In each case the change is caused by the force on the car changing due to some factor like increased friction during braking, gravitational force etc.
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speed is the actual speed of a vehicle at a particular instant of time.
1.3.1 Scalars have magnitude only while vectors have both magnitude and direction. Vectors can be represented by scale diagrams.
Scalars are not represented in this way.
1.3.2 Examples include:
Scalar quantities Vector quantities
Mass Displacement
Time Velocity
Speed Acceleration
Distance Force
Length Momentum
1.3.3 Distance travelled is a measure of the total length of the path an object has travelled. Displacement indicates how far, in a VWUDLJKWOLQHDQREMHFWLVIURPLWVVWDUWLQJSRLQWDQGWKHGLUHFWLRQRILWV¿QLVKSRVLWLRQIURPLWVVWDUWLQJSRVLWLRQ
1.3.4
Object travelling by Distance travelled (km) Displacement (km)
Road 1 75 50 east
Road 2 50 50 east
Road 3 150 50 east
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1.3.6
Wombat Distance travelled (m) Displacement (m)
(directions as compass readings)
Displacement (m) (directions as bearing)
1 58 58 N 62° W 55 b298
2 63 63 N 65° E 58 b065
3 32 32 S 46° E 30 b134
4 33 33 S 22° W 32 b202
1.4.1 ǻr = change in displacement of the object.
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1.5.1 Average speed = total distance covered ÷ total time taken.
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1.5.3 Instantaneous speed measures the speed of on object at a particular instant of time while instantaneous velocity measures the YHORFLW\DWWKDWLQVWDQWDQGWKHUHIRUHUHTXLUHVWKHGLUHFWLRQRIWUDYHODWWKDWLQVWDQWWREHVWDWHGDOVR
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object while average speed uses total distance travelled.
1.5.5 (a) They will be the same, 60 kph.
(b) At P instantaneous velocity is 60 kph b160 while at Q it is 60 kph b055.
(c) 72 kph
(d) 48 kph b083 1.6.1 (a) 1.53 m s–1
(b) 1.53 m s–1 towards the end of the pool 1.6.2 (a) 1.47 m s–1
(b) zero (she ends up at her starting position)
1.6.3
Car travelling by Distance travelled
(km) Displacement (km) Time taken (hr) Average speed of cars (kph)
Average velocity of cars (kph)
Distance up the
slope (m) Time to roll down slope (s)
Average time
(b) Independent variable: distance up the slope.
Dependent variable: average speed.
(c)
(d) Average speed down slope increases as distance up slope increases but at a progressively slower rate.
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can conclude that the plotted variables are directly proportional to each other.
(f)
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(h) 2.6 m s–1
Distance up slope (m)
Average speed (m/s)
Distance up slope (m)
Average speed (m/s)
1.8.1 (a) 8 m
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F DERXW PV–1 north (d) about 3.5 m s–1 north
(e) Car starts at displacement zero and travels for 20 s with increasing velocity (accelerating) until it reaches displacement 56 m north.
E DERXW PQRUWK (c) 5.5 m s–1
Car Average speed
(m s–1)
Average velocity
(m s–1) Acceleration (m s–2) Displacement after 10 s
A 12 12 north 0 120 m north
B about 5.1 1.25 north 1.0 north 38 m south
C about 7.5 about 0.1 north 0.5 north about 70 m south
D 5 5 south 0.5 south 25 m south
2.1.1 (a) 55 m s–1 east
2.1.2 Velocity of A relative to B = – velocity of B relative to A (i.e. opposite direction).
2.1.3 (a) 2.2 m s–1 downstream
2.3.1 An object at rest or moving with constant velocity will remain ar rest or moving with constant velocity while no net (unbalanced) force acts on it.
2.3.2 A car on an icy road will continue with the same speed in the same direction until the wheels stop sliding allowing the road to exert a frictional force on the car through the tyres.
2.3.3 Any object moving with constant speed and turning a corner, for example a geostationary satellite in orbit above Earth.
2.3.4 Force acts towards the centre of curvature of the corner. It is also called a centripetal force.
2.4.1 An unbalanced force from outside the system.
2.4.2 Accelerating.
2.4.3 This idea depends on the convention we choose to make for each situation we deal with. One viewpoint of this is that a positive force acts in the direction of motion of an object causing it to go faster while a negative force acts against the direction of the motion of the object causing it to go more slowly. A positive force could also be considered to be an attractive force (between oppositely charged objects) and a negative force a repulsive force between like charges.
2.5.1 Your diagram should show air resistance acting against the motion, and friction between the tyres and the road acting forwards in the direction of the motion, gravity vertically down and reaction force to gravity perpendicularly up from surface. (Note WKDWIULFWLRQEHWZHHQPRYLQJSDUWVLQWKHHQJLQHGRHVQRWDIIHFWWKHPRWLRQRIWKHFDUSHUVH7KLVIULFWLRQUHGXFHVWKHWRUTXH
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2.5.2 Air resistance and friction act against the driving force to reduce its effect. The driving force causes the forward movement.
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2.5.3 Zero – car is moving with constant speed – i.e. no acceleration therefore no net force.
2.6.1 Speed it up, slow it down or change its direction of travel.
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2.8.1 A positive acceleration is in the direction of motion of an object causing it to go faster while a negative acceleration is opposite the direction of the motion of the object causing it to go more slowly.
2.8.2 Accelerating from rest, accelerating away from a corner, coasting downhill.
2.8.3 Braking as it approaches a corner or stop sign, coasting uphill (i.e. foot not on accelerator).
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2.9.3
Mass Weight
Measured in kg Measure in newtons
Cannot be zero Can be zero (if no gravitational field)
Does not change with position Changes according to position of object
Measure of amount of matter in an object Measure of force of gravity on an object
Is a scalar quantity Is a vector quantity
2.10.1 Forward force = friction between the tyres and the road Retarding forces = air resistance
2.10.2 Forward force = friction between the tyres and the road Retarding forces = air resistance
2.10.3 Forward force = friction between the tyres and the road
Retarding forces = air resistance, friction between brake pads and wheel drums 2.10.4 Forward force = friction between the tyres and the road
Retarding forces = air resistance
2.10.5 Forward force = friction between the tyres and the road
Retarding forces = air resistance, component of gravity down the slope
2.10.6 Forward force = friction between the tyres and the road, component of gravity down the slope Retarding forces = air resistance
2.10.7 Forward force = friction between the tyres and the road Retarding forces = air resistance
Turning force = component of the frictional force between the tyres and the road perpendicular to the direction of travel produced as the wheels change direction.
2.11.1 The acceleration caused by a net force acting on an object is directly proportional to the force and inversely proportional to the PDVVRIWKHREMHFW25ZLWKLQDSDUWLFXODUIUDPHRIUHIHUHQFHWKHUDWHRIFKDQJHLQWKHPRPHQWXPRIDERG\LVHTXDOWRWKHQHW
force acting on it (see Year 12 work).
2.11.2
2.11.3
2.11.4
2.12.1 About 33.3 N against the motion.
2.12.3 (a) 2 m s–2 north (c) 24 N both directions 2.13.3 (a) 6.25 m s–2 b307
(b) 6.25 m s–2 b307 (c) About 31 m s–1 b307 (d) About 78 m b307
2.13.4 (a) Show gravity down on each mass, and tension in each side of the string acting both ways.
(b) 3.27 m s–2 Y moving down (c) Force on X = about 6.5 N up
Force on Y = about 13 N down (d) About 26.1 N acting both ways in string
2.13.5 (a) Show gravity down on each mass, reaction force up on mass X and tension in both bits of the string acting in both directions.
(b) 7 m s–2 Y moving down (c) Force on X = 14 N right
Force on Y = 35 N down (d) 14 N acting in both directions 2.13.6 (a) 29.4 N
2.13.8 (a) Stopped or moving with constant velocity.
(b) Accelerating forwards.
(c) Accelerating backwards or braking.
2.13.9 (a) Weight force vertically down, tension in string (acting both ways) and a third force (= ma) horizontally to the left (pulling the ball aside).
(b) 29.85 N
(c) 1.73 m s–2
(d) 14.3° towards the front of the bus 2.14.1 X stops in 22.5 m so does not hit the wall.
Y turns a curve with a radius of 45 m, so Y hits the wall.
2.14.2 (a) 0.3 m s–1 (b) 0.225 m s–2
(c) 0.034 N towards centre of curve
2.14.3 (a) 75 m s–1 (b) 28.125 m s–2
(c) Friction between the tyres and the road – the inertia of the car tries to keep it going straight and the friction opposes this, pulling the car around in the curve.
(d) 4.21 × 104 N
(e) Towards the centre of the curve.
(f) Will be four times smaller = 1.05 × 104 N.
2.15.1 (a)
Run Accelerating force (N)
Time to travel 1.0 m (s)
Initial speed of trolley (m s–1)
Average speed of trolley (m s–1)
Final speed of trolley (m s–1)
Acceleration (m s–2)
Force (F units)
(c) The acceleration produced by forces applied to a constant mass is directly proportional to the force applied.
2.15.2 (a)
Run Trolley mass (kg)
(c) The acceleration produced by a constant force acting on various masses is indirectly proportional to the mass.
(d) F = ma
(e) Experiment 1, force = 3.75 N (use gradient of graph).
Experiment 2, force = 0.6 N.
2.16.1 (a) 13 m s–1 b203
2.17.1 You need to draw vectors to add F1 and F2DQGVKRZWKDWWKHWKLUGYHFWRULVHTXDOWR)3. If all angles are drawn correctly, F3 will be vertical. If you get lost, ask your teacher for help.
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potential energy the objects loses).
3.2.1 (a) 2400 J
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600 J done to accelerate it in the opposite direction.
3.3.1 (a) 1.125 × 105 J
(b) 0
(c) Kinetic energy has been changed into other forms – sound during the collision, deformation of the car, heat involved LQWKDWGHIRUPDWLRQEUHDNLQJERQGVEHWZHHQPROHFXOHVPDNLQJXSVXEVWDQFHVDQG¿QDOO\GLVVLSDWHGDVNLQHWLFHQHUJ\
of air particles.
3.4.1 (a) The bending of car panels and other metal parts, the breaking of glass and plastic absorbs most of the kinetic energy of the car.
(b) The sound associated with collisions as parts break and bend and move into and across each other absorbs some of the FDU¶VRULJLQDOKE.
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3.5.1 In the absence of any external forces, the total energy of a system remains constant.
3.5.2 The energy eventually dissipates as molecular motion of the molecules in the air.
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4.4.1 (a) They would continue to move forwards at 70 kph because of their inertia until the force of their seatbelts stopped them.
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(c) Crumple sections increase the time of the collision and therefore reduce the forces involved in the collision (I = FT), so, while the models would still continue to move forwards until their seatbelts stopped them, the decelerating force of the belts would be less (acting over a longer time) so any detrimental effect on the models would be reduced.
(d) Man = 5833.3 N opposing the motion.
Child = 2430.6 N opposing the motion.
(e) 19.44 m s–1 (70 kph)
(f) There is no forward force acting on them, they simply continue forwards because they are moving forwards until a backward force stops them.
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would be strong enough, so for most mums – impossible to hold the child.
4.4.2 (a) 16.6 m s–2 east
4.5.1 Momentum is conserved. If you have problems with this analysis, see your teacher for assistance.
4.6.1 2.0 m s–1 north 4.6.2 6500 kg
4.6.3 The car continues forwards at 33.3 kph.
4.7.1 (a) In the absence of external forces, the total momentum of a system remains the same.
(b) When the truck hits the wall it puts an impulse on the wall. This, while not collapsing the wall, will cause it to move (vibrate, shake) a little. Hence the momentum of the truck transfers to the wall and then into molecular motion of air SDUWLFOHVLQFRQWDFWZLWKWKHZDOO7KHZDOOSXWVDQHTXDOEXWRSSRVLWHLPSXOVHRQWKHWUXFN7KLVVWRSVWKHWUXFN
5.1.1 An object will stay at rest or moving with constant velocity until an unbalanced force acts on it.
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hit (the net force) the windscreen and go through it, or hit the steering wheel and dash and receive injuries.
5.3.1 When you walk along and then step off a moving walkway at normal walking speed, the inertia you have due to the motion of WKHZDONZD\µWKURZV¶\RXIRUZDUGVZLWKPRUHVSHHGWKDQ\RXVRPHWLPHVH[SHFW
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actually your forward inertia trying to keep you moving straight ahead.
If you are sitting in a car moving with constant velocity in a straight line, your inertia is not apparent. It only becomes noticeable when the car brakes.
5.4.1 (a) If you are travelling more slowly, then your momentum is less, so in the event of a collision, the impulse on you due to the collision will be less, both because you do not have as much momentum to lose and also because the time of the collision will probably be shorter.
(b) During a collision, as your inertia causes you to continue to move forwards, the airbag ensures that you lose your momentum slowly, by making the time of collision with the bag much longer than it would be if you hit the windscreen. Therefore, while the impulse will be the same, the force involved will be less.
(c) Crumple zones in vehicles are designed to increase the time of the collision and so while the momentum lost (the impulse imparted to the car and you) is the same, the forces involved will be smaller.
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5.5.2 One reason is that the impulse of the airbag on the child, whose bones are softer can cause more injury than a similar impulse on an adult.
5.5.3 The plastic bumper bar crumples more easily than a steel bar and so momentum of the collision is absorbed in the crumpling, LQFUHDVLQJWKHWLPHRIWKHFROOLVLRQDQGVRUHGXFLQJWKHIRUFHRQWKHFDUDQGLWVRFFXSDQWV/HVVLQMXU\ZLOOWKHUHIRUHEHD
possibility.
5.6.1 Crumple bars, airbags, plastic components instead of all steel, seatbelts, engines that move downwards under the driver instead of straight back into the driver.
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the time of the collision or, in the case of the engine movement, totally avoiding an impact.