Analysing Motion
Forces in Action
Energy and Motion
Physics of Sport
Scientific Investigations
100
What does a vector quantity have?
Both size (magnitude) and direction
100
An object of mass 43 kilograms has a net force of 86 N applied to it. Calculate its acceleration.
Using Newton’s Second Law of Motion:
Fnet = ma
86 = 43a
a = 86/43
= 2.0ms−2
100
Two identical toy cars are travelling directly towards each other at 5ms−1. They have a head-on collision. They are stuck together after the collision. Assume friction is negligible.
What is their combined speed after the collision?
According to the Law of Conservation of Momentum, the sum of the momentum before the collision is equal to the momentum after the collision. As both cars have the same mass and opposite velocities before the collision, their momentums are equal and opposite. Therefore, the sum of their momentum is zero. After the collision they have zero momentum; hence, their speed after colliding is 0m s−1.
100
A basketball rebounds at 30 m s–1 after it hits the floor. Calculate the COR if it has lost 10 m s–1 speed in the bounce.
Speed before bounce = 30 ms–1 + 10 ms–1 = 40 ms–1, speed after bounce = 40 ms–1
e=speed after bounce / speed before bounce
=3040
=0.75
The COR of the basketball is 0.75.
100
Rani conducted an investigation to test the effect of the brand of tennis racquet on the speed of a serve.
In this investigation, the dependent variable is...
the speed of the serve
200
A track cyclist warming up for a race completes three laps of a 250-metre250-metre velodrome track.
What is their displacement?
Displacement is the change in position. If the cyclist has returned to their starting position, that is, completed three full laps, then their displacement is zero.
200
A car of mass 2250 kilograms is travelling at 20 m s−1. Calculate its momentum.
Δp=pf−pi
=mvf−mvi
=0.058×(155/3.6)−0.058×0
=2.5kgms−1
200
Two Physics students, Caleb and Brady, are standing at rest next to each other on skateboards. They push against each other and move off in opposite directions. The friction on the floor is negligible. Caleb has a mass of 75kilograms kilograms and was moving at a speed of 5m s−1 immediately after he lost contact with Brady. Brady has a mass of 60kilograms.
What is the impulse that Caleb exerted on Brady?
Ion Brady by Caleb=Ion Caleb by Brady
=mCalebΔvCaleb
=75×5
=375 Ns
200
What is the angular speed of a cricket ball that is spinning at 39 revolutions per second?
One revolution per second = 2π
ω=Δθ / Δt
=39×2π
=78π
=245radians per second
200
What would the measure of uncertainty be in the following ruler?
0.025 cm
Even though the markings are 0.1 cm, you can tell if a measurement is halfway between two markings, so can measure to 0.05 cm. Uncertainty is half of the value, which is 0.025 cm.
300
The Airbus A380 aircraft has a cruising speed 1060km h−1.
How many metres does it travel in 1second1second when cruising at this speed?
We need to convert the speed from km h−1 to ms−1.
v=1060km h−1
=1060/3.6m s−1
=294m s−1
Therefore, it will travel 294metres in a second.
300
A student sits at the end of pipe attached to a shifter to apply a force of 735 N at a perpendicular distance of 125 centimetres from a wheel nut that they are struggling to undo. Calculate the torque applied to the nut.
τ = r⊥F
= 1.25×735
≈ 919 Nm
300
Tae creates a toy for her cats to play with by hanging a fluffy object at the bottom of a spring. The spring constant is 5 Nm−1. One of the cats is able to stretch the spring by 10centimetres.
How much energy has the cat stored in the spring?
0.025J
300
What is the Magnus effect?
An effect that causes a spinning ball to swerve in the direction of the spin
300
systematic errors affect what?
They can affect the accuracy of a reading.
400
A shopping trolley rolls down a hill in a straight line with a constant acceleration of 3.00m s−2. It starts at rest beside a car and travels 100metres before it collides with a picket fence.
How fast is the shopping trolley travelling the instant before it collides with the fence?
u=0, a=3, s=100
v2=u2+2as
=(0)2+2(3)(100)
=600
v=24.5ms−1
400
A cycle tourist is towing all of their camping equipment, clothes and food behind their pushbike in a bike trailer. Whilst pedalling at a reasonable pace they produce a driving force of 172 N acting forwards from the rear wheel of their bike. The road friction and air resistance opposing the motion of the bike and trailer is equal to 34 N acting backwards (20 N on the bike and 14 N on the trailer). The total mass of the cyclist and bike is 95 kilograms. The total mass of the trailer and all of its payload is 20 kilograms.
Determine the tension force in the link between the trailer and the bike.
Determine the acceleration of the system as a whole (bike and trailer).
Fnet = 172−34 = 138N
a = Fm = 138(95+20) = 1.2ms−2 [1mark]
To determine the tension force in the link, break the system at the link and analyse either the bike or trailer separately. In this solution, the bike and cyclist are analysed.
Determine the net force acting on the bike from the acceleration calculated:
F = ma = 95×1.2 = 114N [1mark]
Take the sum of forces on the bike to determine the unknown tension force:
Fnet = Ftension = Fdriving − Fresistance − Ftension
114 = 172−20−Ftension
Ftension = 172−20−114 = 38N [1mark]
The tension in the link is 38 N.
400
To assist them in their studies of motion in Physics, Greg and Bailey are riding on a roller coaster. The combined mass of the two students and the carriage is 369kilograms. As part of the ride they stop momentarily at the highest point in the track. The cart then accelerates down a steep slope, dropping 40metres in vertical height at the end of the slope.
What is the total kinetic energy of the cart and students at the end of the slope?
144648J
400
As the skydiver falls, he encounters the force of air resistance. When is the skydiver said to have reached a terminal velocity?
The force of air resistance is equal to the force of gravity.
400
What is the difference between an aim and hypothesis?
The aim outlines the purpose of the investigation, but the hypothesis is a testable prediction.
500
A diver is standing at the top of a 75-metre tall cliff. They leap off the cliff with an initial vertical velocity of 3ms−1. Assume that their acceleration throughout the dive is 9.8ms−2 directly downwards.
How long will it be from the beginning of their leap until the instant they hit the water below? (to three significant figures)
Assume that upwards motion is defined as positive.
Find the velocity at which they strike the water:
u=3ms−1, s=−75m, a=−9.8ms−2
v2=u2+2as
=32+2(−9.8)(−75)
=1479
v=−38.46ms−1 [1mark]
As upwards motion is positive and at the end of the dive they must be moving downwards, the value must be negative.
Now calculate the total time:
v=−38.46, u=3ms−1, a=−9.8ms−2
t=(v−u)/a
=(−38.46−3) / −9.8
=4.23s [1mark]
The time taken is 4.23seconds.
Note: Students may be inclined to break the motion into upwards and downwards segments and analyse separately; however, as the acceleration is constant and continuous throughout, this is not necessary.
500
A small rocket of mass 2500 kg is launched up along an inclined ramp at an angle of 42 degrees from the horizontal. During the launch, the rocket engine provides a constant thrust of 18 000 N.
Determine the acceleration of the rocket during its launch. It is reasonable to consider air resistance and friction to be negligible in this situation.
In this situation, a component of the force due to gravity will act down the ramp to oppose the motion of the rocket.
Fgx=mgsinθ
=2500×9.8×sin(42°)
=16394N [1mark]
To determine the acceleration of the rocket, calculate the net force along the ramp by taking the sum of forces.
Fnet = Fthrust − Fgx
= 18 000 − 16 394
= 1606 N [1 mark]
Hence, calculate the acceleration of the rocket:
a=F/m
=1606/2500
=0.64ms−2 (1mark)
500
A physics student is waiting tables at a restaurant. They have been doing this work for some time and have perfected the ability to carry a tray of drinks across the room in a purely horizontal motion at a constant speed. Is the student doing work on the tray of drinks during this constant speed motion? Refer to relevant physics principles in your response.
The student is not doing any work on the tray during the motion described [1 mark].
For work to be done there must be a force applied and a displacement in the direction of that force. In this instance the student would be exerting an upwards force on the tray to balance the downwards force due to gravity on the tray. This is perpendicular to the horizontal motion of the tray. [1 mark]
500
A skateboarder jumps a horizontal distance of 2 metres, taking off at a speed of 5 m s–1. The jump takes 0.42 seconds to complete.
What was the skateboarder’s initial horizontal velocity?
s = 2 m, t = 0.42 s, v = ?
v=s/t=2.0/0.42=4.76=4.8ms−1
500
Theories are
well-supported ideas for which evidence has been gained from investigations, research and observations