Forces and Motion — Free IB MYP4 Physics Questions

1QuestionFree Fall and the Effect of GravityConcept Practice

2 marks~3 minCriterion A

During a skydive, a skydiver jumps from an aircraft and falls toward Earth before deploying a parachute.

a

Identify one real-world safety feature of a parachute that is directly linked to the effects of gravity and air resistance. [1]

b

Explain how the design of a parachute uses the relationship between gravitational force and air resistance to ensure the skydiver lands safely. [1]

Solutions

2QuestionFree Fall and the Effect of GravityConcept Practice

2 marks~3 minCriterion D

GPS satellites rely on Einstein's theory of relativity to correct for gravitational time dilation. Without this correction, GPS positions would drift by several kilometers each day. Identify one positive societal impact of this scientific discovery.

Solutions

3QuestionFree Fall and the Effect of GravityConcept Practice

2 marks~3 minCriterion B

A ball is dropped from rest. The diagram shows the distance fallen at 0.1 s, 0.2 s, 0.3 s, and 0.4 s.

Time (s): 0.1 0.2 0.3 0.4
Distance (m): 0.05 0.20 0.45 0.80

a

[1 mark] Outline the pattern in the distances as time increases.

b

[1 mark] Predict the distance fallen at 0.5 s, assuming the pattern continues.

c

[1 mark] State the general relationship between distance fallen and time for an object in free fall.

Solutions

4QuestionCalculating Weight Using W = mgConcept Practice

4 marks~6 minCriterion C

A student of mass 60 kg stands on the surface of Earth, where

g = 9.8 \text{ N kg}^{-1}

. On the Moon,

g = 1.6 \text{ N kg}^{-1}

.

a

State the equation relating weight, mass, and gravitational field strength. [1]

b

Calculate the weight of the student on Earth. [1]

c

The student claims that because they feel "lighter" on the Moon, their mass must have decreased. Evaluate this claim, using

W = mg

to justify your reasoning. [2]

Solutions

5QuestionTerminal Velocity in Free Fall - Basic LevelConcept Practice

2 marks~3 minCriterion C

The velocity-time graph below shows the motion of a skydiver from the moment they jump out of a plane until they reach the ground. Describe the trend shown in the graph using scientific language. In your description, identify the point where air resistance equals weight.

Solutions

6QuestionTerminal Velocity in Free Fall - Basic LevelConcept Practice

2 marks~3 minCriterion D

A skydiver jumps from an airplane and uses a parachute to slow their descent. The parachute is made of nylon, a synthetic material. Outline one potential environmental impact associated with the production or disposal of nylon parachutes.

Solutions

7QuestionTerminal Velocity in Free Fall - Basic LevelConcept Practice

2 marks~3 minCriterion A

A skydiver falls vertically. A diagram shows two forces acting on the skydiver: a downward arrow labelled weight and an upward arrow labelled F.

a

Identify the force F. [1]

b

The skydiver reaches terminal velocity. Explain why the skydiver's acceleration is zero at this point. [1]

Solutions

8QuestionTerminal Velocity in Free Fall - Basic LevelConcept Practice

2 marks~3 minCriterion B

Outline the steps of an experiment to investigate how the shape of an object affects its terminal velocity. The experiment uses different shaped pieces of plasticine of equal mass, a tall measuring cylinder filled with viscous liquid (e.g., honey or glycerol), a ruler, and a timer. The image shows the experimental setup.

Solutions

9QuestionForce Diagrams and Vector RepresentationConcept Practice

2 marks~3 minCriterion A

The diagram shows a book resting stationary on a horizontal table. Two arrows act on the book: one pointing vertically upward from the table surface, one pointing vertically downward. Both arrows are equal in length.

(a) Name the force represented by each arrow. [2]

Solutions

10QuestionNewtons Third Law Action and Reaction PairsConcept Practice

2 marks~3 minCriterion C

During a rocket launch, engines expel exhaust gases downward at high speed.

a

State the SI unit for force. [1]

b

A student claims: "The exhaust gases push the rocket upward, but the rocket does not push back on the gases." Apply Newton's third law to explain why this claim is incorrect, and identify both forces in the action–reaction pair, including the direction of each force. [1]

Solutions

11QuestionForce Diagrams and Vector RepresentationConcept Practice

2 marks~3 minCriterion D

A suspension bridge cable is anchored so that it carries a tension of

5000 \, \text{N}

at

30°

above the horizontal.

a

Calculate the vertical component of this tension force. [1]

b

Identify one assumption made when modelling the cable as a single straight force vector, and explain how this assumption could affect the accuracy of the structural design. [1]

Solutions

12QuestionCalculating Net Force in One and Two DimensionsConcept Practice

2 marks~3 minCriterion A

A rescue drone applies two simultaneous thrust forces to drag a supply crate across flat ground: 3 N directed east and 4 N directed north. The two forces act at right angles to each other.

Calculate the magnitude of the net force acting on the crate. [2]

Solutions

13QuestionIdentifying Balanced and Unbalanced Force ScenariosConcept Practice

2 marks~3 minCriterion D

A construction crane holds a 2400 kg steel beam stationary at height before positioning it.

Explain why the forces acting on the beam are balanced in this situation. [1]

Discuss what would happen to the beam's motion if the cable tension suddenly decreased, and explain the societal consequence of such a failure at a busy construction site. [1]

Solutions

14QuestionCalculating Acceleration and Area Under GraphsConcept Practice

2 marks~3 minCriterion C

A car travels along a straight road. The velocity–time graph shows three sections: A, B, and C. In section A the line rises steeply, in section B the line is horizontal, and in section C the line falls to zero.

a

Identify the section of the graph where the acceleration of the car is zero. [1]

b

Explain how the gradient of a velocity–time graph determines whether acceleration is positive, negative, or zero. [1]

Solutions

15QuestionInterpreting Distance-Time GraphsConcept Practice

2 marks~3 minCriterion A

A runner's motion over 20 seconds is shown in the distance–time graph below.

Segment A: 0–5 s, horizontal at 0 m.
Segment B: 5–12 s, rises from 0 m to 40 m.
Segment C: 12–20 s, rises from 40 m to 100 m.

a

State the speed of the runner during Segment A. [1]

b

Deduce which segment, B or C, represents faster motion. Support your answer with calculated speeds. [1]

Solutions

16QuestionCircular Motions ExamplesConcept Practice

2 marks~3 minCriterion A

A car of mass 1200 kg travels at a constant speed of 15 m/s around a flat, circular curve of radius 50 m. The centripetal force is provided entirely by friction between the tyres and the road.

Calculate the centripetal force acting on the car. [2]

Solutions

17QuestionCalculating Weight Using W = mgAssessment Practice

12 marks~18 minCriterion D

An elevator cabin made of steel has a mass of 800 kg. A redesigned cabin using an aluminium alloy has a mass of 480 kg. Both cabins carry a maximum passenger load of 400 kg. Take

g = 10 \text{ N kg}^{-1}

.

a

Calculate the weight of each fully loaded cabin and determine the reduction in weight when the aluminium cabin is used. [3]

b

Explain how the reduced cabin mass affects the motor's energy requirements and the design of the counterweight system. [4]

c

Discuss one limitation of using

W = mg

to model forces in a real, moving elevator, and evaluate whether this limitation makes the formula unsuitable for engineering design. [5]

Solutions

18QuestionDistinguishing Mass from WeightAssessment Practice

3 marks~5 minCriterion B

A student measures the weight of the same object on several planets and records the gravitational field strength of each planet. The graph shows weight (N) on the y-axis (0–300 N) and gravitational field strength (N/kg) on the x-axis (0–30 N/kg). The data points form a straight line passing through the origin.

The mass of the object remains constant throughout.

Explain the relationship shown in the graph, linking it to the formula

W = mg

, and state what the gradient of the line represents. [3]

Solutions

19QuestionCalculating Weight Using W = mgAssessment Practice

3 marks~5 minCriterion C

The graph below shows weight (

W

, in N) on the

y

-axis plotted against mass (

m

, in kg) on the

x

-axis for several objects on Earth. The data points form a straight line through the origin.

a

State what the slope of this graph represents, and give its approximate value with units. [1]

b

Using

W = mg

, explain why the graph is a straight line passing through the origin. [1]

c

A student claims that the slope of a weight–mass graph would be identical on the Moon. Evaluate this claim. [1]

Solutions

20QuestionCalculating Weight Using W = mgAssessment Practice

12 marks~18 minCriterion A

A bar chart shows the weight of a 1.0 kg mass on the surface of four bodies in our solar system. The weights recorded are:

Earth: 9.8 N
Mars: 3.7 N
Jupiter: 24.8 N
Moon: 1.6 N

Assume negligible air resistance.

a

Using

W = mg

, deduce the gravitational field strength,

g

, at the surface of each body. Show all working. [4]

b

Explain why an astronaut of fixed mass weighs significantly less on the Moon than on Earth, using your values from part (a) and the relationship

W = mg

. [3]

c

Analyse how the size and composition of a planetary body affect its surface gravitational field strength, using the four bodies above as evidence. [5]

Solutions

21QuestionTerminal Velocity in Free Fall - Basic LevelAssessment Practice

4 marks~6 minCriterion B

A skydiver with a mass of 70 kg jumps from a plane. After some time, they reach a terminal velocity of 55 m/s. At this point, they are falling straight down as shown in the diagram.

a

State the relationship between the skydiver's weight and the air resistance force when they are at terminal velocity. [1 mark]

b

Predict what will happen to the skydiver's terminal velocity if their mass increases to 85 kg (same parachute). [1 mark]

c

Justify your prediction in (b) using the relationship between weight, air resistance, and terminal velocity. Explain how the forces must change to reach a new terminal velocity. [4 marks]

Solutions

22QuestionTerminal Velocity in Free Fall - Basic LevelAssessment Practice

12 marks~18 minCriterion C

Four skydivers of different masses jump simultaneously from the same aircraft at the same altitude. A classmate claims that all skydivers must reach the same terminal velocity because gravitational acceleration is identical for all falling objects. The velocity–time graph shows each skydiver's motion from the moment of jumping until they open their parachutes. All skydivers adopt the same body position throughout free fall.

a

Explain why a skydiver reaches terminal velocity during free fall. [3]

b

Interpret the graph to evaluate the classmate's claim. [4]

c

Analyse how a skydiver could use body position to deliberately alter their terminal velocity during a jump, referring to the forces involved. [5]

Solutions

23QuestionApplications in Engineering and SportsAssessment Practice

3 marks~5 minCriterion A

A badminton shuttlecock falls vertically from rest. A graph of cross-sectional area against terminal velocity shows that as cross-sectional area increases, terminal velocity decreases.

Explain why a shuttlecock with a larger cross-sectional area reaches a lower terminal velocity. [3]

Solutions

24QuestionApplications in Engineering and SportsAssessment Practice

12 marks~18 minCriterion D

A skydiver of mass 75 kg jumps from a stationary aircraft. The table below shows the skydiver's velocity at one-second intervals. Air resistance is not negligible.

g = 9.8 \text{ m s}^{-2}

.

Time (s)	0	1	2	3	4	5	6	7
Velocity (m s $^{-1}$ )	0	20	40	48	50	50	50	50

a

Calculate the skydiver's acceleration during the first two seconds and explain why this value is less than

g

. [3]

b

Analyse how the forces acting on the skydiver change between

t = 0

s and

t = 4

s, and deduce the magnitude of the air resistance force at terminal velocity. [5]

c

Evaluate how well the data supports the physics model of terminal velocity. In your evaluation, consider whether terminal velocity has been reached, what the data reveals about the relationship between speed and air resistance, and at least one limitation of the dataset. [4]

Solutions

25QuestionLaw of conservation of momentumAssessment Practice

8 marks~12 minCriterion D

A satellite manufacturer is considering replacing chemical thrusters with reaction wheels for attitude control. Reaction wheels spin internal flywheels to reorient the satellite without expelling propellant. However, the mechanical components may wear out, potentially shortening the satellite's operational lifespan and requiring earlier replacement launches.

a

Explain how conservation of angular momentum allows reaction wheels to reorient a satellite without expelling mass. [3]

b

Discuss the environmental trade-off between reduced launch emissions from eliminating propellant and the increased resource use and emissions associated with more frequent satellite replacements caused by mechanical failure. [3]

c

Evaluate the ethical responsibility of satellite operators in balancing the risk of increased space debris from premature satellite failure against the benefit of reduced atmospheric pollution from fewer propellant launches. [2]

Solutions

26QuestionTypes of Forces Contact and Non-ContactAssessment Practice

6 marks~9 minCriterion B

You are investigating how surface area affects air resistance. Paper cones of different diameters are dropped from a height of 2.0 m and the time taken to fall is recorded.

Diameter (cm)	10	15	20	25	30
Fall time (s)	1.2	1.5	1.9	2.4	3.0

a

Construct a graph of fall time (y-axis) against diameter (x-axis). Describe the pattern shown by your graph. [2]

b

Interpret the graph to predict the fall time for a cone of diameter 35 cm, and explain the reasoning behind your prediction. [2]

c

Analyse how increasing surface area affects the motion of a falling cone. In your answer, justify your conclusion using Newton's second law. [2]

Solutions

27QuestionCollisionsAssessment Practice

4 marks~6 minCriterion D

Modern cars are designed with crumple zones that collapse during a collision, extending the time over which the impact force acts.

A car of mass 1500 kg is travelling at 20 m/s when it strikes a solid wall and comes to rest. Without a crumple zone, the collision lasts 0.10 s. With a crumple zone, the same collision lasts 0.30 s.

a

Calculate the initial momentum of the car. [1]

b

Show that the average force on the car is three times greater without the crumple zone than with it. [2]

c

Evaluate the use of crumple zones in vehicle design. In your answer, refer to the physics of momentum and force, and consider at least one real-world trade-off. [1]

Solutions

28QuestionNewtons Second Law F = maAssessment Practice

6 marks~9 minCriterion A

A laboratory cart is pushed along a frictionless air track. Different horizontal forces are applied, and the resulting accelerations are recorded below.

Force (N)	5.0	10.0	15.0	20.0	25.0
Acceleration (m/s²)	2.0	4.0	6.0	8.0	10.0

a

Construct a graph of acceleration (y-axis) against force (x-axis). Draw a line of best fit and determine its gradient. [2]

b

Explain how the gradient of your graph is related to the mass of the cart, using Newton's second law. [2]

c

A second, identical cart is attached to the first, doubling the total mass. Analyse how this change would affect the gradient of the acceleration–force graph and deduce the new gradient. [2]

Solutions

29QuestionNewtons Second Law F = maAssessment Practice

3 marks~5 minCriterion C

The graph below shows how the acceleration of a trolley of constant mass varies with the net force applied to it. The data points lie on a straight line passing through the origin, with the line passing through the points (0, 0) and (10 N, 5 m/s²).

Explain why the graph is a straight line through the origin. [3]

Solutions

30QuestionFriction and Its Role in BalanceAssessment Practice

3 marks~5 minCriterion A

The graph shows how friction force varies with applied force for a 2.0 kg box initially at rest on a horizontal surface. The applied force is increased gradually from 0 N to 10 N.

Explain why the friction force suddenly drops from 6 N to 4 N when the box begins to move. [3]

Solutions

31QuestionHooke's Law and turning effectAssessment Practice

9 marks~14 minCriterion C

A student investigates how three springs (A, B, C) stretch under applied forces by hanging masses and measuring extension with a ruler.

Spring A — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 2.5, 5.0, 7.5, 10.0, 12.5

Spring B — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 1.0, 4.0, 9.0, 16.0, 25.0

Spring C — Force (N): 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 | Extension (cm): 0.0, 3.0, 6.0, 9.0, 12.0, 15.0

a

Construct a graph of extension (cm) against force (N) for all three springs on the same axes. [3]

b

Calculate the spring constant

k

(in N/cm) for Spring A. Show your working. [2]

c

A fourth spring, Spring D, has a spring constant of

k = 0.40

N/cm. Using Hooke's law, calculate the extension of Spring D when a force of 3.5 N is applied. Then evaluate whether Spring B could be described by the same law at 3.5 N, justifying your answer with reference to your graph and the pattern in Spring B's data. [4]

Solutions

32QuestionHooke's Law and turning effectAssessment Practice

12 marks~18 minCriterion D

A sports-medicine engineer is designing a running blade prosthetic for a below-knee amputee. The blade is modelled as a spring with spring constant

k = 85 \ \text{N m}^{-1}

. During a stride, the blade compresses by

x = 0.040 \ \text{m}

under the athlete's weight. Carbon-fibre blades cost approximately 15 000 dollars; polypropylene alternatives cost approximately 800 dollars but have a lower, less tunable

k

.

a

State Hooke's Law and calculate the restoring force the blade exerts during compression. [2]

b

Analyse how the choice of spring constant influences both the biomechanical performance and the manufacturing cost of a prosthetic running blade. [4]

c

Evaluate the ethical and environmental implications of the cost gap between carbon-fibre and polypropylene prosthetic blades, considering equity of access and the environmental impact of each material across its full lifecycle. [6]

Solutions

33QuestionIdentifying Balanced and Unbalanced Force ScenariosAssessment Practice

12 marks~18 minCriterion A

A 10 kg storage crate is pushed horizontally across a warehouse floor. Two horizontal forces act on it:

- Applied force

F_A = 50\ \text{N}

to the right
- Frictional force

F_f = 20\ \text{N}

to the left

The crate starts from rest.

a

Deduce the net horizontal force acting on the crate, including its direction. [2]

b

Calculate the acceleration of the crate during the first 3 seconds, stating its direction. [3]

c

At

t = 3\ \text{s}

, the applied force is removed. Analyse how the motion of the crate changes after this moment, justifying your answer with Newton's laws and a calculation of the new acceleration. [7]

Solutions

34QuestionCalculating Net Force in One and Two DimensionsAssessment Practice

6 marks~9 minCriterion B

A student uses a force table to investigate how two perpendicular forces combine. Forces are applied to a central ring, and the resultant magnitude is measured. The recorded data are:

Force $F_1$ (N)	3	6	5	9
Force $F_2$ (N)	4	8	12	12
Resultant $R$ (N)	5	10	13	15

a

Analyse the data to deduce the mathematical relationship between

F_1

,

F_2

, and

R

. Support your answer with calculations from at least two data sets. [2]

b

Apply your relationship to predict the resultant force when perpendicular forces of 8 N and 15 N act on the ring. Show your substitution and result. [2]

c

A technician claims that doubling both perpendicular forces always doubles the resultant. Evaluate this claim using your relationship, and state whether the claim holds for all pairs of perpendicular forces or only for specific cases. [2]

Solutions

35QuestionHooke's Law and turning effectAssessment Practice

10 marks~15 minCriterion C

A spring-loaded door closer resists opening by compressing a spring. The graph below shows the spring force as a function of door opening distance.

The force is applied at 0.8 m from the hinge. Assume the hinge is frictionless and the spring force acts perpendicular to the door throughout.

a

State Hooke's Law and use the graph to determine the spring constant

k

, including units. [3]

b

Calculate the torque exerted on the door when the spring is compressed by 0.5 m. Show your working. [3]

c

A student claims: "Because the spring force increases linearly with compression, the torque must also increase linearly as the door opens." Evaluate this claim, considering how the angle between the spring force and the door changes as the door opens wider. [4]

Solutions

36QuestionInterpreting Speed-Time GraphsAssessment Practice

8 marks~12 minCriterion D

A car approaches a traffic intersection equipped with an automated braking system. The speed-time graph below shows the car's motion over 10 seconds. The automated system activates at

t = 6\ \text{s}

, when the car is exactly 50 m from the intersection.

a

Interpret the motion of the car during each time interval:

0

to

2\ \text{s}

,

2

to

6\ \text{s}

, and

6

to

10\ \text{s}

. [3]

b

Calculate the distance the car travels between

t = 6\ \text{s}

and

t = 10\ \text{s}

, and deduce whether the car stops before reaching the intersection. [2]

c

Evaluate the effectiveness of the automated braking system, using evidence from the graph and considering reaction time, deceleration, and sensor reliability. [3]

Solutions

37QuestionInterpreting Speed-Time GraphsAssessment Practice

6 marks~9 minCriterion B

Five identical cars brake to a stop on the same dry road surface. Each car starts at a different initial speed

v

and decelerates uniformly until it stops. The stopping time

t

for each car is recorded below.

Car A	$v = 10$ m/s	$t = 2.5$ s
Car B	$v = 15$ m/s	$t = 3.75$ s
Car C	$v = 20$ m/s	$t = 5.0$ s
Car D	$v = 25$ m/s	$t = 6.25$ s
Car E	$v = 30$ m/s	$t = 7.5$ s

a

Calculate the stopping distance

d

for each car using the area under its speed-time graph. [2]

b

Interpret the relationship between initial speed

v

and stopping distance

d

. State the mathematical form of this relationship. [2]

c

Given that

d = \frac{1}{2}vt

and that deceleration is constant, justify mathematically why

d

is related to

v

in the way you identified in (b). [2]

Solutions

38QuestionCalculating Speed from a GraphAssessment Practice

8 marks~12 minCriterion B

A cyclist rides along a straight road. The distance–time graph shows four successive 2-second intervals, each at constant speed. The distances covered in the first three intervals are 5 m, 15 m, and 30 m respectively. The fourth segment is not drawn.

Graph: Time (s) on the horizontal axis (0 to 8 s); distance (m) on the vertical axis (0 to 110 m). Four straight-line segments, each 2 s wide. Segment 1: (0, 0) to (2, 5). Segment 2: (2, 5) to (4, 20). Segment 3: (4, 20) to (6, 50). Segment 4: not drawn.

a

Calculate the speed of the cyclist in each of the first three intervals. [3]

b

The gradient of each segment represents the cyclist's speed. Interpret how the gradients change across the three intervals and identify the numerical pattern in the speeds. [2]

c

A sports scientist claims the pattern in the speeds will continue into the fourth interval. Evaluate this claim by predicting the distance covered between

t = 6\ \text{s}

and

t = 8\ \text{s}

, and state the total distance at

t = 8\ \text{s}

. [3]

Solutions

39QuestionCalculating Acceleration and Area Under GraphsAssessment Practice

8 marks~12 minCriterion C

A cyclist starts from rest and accelerates uniformly from rest along a straight road. The velocity–time graph below shows the cyclist's motion over 10 seconds. Air resistance is negligible.

a

Deduce the cyclist's acceleration during the first 6 seconds. [2]

b

The cyclist's coach claims that the acceleration is constant throughout the entire 10 seconds. Justify this claim using values calculated from the graph. [2]

c

A second cyclist travels the same 10-second journey at a constant velocity equal to the average velocity of the first cyclist. Analyse which cyclist covers more distance, and explain what this reveals about the motion of the first cyclist. [4]

Solutions

40QuestionInterpreting Distance-Time GraphsAssessment Practice

5 marks~8 minCriterion A

A cyclist's motion over 40 seconds is shown in the distance–time graph below.

Segment A:

t = 0

s to

t = 10

s, distance increases from 0 m to 50 m.
Segment B:

t = 10

s to

t = 20

s, distance remains constant at 50 m.
Segment C:

t = 20

s to

t = 40

s, distance increases from 50 m to 150 m.

a

Deduce the speed of the cyclist during Segment A. [1]

b

Interpret what the gradient of Segment B tells you about the cyclist's motion, and calculate the speed during Segment C. [2]

c

Analyse how the gradients of Segments A and C compare, and evaluate what this reveals about the cyclist's motion across the full 40 seconds. [2]

Solutions

41QuestionDescribing Motion Qualitatively and QuantitativelyAssessment Practice

8 marks~12 minCriterion D

A self-driving car travels at

20 \text{ m/s}

when a pedestrian steps into the road

60 \text{ m}

ahead. The sensor system has a reaction time of

0.2 \text{ s}

before braking begins. Two braking profiles are available: a smooth profile with constant deceleration

3.0 \text{ m/s}^2

, and an emergency profile with constant deceleration

8.0 \text{ m/s}^2

.

a

Calculate the total stopping distance for the smooth braking profile. Use

v^2 = u^2 + 2as

to find the braking distance. [3]

b

Deduce, using a calculation for the emergency profile, which braking profile prevents a collision. [3]

c

Evaluate whether programming the smooth profile as the default is ethically justifiable, considering how risk is distributed between passengers and pedestrians and how real-world conditions affect the reliability of the stopping-distance model. [2]

Solutions

42QuestionCentripetal and Centrifugal ForcesAssessment Practice

12 marks~18 minCriterion D

A space elevator is a proposed structure that would transport cargo from Earth's surface to geostationary orbit. A cable, anchored at the equator and held taut by Earth's rotation, would allow electric climbing vehicles to ascend to orbit. The cable must withstand enormous tension and would be made from ultra-high-strength materials such as carbon nanotubes. The structure would reach approximately 36 000 km, passing through the troposphere, stratosphere, and mesosphere before reaching geostationary orbit.

a

Explain the environmental costs associated with extracting and processing the large quantities of carbon nanotube material required for the cable. [3]

b

Analyse how the choice of energy source for the climbing vehicles affects the overall environmental impact of operating the space elevator. [4]

c

Evaluate the environmental consequences of a catastrophic cable failure, considering the physical behaviour of the falling cable, the regions of the atmosphere it would pass through, and the long-term ecological effects. [5]

Solutions

43QuestionCircular Motions ExamplesAssessment Practice

4 marks~6 minCriterion B

A planet orbits a star in a circular path. The graph below shows orbital speed plotted against orbital radius for several planets in the same star system.

a

Deduce the relationship between orbital speed

v

and orbital radius

r

shown in the graph. [1]

b

A planet orbits at radius

r = 1.5 \times 10^{11}

m with orbital speed

v = 3.0 \times 10^{4}

m s

^{-1}

. Calculate its orbital period. [2]

c

Justify why a planet at half this orbital radius would have a shorter orbital period, referring to gravitational force, centripetal force, and orbital speed. [1]

Solutions

44QuestionCircular Motions ExamplesAssessment Practice

4 marks~6 minCriterion D

A hospital centrifuge spins blood samples at 3000 rpm. The radius from the centre to each sample is 0.15 m. Centripetal acceleration is given by

a_c = \dfrac{v^2}{r}

, where

v

is the linear speed and

r

is the radius. The acceleration due to gravity is

g = 9.8

m/s

^2

.

a

Calculate the linear speed

v

of a blood sample in the centrifuge. [1]

b

Deduce the centripetal acceleration of the sample and determine how many times greater it is than

g

. [2]

c

Evaluate whether a centrifuge is a suitable tool for emergency blood diagnostics, considering both the physics of separation and one limitation of this model. [1]

Solutions

45QuestionCircular Motions ExamplesAssessment Practice

4 marks~6 minCriterion C

A car travels at a constant speed around a circular roundabout of radius

36 \, \text{m}

. The car's speed is

12 \, \text{m/s}

.

a

State the direction of the centripetal acceleration acting on the car. [1]

b

Calculate the centripetal acceleration of the car using

a_c = \dfrac{v^2}{r}

. [1]

c

The car maintains a constant speed throughout its journey around the roundabout. Evaluate whether the car is in equilibrium, justifying your answer with reference to Newton's first law of motion. [2]

Solutions

46QuestionCentripetal and Centrifugal ForcesAssessment Practice

4 marks~6 minCriterion C

A racing car travels around a banked curve of radius

r

, where the road surface is inclined at angle

\theta

to the horizontal. The maximum safe cornering speed is given by

v = \sqrt{rg\tan\theta}

, where

g

is the gravitational field strength.

a

Explain why banking a road allows a car to corner at a higher speed than on a flat road. [1]

b

Identify the vertical and horizontal components of the normal reaction force

N

acting on the car, and explain which component provides the centripetal force. [2]

c

Evaluate how doubling the banking angle

\theta

affects the maximum safe speed

v

, using the equation

v = \sqrt{rg\tan\theta}

to justify your answer. [1]

Solutions

47QuestionCircular Motions ExamplesAssessment Practice

5 marks~8 minCriterion A

A student investigates centripetal force by swinging a 0.50 kg mass in a horizontal circle of fixed radius. She measures the centripetal force

F_c

for different speeds

v

and plots

F_c

against

v^2

. The graph is a straight line through the origin with gradient

0.62\ \text{N\,s}^2\text{m}^{-2}

.

a

State the equation for centripetal force and deduce an expression for the gradient of this graph in terms of

m

and

r

. [2]

b

Calculate the radius

r

of the circle. [1]

c

The student repeats the experiment with the same mass but doubles the radius. Analyse how this change affects the gradient of the

F_c

against

v^2

graph, and explain what this implies about the centripetal force required to maintain the same speed. [2]

Solutions

48QuestionCircular Motions ExamplesAssessment Practice

2 marks~3 minCriterion D

A roller coaster completes a vertical loop of radius

r = 15\ \text{m}

. A passenger of mass

m = 70\ \text{kg}

travels at

v = 12\ \text{m/s}

at the top of the loop.

F_c = \frac{mv^2}{r}

a

Calculate the centripetal force acting on the passenger at the top of the loop. [1]

b

The calculation assumes the passenger's speed is constant throughout the loop. Explain how a change in speed due to gravity would affect the force experienced by the passenger and their comfort. [1]

Solutions

Forces and Motion — Free MYP4 Physics Practice Questions