MYP 4 & 5 · Physics
P1 - Forces and energy
65 questions across 17 sub-topics
Use the Sub-Topic filter above to focus on one.
P1.1 - Measurement, units, scalars and vectors
P1.2 - Distance, displacement, speed and velocity
P1.3 - Acceleration and motion graphs
P1.4 - Kinematic equations (SUVAT) and multi-stage motion
P1.6 - Resultant forces and free-body diagrams
P1.7 - Friction, drag, terminal velocity and stopping distance
P1.8 - Newton's laws, momentum and impulse
P1.9 - Gravity, mass, weight and gravitational fields
P1.11 - Elasticity, Hooke's law and force-extension graphs
P1.12 - Moments and equilibrium
P1.13 - Pressure in solids, liquids and gases
P1.14 - Atmospheric pressure, Pascal's principle and hydraulic systems
P1.15 - Work, kinetic energy and gravitational potential energy
P1.17 - Energy stores, transfers, conservation and Sankey diagrams
P1.18 - Power and efficiency
P1.19 - Renewable and non-renewable energy resources
P1.20 - Environmental impact and sustainable energy choices
P1.1 - Measurement, units, scalars and vectors 1 question
QUESTION 1
4 marks
Criterion A
Easy
Scalars and vectors
Answer the following questions about scalar and vector quantities.
a.
State the difference between a scalar and a vector.
[2] b.
Which one of speed, time, mass and force is a vector quantity?
[1] c.
Which is a scalar: 14 kg; 300 kN downward; 24 m s−1 west; or 1 m s−2 upward?
[1] Show complete worked solution
(a)
A scalar has magnitude only. A vector has both magnitude and direction.
(b)
Force is a vector because it has magnitude and direction.
(c)
14 kg is a scalar because no direction is associated with mass.
P1.2 - Distance, displacement, speed and velocity 3 questions
QUESTION 1
6 marks
Criterion A
Medium
Cyclist journey
A cyclist travels 1500 m from home to a shop in 300 s. On the return journey, the cyclist accelerates uniformly from 2.0 m s−1 at 2.4 m s−2.
a.
State the equation linking average speed, distance moved and time taken.
[1] b.
Calculate the cyclist’s average speed on the outward journey.
[2] c.
Calculate the time taken to reach 10 m s−1 on the return journey.
[3] Show complete worked solution
(a)
\[\text{average speed}=\frac{\text{distance moved}}{\text{time taken}}\]
(b)
\[v=\frac{1500}{300}=5.0\ \mathrm{m\,s^{-1}}\]
(c)
\[a=\frac{v-u}{t}\]\[t=\frac{10-2.0}{2.4}=3.3\ \mathrm{s}\]
QUESTION 2
11 marks
Criterion C
Hard
Analysing a swimmer’s distance-time graph
A swimmer completes one 20 m length. A camera covers 20 m at constant speed in 25 s.
a.
Determine the swimmer’s finishing time.
[1] b(i).
Find the time spent at constant speed.
[1] b(ii).
State the resultant force during constant-speed straight-line motion.
[1] c.
Identify where the swimmer is fastest.
[1] d(i).
State the speed equation.
[1] d(ii).
Calculate camera speed.
[2] d(iii.
Represent the camera on the graph.
[2] e.
Decide whether the camera can film the swimmer for the whole length.
[2] Show complete worked solution
(a)
Read the time where the graph reaches 20 m: 27 s.
(b(i))
The straight segment runs from 15 s to 27 s, so the duration is 12 s.
(b(ii))
Zero; the forces are balanced.
(c)
Where the distance-time graph has the greatest gradient.
(d(i))
\[v=\frac{s}{t}\]
(d(ii))
\[v=\frac{20}{25}=\boxed{0.80\ \mathrm{m\,s^{-1}}}\]
(d(iii)
Draw a straight line from (0 s, 0 m) to (25 s, 20 m).
(e)
Yes, if the camera line stays at or above the swimmer graph. It is never behind the swimmer.
QUESTION 3
5 marks
Criterion A
Medium
Coin leaving a balcony
A coin rolls in a straight line across a balcony at a steady speed of 0.46 m s−1. It then leaves the edge and falls from rest, reaching 78.4 m s−1 after 8.0 s.
a.
Calculate the distance travelled across the balcony in 2.4 s.
[3] b.
Calculate the coin’s acceleration while it falls.
[2] Show complete worked solution
(a)
\[s=vt=(0.46)(2.4)=1.104\ \mathrm{m}\]\[s\approx1.1\ \mathrm{m}\]
(b)
\[a=\frac{v-u}{t}=\frac{78.4-0}{8.0}=9.8\ \mathrm{m\,s^{-2}}\]
P1.3 - Acceleration and motion graphs 5 questions
QUESTION 1
6 marks
Criterion A
Medium
Model car acceleration
A model car accelerates from rest to its top speed in 3.5 s. At top speed it travels 180 m in 9.0 s.
a.
Calculate the car’s maximum acceleration.
[3] b.
Calculate its speed after accelerating from rest for 1.5 s at this rate.
[3] Show complete worked solution
(a)
\[v=\frac{180}{9.0}=20\ \mathrm{m\,s^{-1}}\]\[a=\frac{20-0}{3.5}=5.7\ \mathrm{m\,s^{-2}}\]
(b)
\[v=u+at=0+(5.714\ldots)(1.5)=8.57\ldots\]\[v\approx8.6\ \mathrm{m\,s^{-1}}\]
QUESTION 2
12 marks
Criterion A
Hard
Vehicle and skydiver velocity-time graphs
A vehicle travels at 15 m s⁻¹ for 19 s then stops uniformly at 26 s. The skydiver graph approaches terminal velocity.
a(i).
Calculate vehicle distance in the first 26 s.
[2] a(ii).
The vehicle mass is 1000 kg. Calculate braking-force magnitude.
[4] b(i).
Describe motion from release until terminal velocity.
[4] b(ii).
Explain the change after the parachute opens.
[2] Show complete worked solution
(a(i))
\[s=(19)(15)+\frac12(7)(15)=285+52.5=\boxed{337.5\ \mathrm{m}}\]
(a(ii))
\[a=\frac{0-15}{26-19}=-2.14\ \mathrm{m\,s^{-2}}\]\[|F|=m|a|=(1000)(2.14)=\boxed{2.14\times10^3\ \mathrm{N}}\]
(b(i))
Initially weight is greater than drag, so the skydiver accelerates downward. As speed rises, drag increases and acceleration decreases. When drag equals weight, resultant force is zero and velocity becomes constant.
(b(ii))
Surface area and drag rise sharply while weight is unchanged. The upward resultant force causes deceleration until a new lower terminal velocity is reached.
QUESTION 3
8 marks
Criterion C
Hard
Journey to football training
A student walks from home to football training, realizes that their boots were left at home, walks back, and remains at home for 50 s. The distance–time graph shows the journey.
a.
State how long the student took to reach football training.
[1] b.
Was the student’s walking speed steady? Use the graph to justify your answer.
[2] c.
Calculate the walking speed from home to training.
[2] d.
After returning home, the student travels back by car. The car accelerates uniformly for 10 s and then travels at constant speed for 30 s. Sketch the velocity–time graph on the blank axes.
[3] Show complete worked solution
(a)
The graph reaches training at \(t=300\ \mathrm{s}\).
(b)
Yes. Each walking section is a straight line, so its gradient and therefore the speed are constant within that section.
(c)
\[v=\frac{\Delta s}{\Delta t}=\frac{450}{300}=1.5\ \mathrm{m\,s^{-1}}\]
(d)
Draw a straight rising line from the origin for the first 10 s. Continue with a horizontal line at the reached velocity from 10 s to 40 s. Label both axes and the change at 10 s.
QUESTION 4
10 marks
Criterion C
Hard
Interpreting a velocity–time graph
The graph shows a car’s velocity during the first 100 s of a journey.
a(i).
Describe the motion between 40 s and 60 s.
[1] a(ii).
Describe the motion between 60 s and 100 s.
[1] b.
Calculate the distance travelled between 40 s and 60 s.
[3] c.
Calculate the acceleration between 0 s and 40 s.
[3] d.
After 100 s the car accelerates uniformly for 40 s to 30 m s−1, then travels at that velocity for 60 s. Complete the graph.
[2] Show complete worked solution
(a(i))
The car travels at a constant velocity of 20 m s−1.
(a(ii))
The car slows down. The curve becomes progressively steeper, so the magnitude of its deceleration increases.
(b)
\[s=\text{area under the graph}\]\[s=(20\ \mathrm{s})(20\ \mathrm{m\,s^{-1}})=400\ \mathrm{m}\]
(c)
\[a=\frac{\Delta v}{\Delta t}=\frac{20-0}{40-0}=0.50\ \mathrm{m\,s^{-2}}\]
(d)
From (100 s, 10 m s−1) draw a straight line to (140 s, 30 m s−1). Then draw a horizontal line at 30 m s−1 to 200 s.
QUESTION 5
9 marks
Criterion B
Hard
Investigating acceleration down a ramp
A student investigates a trolley moving down an adjustable ramp using two light gates.
a.
Describe how the equipment can be used to determine the trolley’s acceleration down the ramp.
[6] b.
The student changes both the ramp angle and the distance travelled, then concludes that decreasing the angle increases the trolley’s speed. Explain why this conclusion is invalid and suggest an improvement.
[3] Show complete worked solution
(a)
Attach a card of measured length to the trolley. Release the trolley from the same marked position without pushing it. Use each light gate to measure the card’s interruption time and calculate the speed at each gate. Measure the distance between the gates, or record the time between the two speed measurements. Calculate the acceleration from the change in velocity divided by the time interval. Repeat the measurement and calculate a mean; keep the ramp angle and release point fixed.
(b)
Two variables were changed, so any speed change cannot be attributed to ramp angle alone. Change only the ramp angle, keep the release point and gate positions fixed, and repeat at each angle. The expectation should also be checked: a steeper ramp normally gives a larger component of weight down the slope.
P1.4 - Kinematic equations (SUVAT) and multi-stage motion 1 question
QUESTION 1
4 marks
Criterion A
Hard
Tractor turning
A tractor accelerates uniformly at 2.0 m s−2 over 10 m. Its speed after this acceleration is 7.0 m s−1. It then turns at constant speed until it faces the opposite direction.
a.
Calculate the tractor’s speed before the acceleration.
[3] b.
State whether the tractor accelerates while turning. Explain your answer.
[1] Show complete worked solution
(a)
\[v^2=u^2+2as\]\[u=\sqrt{v^2-2as}=\sqrt{7.0^2-2(2.0)(10)}=3.0\ \mathrm{m\,s^{-1}}\]
(b)
Yes. Velocity includes direction, so the tractor’s velocity changes even though its speed is constant.
P1.6 - Resultant forces and free-body diagrams 4 questions
QUESTION 1
4 marks
Criterion A
Easy
Forces on a moving truck
A truck moves to the right at constant speed. The thrust force is shown.
a(i).
Add the force opposing the motion and label it resistance.
[1] a(ii).
State how resistance changes as the truck’s speed increases.
[1] b.
Add and label one other force acting on the truck.
[2] Show complete worked solution
(a(i))
Draw a horizontal arrow pointing left. At constant speed, it should be the same length as the thrust arrow.
(a(ii))
Resistance increases as speed increases.
(b)
Accept either weight acting vertically downward or the normal contact force acting vertically upward.
QUESTION 2
4 marks
Criterion A
Hard
Comparing car forces
The table gives data for four cars.
| Car | Maximum driving force / N | Mass / kg | Maximum acceleration / m s−2 |
|---|---|---|---|
| Disraeli | 4000 | ? | 5.0 |
| Palmerston | 61 | 1560 | 0.7 |
| Heath TT | ? | 950 | 3.0 |
| Asquith 380 | ? | 790 | 2.0 |
a.
Show that the Heath TT has a greater maximum driving force than the Asquith 380.
[2] b.
Calculate the mass of the Disraeli and complete the table.
[2] Show complete worked solution
(a)
\[F_{\text{Heath}}=ma=(950)(3.0)=2850\ \mathrm{N}\]\[F_{\text{Asquith}}=(790)(2.0)=1580\ \mathrm{N}\]\[2850>1580\]
(b)
\[m=\frac{F}{a}=\frac{4000}{5.0}=800\ \mathrm{kg}\]
QUESTION 3
4 marks
Criterion A
Hard
Two motor scooters
Two identical motor scooters have engines that provide the same maximum driving force. Student A and scooter have a combined mass of 127.5 kg and a maximum acceleration of 2.40 m s−2. Student B and scooter accelerate at 1.70 m s−2. Friction is negligible.
Show that the combined mass of Student B and scooter is 180 kg.
Show complete worked solution
\[F=(127.5)(2.40)=306\ \mathrm{N}\]\[m_B=\frac{F}{a_B}=\frac{306}{1.70}=180\ \mathrm{kg}\]
QUESTION 4
4 marks
Criterion A
Hard
Resultant forces on balloons
The diagram shows the forces acting on hot-air balloons A and B.
a.
Determine the magnitude and direction of the resultant force on balloon A.
[2] b(i).
The resultant force on balloon B is zero. Determine the upward force y.
[1] b(ii).
Determine the leftward force x.
[1] Show complete worked solution
(a)
Horizontally, \(2000-1700-300=0\ \mathrm{N}\). Vertically, \(800-300=500\ \mathrm{N}\) downward. The resultant is therefore \(500\ \mathrm{N}\) downward.
(b(i))
\[y=400\ \mathrm{N}\]
(b(ii))
\[x+500=2000\]\[x=1500\ \mathrm{N}\]
P1.7 - Friction, drag, terminal velocity and stopping distance 6 questions
QUESTION 1
3 marks
Criterion A
Easy
Braking parachute
An aircraft travels horizontally at constant speed and constant altitude. During landing, it deploys a braking parachute.
a.
Name the force acting vertically downward on the aircraft.
[1] b.
Explain why deploying the parachute slows the aircraft.
[2] Show complete worked solution
(a)
Weight, caused by gravity.
(b)
The parachute greatly increases air resistance. Resistance then exceeds thrust, giving a resultant force opposite the motion, so the aircraft decelerates.
QUESTION 2
8 marks
Criterion C
Hard
Stopping-distance evidence
Highway data for dry roads are shown.
| Speed / m s⁻¹ | Thinking / m | Braking / m |
|---|---|---|
| 9 | 6 | 6 |
| 13 | 9 | 14 |
| 18 | 12 | 24 |
| 22 | 15 | 38 |
| 27 | 18 | 55 |
| 31 | 21 | 75 |
a.
Calculate stopping distance at 13 m s⁻¹.
[1] b.
Explain why many vehicles and drivers were observed.
[2] c.
Describe three factors other than speed that increase stopping distance and classify each.
[5] Show complete worked solution
(a)
\[s=9+14=\boxed{23\ \mathrm{m}}\]
(b)
A large sample reduces the effect of anomalous individual results and allows a more reliable mean or representative value.
(c)
Tiredness, alcohol/drugs and distraction increase thinking distance. Wet or icy roads, worn tyres/brakes and greater vehicle mass increase braking distance. Three valid factors earn credit, with correct classification.
QUESTION 3
7 marks
Criterion A
Hard
Flying squirrel terminal velocity
A flying squirrel spreads a membrane called a patagium while falling. Its terminal velocity is 8.5 m s−1.
a.
Explain how a falling object reaches terminal velocity.
[4] b.
Explain how spreading the patagium affects terminal velocity.
[1] c.
Sketch a vertical velocity–time graph from release until terminal velocity is reached.
[2] Show complete worked solution
(a)
At first, weight is greater than air resistance, so the object accelerates. As its speed increases, air resistance increases. Eventually air resistance equals weight, so the resultant force and acceleration are zero. The object then continues at constant terminal velocity.
(b)
It increases surface area and air resistance, so the balance with weight is reached at a lower speed. Terminal velocity decreases.
(c)
Draw a curve from the origin whose gradient steadily decreases and which approaches a horizontal line at 8.5 m s−1.
QUESTION 4
3 marks
Criterion A
Hard
Two falling balls
Two balls have the same size and shape but different weights. They are dropped from the same height.
Identify which ball has the lower terminal velocity and explain your answer.
Show complete worked solution
The lighter ball has the lower terminal velocity. At any given speed, the two balls experience approximately the same drag because their size and shape are the same. The lighter ball needs a smaller drag force to balance its smaller weight, so that balance is reached at a lower speed.
QUESTION 5
6 marks
Criterion A
Medium
Components of stopping distance
A vehicle’s stopping distance is made up of thinking distance and braking distance.
a(i).
Name the distance travelled before the brakes begin to act.
[1] a(ii).
State two factors that can increase this distance.
[2] b(i).
Define braking distance.
[1] b(ii).
State two factors that can increase braking distance.
[2] Show complete worked solution
(a(i))
Thinking distance.
(a(ii))
Any two valid factors, such as greater speed, tiredness, alcohol or drugs, distraction, or longer reaction time.
(b(i))
The distance travelled from the moment the brakes begin to act until the vehicle stops.
(b(ii))
Any two valid factors, such as greater speed, wet or icy roads, worn tyres, worn brakes, or greater vehicle mass.
QUESTION 6
5 marks
Criterion A
Medium
Stopping in heavy rain
A driver is travelling in heavy rain. The vehicle’s total stopping distance is 37 m and its braking distance is 28 m.
a.
State and explain one way heavy rain can increase stopping distance.
[2] b.
Suggest one action the driver can take to reduce stopping distance.
[1] c.
Calculate the thinking distance.
[2] Show complete worked solution
(a)
Water reduces friction between the tyres and road, so the braking force is smaller and the vehicle takes a longer distance to stop. Reduced visibility may also increase reaction time.
(b)
Reduce speed and leave a larger following distance; maintaining sound tyres and brakes is also acceptable.
(c)
\[\text{thinking distance}=37-28=9\ \mathrm{m}\]
P1.8 - Newton's laws, momentum and impulse 7 questions
QUESTION 1
1 mark
Criterion A
Easy
Newton’s third law
State Newton’s third law of motion.
Show complete worked solution
When object A exerts a force on object B, object B simultaneously exerts an equal-magnitude force in the opposite direction on object A. The forces act on different objects.
QUESTION 2
10 marks
Criterion A
Hard
Momentum of two skaters
Skater A: 70 kg at 9.0 m s⁻¹ right. Skater B: 50 kg at 6.6 m s⁻¹ right. A catches B and they move together.
a.
State the momentum equation.
[1] b.
Calculate each initial momentum.
[2] c.
Calculate their common velocity.
[2] d(i).
A later pushes B with 100 N. Describe B’s reaction force.
[1] d(ii).
State the force equation.
[1] d(iii.
Calculate B’s acceleration.
[3] Show complete worked solution
(a)
\[p=mv\]
(b)
\[p_A=(70)(9.0)=630\ \mathrm{kg\,m\,s^{-1}}\]\[p_B=(50)(6.6)=330\ \mathrm{kg\,m\,s^{-1}}\]
(c)
\[v=\frac{630+330}{70+50}=\boxed{8.0\ \mathrm{m\,s^{-1}}}\]
(d(i))
B exerts an equal 100 N force on A in the opposite direction.
(d(ii))
\[F=ma\]
(d(iii)
\[a=\frac{F}{m}=\frac{100}{50}=\boxed{2.0\ \mathrm{m\,s^{-2}}}\]
QUESTION 3
7 marks
Criterion A
Hard
Camper van collision
A camper van of mass 2500 kg is travelling at constant speed. A headwind then exerts a 200 N force opposite its motion. Later, the van hits a stationary 10 kg traffic cone, which accelerates at 29 m s−2 in the van’s original direction.
a.
Calculate the van’s deceleration due to the headwind.
[2] b(i).
Calculate the force exerted by the van on the cone.
[2] b(ii).
State the force exerted by the cone on the van.
[1] b(iii.
Assuming this force is the only horizontal force on the van, calculate its deceleration.
[2] Show complete worked solution
(a)
\[a=\frac{F}{m}=\frac{200}{2500}=0.080\ \mathrm{m\,s^{-2}}\]
(b(i))
\[F=ma=(10)(29)=290\ \mathrm{N}\]
(b(ii))
By Newton’s third law, the cone exerts 290 N on the van in the opposite direction.
(b(iii)
\[a=\frac{290}{2500}=0.116\ \mathrm{m\,s^{-2}}\approx0.12\ \mathrm{m\,s^{-2}}\]
QUESTION 4
7 marks
Criterion A
Hard
Stuntperson momentum
A 65 kg stuntperson travels at 14 m s−1 and is brought to rest in 1.3 s.
a(i).
State the equation linking momentum, mass and velocity.
[1] a(ii).
Calculate the stuntperson’s initial momentum, including its unit.
[3] b(i).
State the equation linking force, change in momentum and time.
[1] b(ii).
Calculate the magnitude of the average stopping force.
[2] Show complete worked solution
(a(i))
\[p=mv\]
(a(ii))
\[p=(65)(14)=910\ \mathrm{kg\,m\,s^{-1}}\]
(b(i))
\[F=\frac{\Delta p}{\Delta t}\]
(b(ii))
\[F=\frac{910}{1.3}=700\ \mathrm{N}\]
QUESTION 5
5 marks
Criterion A
Hard
Skater catches a bag
A 60 kg skater travels at 5.0 m s−1 and picks up a stationary bag. The skater and bag then move together at 4.8 m s−1. Friction is negligible.
Calculate the mass of the bag.
Show complete worked solution
\[p_{\text{before}}=(60)(5.0)=300\ \mathrm{kg\,m\,s^{-1}}\]\[(60+m)(4.8)=300\]\[60+m=62.5\]\[m=2.5\ \mathrm{kg}\]
QUESTION 6
8 marks
Criterion A
Hard
Demolition derby collision
A 650 kg car travels at 15 m s−1. It collides head-on with a 750 kg car travelling at 10 m s−1 in the opposite direction. The cars stick together.
a.
Calculate the momentum of the 650 kg car before the collision.
[2] b.
Calculate the velocity of the joined cars after the collision.
[4] c.
Explain how a crumple zone reduces the force on an occupant.
[2] Show complete worked solution
(a)
\[p=(650)(15)=9750\ \mathrm{kg\,m\,s^{-1}}\]
(b)
Take the first car’s direction as positive.\[p_{\text{total}}=(650)(15)+(750)(-10)=2250\ \mathrm{kg\,m\,s^{-1}}\]\[v=\frac{2250}{650+750}=1.61\ \mathrm{m\,s^{-1}}\]\[v\approx1.6\ \mathrm{m\,s^{-1}}\text{ in the first car’s direction}\]
(c)
The same momentum change occurs over a longer time. Since \(F=\Delta p/\Delta t\), increasing the collision time reduces the average force.
QUESTION 7
7 marks
Criterion A
Hard
Dodgem car collision
Dodgem A and rider have a combined mass of 410 kg and travel at +2.0 m s−1. Dodgem B and rider have a combined mass of 440 kg and travel at −1.1 m s−1. After the collision, A travels at −1.2 m s−1 and B travels at velocity v.
a(i).
Calculate the momentum of A before the collision.
[2] a(ii).
The momentum of B before the collision is −484 kg m s−1. Calculate the total momentum before the collision.
[1] b(i).
State the total momentum after the collision.
[1] b(ii).
Calculate v.
[3] Show complete worked solution
(a(i))
\[p_A=(410)(2.0)=820\ \mathrm{kg\,m\,s^{-1}}\]
(a(ii))
\[p_{\text{total}}=820-484=336\ \mathrm{kg\,m\,s^{-1}}\]
(b(i))
By conservation of momentum, \(p_{\text{after}}=336\ \mathrm{kg\,m\,s^{-1}}\).
(b(ii))
\[(410)(-1.2)+440v=336\]\[-492+440v=336\]\[v=\frac{828}{440}=1.88\ldots\approx1.9\ \mathrm{m\,s^{-1}}\]
P1.9 - Gravity, mass, weight and gravitational fields 1 question
QUESTION 1
6 marks
Criterion A
Medium
Mass and weight
A student hangs a 2.0 kg mass from a newton meter. The mean reading is 19.6 N.
a(i).
State the equation linking weight, mass and gravitational field strength.
[1] a(ii).
Calculate the gravitational field strength, including its unit.
[3] b.
Explain how the mass’s weight would differ on the Moon.
[2] Show complete worked solution
(a(i))
\[W=mg\]
(a(ii))
\[g=\frac{W}{m}=\frac{19.6}{2.0}=9.8\ \mathrm{N\,kg^{-1}}\]
(b)
The weight would be smaller because the Moon has a lower gravitational field strength. The mass itself would remain 2.0 kg.
P1.11 - Elasticity, Hooke's law and force-extension graphs 1 question
QUESTION 1
5 marks
Criterion C
Hard
Spring force and extension
A student records the extension of a spring for different applied forces.
| Force / N | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8.25 |
|---|---|---|---|---|---|---|---|---|---|
| Extension / mm | 3 | 6 | 8 | 11 | 14 | 16 | 20 | 27 | 38 |
a.
Plot extension against force and draw an appropriate best-fit line or curve.
[3] b.
State the relationship between force and extension up to 5 N.
[1] c.
The spring’s elastic limit is 7.2 N. State whether it returns to its original length after a force of 7.5 N is removed, and explain.
[1] Show complete worked solution
(a)
Plot force on the horizontal axis and extension on the vertical axis. The data form an approximately straight line up to about 5–6 N, then curve upward. Draw a smooth best-fit trend and label both axes with units.
(b)
Extension is directly proportional to force up to approximately 5 N.
(c)
No. Since 7.5 N exceeds the elastic limit, the spring is permanently deformed and retains an extension.
P1.12 - Moments and equilibrium 5 questions
QUESTION 1
1 mark
Criterion A
Easy
Centre of gravity
Define the centre of gravity of an object.
Show complete worked solution
The centre of gravity is the point through which the object’s entire weight may be considered to act.
QUESTION 2
7 marks
Criterion A
Hard
Electromagnetic crane and moments
A balanced crane supports a 28 000 N counterweight 5.0 m from the pivot. The anvil is 10.0 m from the pivot.
a.
Define an electromagnet.
[1] b(i).
Describe the field around the electromagnet.
[1] b(ii).
Explain why the core is magnetically soft.
[1] c(i).
State the moment equation.
[1] c(ii).
Calculate anvil weight.
[3] Show complete worked solution
(a)
A coil carrying current that produces a magnetic field, usually strengthened by a soft-iron core.
(b(i))
Draw a bar-magnet-like pattern: field lines leave north, curve around and enter south; inside the core they are close and nearly parallel.
(b(ii))
It magnetises strongly when current flows and loses magnetism quickly when switched off, allowing the load to be released.
(c(i))
\[M=F d_\perp\]
(c(ii))
\[(28000)(5.0)=W(10.0)\]\[W=\boxed{14000\ \mathrm{N}}\]
QUESTION 3
6 marks
Criterion A
Hard
Opening a door
A force is applied to a door handle in four different arrangements.
a.
Define the moment of a force.
[1] b.
Identify the arrangement that produces the greatest moment and explain your choice.
[2] c.
A 45 N force acts vertically downward at a perpendicular distance of 0.10 m from the hinge. Calculate the moment, including its unit.
[3] Show complete worked solution
(a)
The moment is the turning effect of a force about a pivot.
(b)
Choose the arrangement with the greatest perpendicular distance between the force’s line of action and the hinge, and with the force acting perpendicular to the door. This maximizes \(M=F d_{\perp}\).
(c)
\[M=F d_{\perp}=(45)(0.10)=4.5\ \mathrm{N\,m}\]
QUESTION 4
7 marks
Criterion A
Hard
Balanced plank
A weightless plank is balanced about a pivot. Force A is 2.0 N and acts 20 cm from the pivot. Force B produces an anticlockwise moment of 0.80 N m. Force C is 8.0 N and acts on the opposite side.
a.
Calculate the moment produced by force A.
[3] b.
Calculate the distance of force C from the pivot.
[4] Show complete worked solution
(a)
\[M_A=F d=(2.0)(0.20)=0.40\ \mathrm{N\,m}\]
(b)
For balance, clockwise moment equals anticlockwise moment.\[M_C=0.40+0.80=1.20\ \mathrm{N\,m}\]\[d_C=\frac{M_C}{F_C}=\frac{1.20}{8.0}=0.15\ \mathrm{m}\]
QUESTION 5
2 marks
Criterion A
Hard
Plank supported by two ropes
A light plank is suspended horizontally by ropes 1 and 2. A box is placed at different positions in situations A and B.
In which situation is the force in rope 1 greater? Explain your answer using moments.
Show complete worked solution
The force in rope 1 is greater in situation B. Taking moments about rope 2, the box is farther from rope 2 in B, so its moment about rope 2 is larger. Rope 1 must therefore exert a larger force to provide the balancing moment.
P1.13 - Pressure in solids, liquids and gases 2 questions
QUESTION 1
5 marks
Criterion A
Medium
Pressure at a surface
A force of 18 N acts normally over an area of 4500 cm².
a.
State how pressure in a liquid at rest changes with depth.
[1] b(i).
State the equation linking pressure, force and area.
[1] b(ii).
Calculate the pressure.
[3] Show complete worked solution
(a)
Pressure increases with depth.
(b(i))
\[p=\frac{F}{A}\]
(b(ii))
\[4500\ \mathrm{cm^2}=0.450\ \mathrm{m^2}\]\[p=\frac{18}{0.450}=40\ \mathrm{Pa}\]
QUESTION 2
6 marks
Criterion A
Hard
Pressure rating of a diving watch
A watch is rated for a pressure difference of at most 245 kPa in salt water. A 0.500 m³ sample has mass 514 kg. Take g=10 N kg⁻¹.
a.
State the equation for pressure difference in a liquid.
[1] b(i).
Calculate the density of the salt water.
[2] b(ii).
Calculate the maximum depth.
[3] Show complete worked solution
(a)
\[\Delta p=\rho g h\]
(b(i))
\[\rho=\frac{m}{V}=\frac{514}{0.500}=1028\ \mathrm{kg\,m^{-3}}\approx1030\ \mathrm{kg\,m^{-3}}\]
(b(ii))
\[h=\frac{\Delta p}{\rho g}=\frac{245000}{(1028)(10)}=23.8\ \mathrm{m}\approx\boxed{24\ \mathrm{m}}\]
P1.14 - Atmospheric pressure, Pascal's principle and hydraulic systems 1 question
QUESTION 1
7 marks
Criterion A
Hard
Hydraulic system
Piston A has area 0.010 m² and applies 25 N. Piston B has area 0.150 m².
a.
Calculate pressure in the liquid.
[2] b.
Explain why piston B experiences a force.
[3] c.
Show that the force at B is 375 N.
[2] Show complete worked solution
(a)
\[P=\frac{F}{A}=\frac{25}{0.010}=\boxed{2500\ \mathrm{Pa}}\]
(b)
The force at A creates pressure in the enclosed liquid. By Pascal’s principle this pressure is transmitted equally throughout the liquid and acts over the area of piston B.
(c)
\[F_B=PA_B=(2500)(0.150)=\boxed{375\ \mathrm{N}}\]
P1.15 - Work, kinetic energy and gravitational potential energy 7 questions
QUESTION 1
5 marks
Criterion A
Medium
Work done by washing machines
Manufacturer data are shown.
| Machine | Power | Cycle time |
|---|---|---|
| A | 600 W | 125 min |
| B | 400 W | 160 min |
| C | unknown | 125 min |
a.
Calculate the work done by machine A, in kJ.
[3] b.
Machine C does 3 930 000 J in 125 min. Calculate its power.
[2] Show complete worked solution
(a)
\[t=125(60)=7500\ \mathrm{s}\]\[W=Pt=(600)(7500)=4.50\times10^6\ \mathrm{J}=4500\ \mathrm{kJ}\]
(b)
\[P=\frac{W}{t}=\frac{3930000}{7500}=524\ \mathrm{W}\]
QUESTION 2
10 marks
Criterion A
Hard
Roller-coaster energy stores and efficiency
A 1500 kg roller-coaster carriage is raised 40 m to W. Use gravitational field strength 10 N kg⁻¹.
a(i).
Identify the two labelled points with equal gravitational potential energy.
[1] a(ii).
Explain the choice.
[1] b(i).
State the gravitational potential energy equation.
[1] b(ii).
Calculate the energy transferred in kJ.
[2] c(i).
Name the energy store of the compressed launch spring.
[1] c(ii).
State the efficiency equation.
[1] c(iii.
Useful kinetic transfer is 18.0 kJ and wasted transfer is 41.5 kJ. Calculate efficiency.
[3] Show complete worked solution
(a(i))
Points at the same vertical height have equal gravitational potential energy.
(a(ii))
\(E_p=mgh\), so with constant \(m\) and \(g\), equal height gives equal \(E_p\).
(b(i))
\[E_p=mgh\]
(b(ii))
\[E_p=(1500)(10)(40)=600000\ \mathrm{J}=\boxed{600\ \mathrm{kJ}}\]
(c(i))
Elastic potential energy store.
(c(ii))
\[\eta=\frac{\text{useful energy output}}{\text{total energy input}}\times100\%\]
(c(iii)
\[E_{in}=18.0+41.5=59.5\ \mathrm{kJ}\]\[\eta=\frac{18.0}{59.5}\times100=\boxed{30.3\%}\]
QUESTION 3
5 marks
Criterion A
Medium
Work done pushing a wheelbarrow
A woman pushes a 20 kg wheelbarrow 15 m along a level path with a horizontal force of 50 N.
a(i).
State the equation for work done.
[1] a(ii).
Calculate the work done.
[2] b.
Explain the effect of friction on the wheel temperature.
[2] Show complete worked solution
(a(i))
\[W=Fd\]where \(d\) is displacement in the force direction.
(a(ii))
\[W=(50)(15)=750\ \mathrm{J}\]
(b)
Work against friction transfers energy to the wheel’s thermal store, so its temperature increases.
QUESTION 4
1 mark
Criterion A
Easy
Energy stores of a flying bird
A bird is flying above the ground.
Identify which of its kinetic and gravitational potential stores contain energy.
Show complete worked solution
Both stores contain energy: it is moving and it is above the ground.
QUESTION 5
3 marks
Criterion A
Medium
Gravitational potential energy on stairs
A 65 kg student climbs through a vertical height of 10 m. Take g=10 N kg⁻¹.
a.
State the equation for gravitational potential energy.
[1] b.
Calculate the increase in the store.
[2] Show complete worked solution
(a)
\[\Delta E_p=mg\Delta h\]
(b)
\[\Delta E_p=(65)(10)(10)=6500\ \mathrm{J}\]
QUESTION 6
5 marks
Criterion A
Hard
Ball thrown vertically upward
At its highest point, a ball has gained 4.0 J in its gravitational potential store. Air resistance is negligible. It later reaches 8.9 m s⁻¹.
a.
State its kinetic energy just before reaching the launch height again.
[1] b.
State the kinetic-energy equation.
[1] c.
Calculate the ball’s mass.
[3] Show complete worked solution
(a)
Conservation of energy gives 4.0 J in the kinetic store.
(b)
\[E_k=\frac12mv^2\]
(c)
\[m=\frac{2E_k}{v^2}=\frac{2(4.0)}{8.9^2}=0.101\ \mathrm{kg}\approx\boxed{0.10\ \mathrm{kg}}\]
QUESTION 7
9 marks
Criterion A
Hard
Roller-coaster energy conservation
A 105 kg cart moves at 2.39 m s⁻¹ before descending 20.2 m. Take g=10 N kg⁻¹ and neglect friction.
a.
Calculate its initial kinetic energy.
[2] b(i).
Calculate the gravitational potential energy lost.
[2] b(ii).
State what happens to this energy.
[1] c.
Calculate the speed at the bottom.
[4] Show complete worked solution
(a)
\[E_{k,i}=\frac12(105)(2.39)^2=300\ \mathrm{J}\]
(b(i))
\[\Delta E_p=(105)(10)(20.2)=21210\ \mathrm{J}\approx2.12\times10^4\ \mathrm{J}\]
(b(ii))
It is transferred to the cart’s kinetic energy store.
(c)
\[E_{k,f}=300+21210=21510\ \mathrm{J}\]\[v=\sqrt{\frac{2E_{k,f}}{m}}=\sqrt{\frac{2(21510)}{105}}=20.2\ \mathrm{m\,s^{-1}}\]
P1.17 - Energy stores, transfers, conservation and Sankey diagrams 7 questions
QUESTION 1
3 marks
Criterion A
Easy
Energy stores in common processes
For each process, identify the energy store from which energy is transferred.
Match the four processes—falling skydiver, nuclear reaction, relaxing spring and burning coal—to gravitational potential, nuclear, elastic potential and chemical stores.
Show complete worked solution
Falling skydiver → gravitational potential store; nuclear reaction → nuclear store; relaxing spring → elastic potential store; burning coal → chemical store.
QUESTION 2
4 marks
Criterion A
Easy
Heating water in a kettle
A kettle of cold water is connected to the mains and brought to the boil.
a.
Name the energy store of the water that increases.
[1] b.
State how energy is transferred from the mains to the kettle.
[1] c.
State the principle of conservation of energy.
[2] Show complete worked solution
(a)
The thermal energy store of the water increases.
(b)
Energy is transferred electrically.
(c)
Energy can be stored, transferred between stores or dissipated, but the total energy is conserved: energy cannot be created or destroyed.
QUESTION 3
1 mark
Criterion A
Easy
Energy transfer to an electric heater
An electric heater is connected to the mains.
Select the correct description of the energy transfer.
Show complete worked solution
Energy is transferred electrically to the thermal energy store of the heater.
QUESTION 4
5 marks
Criterion A
Medium
Weight lifter and falling weights
A weight lifter raises a set of weights and holds them above his head.
a.
Describe the energy transfers while the weights are raised.
[3] b.
Describe the transfer when the weights are released.
[2] Show complete worked solution
(a)
Energy is transferred mechanically from the chemical store of the lifter’s muscles to kinetic stores of the arms and weights, and then to the gravitational potential energy store of the raised weights.
(b)
Energy is transferred mechanically from the gravitational potential energy store to the kinetic energy store of the falling weights.
QUESTION 5
4 marks
Criterion A
Medium
Golf club striking a ball
A moving golf club strikes a stationary ball.
Describe the energy transfers, beginning with the club.
Show complete worked solution
The club initially has energy in its kinetic store. Energy is transferred mechanically to the ball’s kinetic store. Some is transferred to thermal stores of the club, ball and surroundings, and some is carried away by sound.
QUESTION 6
5 marks
Criterion C
Hard
Clock Sankey diagram
A clock receives 200 J. Its incomplete Sankey diagram is drawn on a square grid.
a.
Calculate the energy represented by one grid square.
[1] b.
The useful arrow is 5 squares wide. Calculate useful output.
[1] c.
Four fifths of the 150 J wasted output heats the surroundings and one fifth is carried by sound. Complete and label the Sankey diagram.
[3] Show complete worked solution
(a)
The input arrow is 20 squares wide, so \[\frac{200\ \mathrm{J}}{20}=10\ \mathrm{J\ per\ square}\]
(b)
\[E_u=5(10)=50\ \mathrm{J}\]
(c)
Thermal output: \[\frac45(150)=120\ \mathrm{J}\]Sound output: \[\frac15(150)=30\ \mathrm{J}\]Draw widths in the ratio input : useful : thermal : sound = \(20:5:12:3\).
QUESTION 7
5 marks
Criterion C
Hard
Crane Sankey diagram
A crane receives 100 kJ. The diagram shows 20 kJ transferred to the cable and hook and 50 kJ wasted.
a.
Suggest one store that receives wasted energy.
[1] b.
Calculate the useful transfer to the raised weight.
[1] c.
During the fall, 1.5 kJ is dissipated. Sketch a labelled Sankey diagram for the fall.
[3] Show complete worked solution
(a)
A thermal energy store of the motor, cable or surroundings.
(b)
\[E_u=100-20-50=30\ \mathrm{kJ}\]
(c)
Of the initial \(30\ \mathrm{kJ}\), \(28.5\ \mathrm{kJ}\) reaches the kinetic store and \(1.5\ \mathrm{kJ}\) is transferred to thermal stores and sound. Draw proportional arrows in the ratio \(30:28.5:1.5\).
P1.18 - Power and efficiency 5 questions
QUESTION 1
1 mark
Criterion A
Easy
Comparing washing-machine efficiency
Four washing machines have the energy data shown.
| Machine | Input / J | Useful output / J |
|---|---|---|
| A | 4.00×10⁴ | 2.52×10⁴ |
| B | 4.00×10⁴ | 2.80×10⁴ |
| C | 4.00×10⁴ | 2.95×10⁴ |
| D | 4.00×10⁴ | 2.98×10⁴ |
Identify the most efficient machine and justify your choice.
Show complete worked solution
All four receive the same input energy. Machine D has the greatest useful output, so it has the greatest efficiency.
QUESTION 2
5 marks
Criterion A
Medium
Efficiency of an electric fan
An electric fan receives 7250 J. A total of 2.0 kJ is wasted.
a.
Suggest one way in which energy is wasted.
[1] b.
Calculate the efficiency as a percentage, to 2 significant figures.
[4] Show complete worked solution
(a)
Some energy is transferred to thermal energy stores of the fan and surroundings, or carried away by sound.
(b)
Convert the wasted energy: \[2.0\ \mathrm{kJ}=2000\ \mathrm{J}\]Useful output: \[E_u=7250-2000=5250\ \mathrm{J}\]Hence \[\eta=\frac{5250}{7250}\times100\%=72.4\ldots\%\approx\boxed{72\%}\]
QUESTION 3
1 mark
Criterion A
Hard
Boiling time of an inefficient kettle
A kettle is 76% efficient and receives 2500 J each second. The water needs 418 000 J to boil.
Select the correct operating time and show the calculation used to decide: 2.8 min, 22 s, 167 s or 220 s.
Show complete worked solution
Useful power: \[P_u=0.76(2500)=1900\ \mathrm{W}\]Then \[t=\frac{E}{P_u}=\frac{418000}{1900}=\boxed{220\ \mathrm{s}}\]
QUESTION 4
1 mark
Criterion A
Easy
Definition of power
Power describes how quickly energy is transferred.
State the definition of power.
Show complete worked solution
Power is the rate of energy transfer or work done: \[P=\frac{E}{t}=\frac{W}{t}\]
QUESTION 5
7 marks
Criterion A
Hard
Power of a replacement engine
An old engine transfers 1.87×10³ kJ in 1.00 h. A replacement is 45% more powerful.
a.
Calculate the power of the new engine.
[4] b.
Explain the effect on time taken to accelerate to the same speed.
[3] Show complete worked solution
(a)
\[E=1.87\times10^3\ \mathrm{kJ}=1.87\times10^6\ \mathrm{J},\quad t=3600\ \mathrm{s}\]\[P_{old}=\frac{1.87\times10^6}{3600}=519.4\ \mathrm{W}\]\[P_{new}=1.45(519.4)=\boxed{753\ \mathrm{W}}\]
(b)
The new engine transfers more energy each second. The same increase in kinetic energy is therefore delivered in less time, so the acceleration time decreases.
P1.19 - Renewable and non-renewable energy resources 5 questions
QUESTION 1
1 mark
Criterion A
Easy
Renewable energy source
The options are coal, nuclear fuel, wind and oil.
Identify the renewable resource.
Show complete worked solution
Wind is renewable because it is naturally replenished.
QUESTION 2
1 mark
Criterion D
Easy
Disadvantage of non-renewable resources
Consider environmental effects of non-renewable electricity generation.
Identify one valid disadvantage.
Show complete worked solution
Burning some non-renewable fuels releases sulfur dioxide, which can cause acid rain.
QUESTION 3
6 marks
Criterion D
Hard
Natural-gas power station
Natural gas is burned to generate electricity.
a.
Describe the energy-transfer pathway.
[4] b.
Give two advantages of natural gas generation.
[2] Show complete worked solution
(a)
Burning transfers energy from the fuel’s chemical store to the thermal store of water, producing steam. The steam transfers energy mechanically to turbines and a generator. The generator transfers energy electrically to the grid.
(b)
It is reliable and can respond to demand; it releases much energy at relatively low cost. Existing infrastructure is also widely available.
QUESTION 4
2 marks
Criterion D
Medium
Wave-power converter
Electricity is generated from sea waves using a converter.
a.
State one practical disadvantage.
[1] b.
Describe the energy transfer.
[1] Show complete worked solution
(a)
Wave converters can obstruct or endanger boats and their output varies with wave conditions.
(b)
Energy is transferred mechanically from the kinetic store of the waves to the kinetic stores of the turbine and generator, then electrically to the grid.
QUESTION 5
5 marks
Criterion D
Medium
Using solar energy
Solar energy can generate electricity or heat water.
a.
Name a device that directly generates electricity.
[1] b.
Describe another way solar energy heats domestic water.
[2] c.
Give two reasons small solar systems are rarely connected directly to a national grid.
[2] Show complete worked solution
(a)
A photovoltaic solar cell.
(b)
A solar thermal collector absorbs sunlight and transfers energy by heating to water flowing through it; the hot water is stored or supplied to the home.
(c)
Their output is intermittent and relatively small, while grid connection and control equipment can cost more than the value of the electricity supplied.
P1.20 - Environmental impact and sustainable energy choices 4 questions
QUESTION 1
7 marks
Criterion D
Hard
Geothermal and wind power
Compare geothermal and wind generation.
a(i).
Complete the geothermal energy pathway: hot rocks → water → turbine and generator.
[3] a(ii).
Give one advantage and one disadvantage of geothermal power.
[2] b.
Give one advantage and one disadvantage of wind power.
[2] Show complete worked solution
(a(i))
Thermal store of hot rocks → thermal store of water/steam → kinetic stores of turbine and generator.
(a(ii))
Advantage: renewable with low running emissions. Disadvantage: high drilling costs and few suitable locations.
(b)
Advantage: renewable with no fuel or atmospheric pollution during operation. Disadvantage: intermittent output and visual/noise or habitat impact.
QUESTION 2
11 marks
Criterion D
Hard
Evaluating electricity resources
A seasonal generation chart includes the readings shown.
| Summer 2014 resource | Electricity / 10⁹ kWh |
|---|---|
| biofuel | 6 |
| hydroelectric | 1 |
a(i).
State the biofuel and hydroelectric values for summer 2014.
[2] a(ii).
Identify the resource usually producing the most electricity.
[1] a(iii.
Explain why summer solar generation exceeds winter generation.
[1] b.
Give one advantage and one disadvantage of non-renewables.
[2] c.
If fossil fuels supply 59.2% and renewables 23.9%, calculate nuclear proportion.
[1] d.
Give two advantages and two disadvantages of nuclear power compared with fossil fuels.
[4] Show complete worked solution
(a(i))
Biofuel \(=6\times10^9\ \mathrm{kWh}\); hydroelectric \(=1\times10^9\ \mathrm{kWh}\).
(a(ii))
Wind power.
(a(iii)
Summer usually has longer daylight and greater solar intensity.
(b)
Advantage: reliable, controllable output. Disadvantage: finite fuels and, for fossil fuels, carbon dioxide and air pollution.
(c)
\[100-59.2-23.9=\boxed{16.9\%}\]
(d)
Advantages: very low operational carbon dioxide and high energy density/reliable output. Disadvantages: long-lived radioactive waste, high construction/decommissioning cost, and accident risk.
QUESTION 3
4 marks
Criterion D
Hard
Nuclear power and the environment
A nuclear power station heats water to produce steam.
a.
Describe the transfer that produces the steam.
[1] b(i).
Explain why operation contributes little carbon dioxide.
[1] b(ii).
Give two environmental risks.
[2] Show complete worked solution
(a)
Energy is transferred by heating from the nuclear store of the fuel to the thermal store of the water.
(b(i))
No fossil fuel is burned in the reactor, so electricity generation itself releases little or no carbon dioxide.
(b(ii))
Radioactive waste remains hazardous and is difficult to store; accidents or leaks can contaminate ecosystems. Fuel mining and processing also cause impacts.
QUESTION 4
7 marks
Criterion D
Hard
Generating electricity using water
Water stored behind a hydroelectric dam flows through turbines.
a.
Describe the energy-transfer pathway.
[2] b.
Give two ways a dam can damage the environment.
[2] c.
Name the process of pumping water back to the high reservoir when demand is low.
[1] d.
Give two advantages of tidal barrages.
[2] Show complete worked solution
(a)
The water’s gravitational potential store transfers to its kinetic store, then mechanically to turbine and generator kinetic stores, and finally electrically to the grid.
(b)
Flooding destroys habitats and changes the landscape; rotting flooded vegetation may release greenhouse gases and river ecosystems can be disrupted.
(c)
Pumped storage.
(d)
Tides are renewable and predictable. Operation needs no fuel and releases little atmospheric pollution.