IB Physics SL A.2 Forces and momentum Questions

SLSL HLHL

Practise IB Physics SL A.2 by analysing force diagrams and field interactions, calculating impulse in collisions, and explaining circular-motion forces.

217 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

Link the stated motion to a resultant force: equilibrium allows non-zero individual forces, while turning needs an inward force at constant speed.
Identify third-law forces on different bodies with equal magnitudes and opposite directions; do not pair two balancing forces on one body.
In a free-body diagram show actual interactions with appropriate labels, attachment and relative lengths; a resultant is not another force.
Resolve force components using the angle’s actual reference, then test whether the available directions can give the required resultant.
Choose one body or the connected system before applying Fnet = ma; include all moving mass and separate applied, contact and resistive forces.
For lifts and sudden releases, set force signs from acceleration and update only the masses or forces that actually change.
Use the graph quantity requested by Newton’s second law: local velocity gradient, initial tangent, acceleration peak or time average.
Select static or dynamic friction from the contact state; use the correct normal load at each interface and distinguish capacity from actual force.
Connect friction to stopping by force balance or work–energy, and keep the specified surface or bounce assumptions explicit.
For a loaded spring, distinguish extension from total length; for weight use the supplied local g rather than assuming Earth’s value.
Identify the relevant field force and its directional condition before calculating or explaining a motion.
For fluid motion, oppose velocity with drag and include buoyancy and weight in terminal balance; a rising drop has drag and weight downwards.
In buoyancy calculations distinguish fluid density and displaced volume from object density and total volume, and read freeboard separately.
State momentum conservation with its zero-external-resultant condition, name the system and sum signed momenta rather than speed magnitudes.
In one-dimensional impact or recoil, use the immediate pre-impact velocities and the correct separate or captured final masses.
Use signed momentum change or force–time area for impulse, then distinguish mean force, peak force and the exact contact interval.
In vertical contact problems distinguish the requested support or thrust from the resultant before applying momentum change over time.
Explain cushioning through the same stopping momentum change over a longer time, reducing average force without removing the impulse.
Keep energy and momentum distinct: calculate kinetic-energy loss or retained fraction after a collision, and allow internal energy to create KE.
For energy explanations, name contact work and the receiving deformation or internal-energy store; separate impact from conservative travel.
Use momentum to constrain nuclear recoil energy ratios and reaction thresholds, and convert an energy ratio to a fraction when required.
For propulsion or material streams, use mass flow rate × velocity change, with the stated system and time interval.
For circular motion, construct the inward radial resultant from real forces, with separate vertical balance in a horizontal circle.
At top or bottom vertical-circle points, include weight in the radial sum and state a contact condition rather than only a force value.
Before comparing circular quantities, identify whether angular speed, linear speed or available inward force is fixed.
Convert between angular speed, tangential speed and period with the actual distance from the axis and consistent rotation/time units.
For circular-motion reasoning, justify force work, experimental error and banking conclusions within their stated model.

Covered syllabus points

A.2.1—Newton’s three laws of motion A.2.2—Forces as interactions between bodies A.2.3—Free-body diagrams A.2.4—Resultant force from diagrams A.2.5—Contact forces A.2.6—Normal force A.2.7—Frictional force A.2.8—Tension A.2.9—Hooke’s law restoring force A.2.10—Viscous drag A.2.11—Buoyancy A.2.12—Field forces A.2.13—Weight A.2.14—Electric force Fe A.2.15—Magnetic force Fm A.2.16—Linear momentum conservation A.2.17—Impulse A.2.18—Impulse-momentum change A.2.19—Newton’s second law forms A.2.20—Elastic and inelastic collisions A.2.21—Explosions A.2.22—Collision energy A.2.23—Centripetal acceleration A.2.24—Centripetal force A.2.25—Direction change in circular motion A.2.26—Angular and linear speed

Exam points

Link rest or constant straight-line velocity to zero resultant force, while allowing non-zero individual forces.
In a first-law explanation, state the law and explicitly connect the given steady motion to balanced forces.
Explain slowing from the direction of the resultant force; naming F = ma alone does not explain the motion.
Identify third-law forces on different bodies with equal magnitudes and opposite directions; weight and normal on one body are not a pair.
Apply Newton’s third law throughout a collision; do not make it conditional on conservation of kinetic energy.
For a ball–racket or blade–air explanation, name both forces and their opposite directions rather than an undefined reaction.
Draw interaction-pair arrows with equal lengths, correct labels and opposite directions through the two bodies.
Use the first law to explain a turning passenger’s tendency to continue tangentially and the inward restraint force.
At pendulum release, use the tangential weight component in F = ma to obtain initial acceleration g sinθ.

[Maximum number: 2]

A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest by a cable pulled by a motor that exerts a horizontal force on the glider throughout the launch.

Explain, using appropriate laws of motion, how the forces acting on the glider maintain it in level flight.

Exam points

Name the force on each of two interacting bodies; equal and opposite contact forces remain a pair during acceleration.
For two blocks pushed together, distinguish the external force driving both blocks from the smaller force accelerating just the front block.
Separate a third-law pair from forces balancing on one system; an upward-accelerating lift has a non-zero resultant force.

[Maximum number: 1]

An elevator (lift) and its load accelerate vertically upwards.

Which statement is correct in this situation?

The net force on the load is zero.

The tension in the cable is equal but opposite to the combined weight of the elevator and its load.

The normal reaction force on the load is equal but opposite to the force on the elevator from the load.

The elevator and its load are in translational equilibrium.

Exam points

Draw the forces on the chosen body with arrows touching it; label weight, tension, normal and friction by force names or accepted symbols.
On a slope, keep weight vertical, normal perpendicular to the surface and friction along the surface in its required direction.
Use arrow lengths and components to show the stated balance or acceleration; do not assume every opposing pair has equal magnitude.
For a cylinder-wall rider, show weight down, friction up and a normal force towards the centre; add no separate centripetal force.
For a ball on a string, draw tension towards the support and weight down; match the vertical tension component to the required motion.
For a rough-ground, smooth-wall ladder, include weight, both normal forces and ground friction; omit wall friction.
Complete the given glider diagram with backward drag and downward weight, without inventing an engine thrust.
For a stationary floating cork, identify upward buoyancy and downward weight as the forces on the cork.
For a car at maximum speed on a banked bend, select normal perpendicular to the road and friction down the bank.

[Maximum number: 1]

A cylindrical cork of height H and cross-sectional area A is floating stationary in water. Its depth below the water surface is D.

Draw and label the forces acting on the cork.

Weight and Buoyancy drawn in proper directions (by eye) and correctly identified

Allow any sensible identification of the forces (e.g. mg for $F_{g}$ )

Do not allow "gravity" for weight.

Exam points

Resolve along a chosen axis using the labelled angle; vector equilibrium does not mean adding all force magnitudes.
Use the tension components to compare horizontal electric force with weight; at 45° to vertical the two magnitudes are equal.
Check whether the available force directions can produce the required motion: a horizontal normal alone cannot balance weight.
For a stationary ladder, explain that wall normal equals ground friction because the horizontal resultant is zero.
When motion changes to constant speed on a straight incline, reset the force balance: a freely hanging string points vertically down.
For two forces of sizes A and B, test whether the required resultant lies between |A − B| and A + B.

[Maximum number: 2]

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Exam points

Resolve perpendicular to the slope: with no other perpendicular force or acceleration, use N = mg cosθ rather than mg sinθ.
As a supporting incline steepens, distinguish the decreasing normal force from the unchanged weight.

[Maximum number: 2]

This question is about the forces on a skier.

A skier is pulled up a hill by a rope at a steady velocity. The hill makes an angle of $12^{\circ}$ with the horizontal. The mass of the skier and skis is 73 kg . The diagram below shows three of the forces acting on the skier.

Calculate the magnitude of the normal reaction acting on the skier.

$\quad(N=) m g \cos \theta /$ correct substitution;

\left(=73 \times 9.81 \times \cos 12^{\circ}=\right) 700 \mathrm{~N} ;

Exam points

Separate applied force from resultant force before finding sliding friction and μ = Ff/N.
Use frictional work or constant deceleration to connect sliding coefficient, initial speed and stopping distance.
For horizontal sliding with the same μ, friction grows with mass but deceleration μg is mass-independent.
Resolve along the contact surface before finding friction; include any cable tension rather than using the weight component alone.
For a downward-accelerating climber, use mg − Ff = ma to find the upward rope friction.
At impending sliding use maximum static friction: μsN; on a freely supported incline μs = tanθ0 and N = mg cosθ0.
Explain that friction coefficients are dimensionless because they are ratios of friction force to normal force.
Explain acceleration after motion begins by the drop from limiting static friction to smaller dynamic friction under the same push.
Use static friction to provide horizontal circular motion; on a Rotor wall require μN ≥ mg with N = mRω².
For the hoop’s supplied a = g sinθ/2, combine linear balance with Ff ≤ μmg cosθ; slipping starts at tanθ = 2μ.
Track each contact separately in stacked-block problems: friction can accelerate the upper block and oppose the lower block’s motion.
In the specified bounce model, greater sliding friction reduces horizontal rebound speed and gives a steeper rebound angle.

[Maximum number: 3]

A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of $64 \mathrm{~m} \mathrm{~s}^{-1}$ . The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms .

The student models the bounce of the tennis ball to predict the angle $\theta$ at which the ball leaves a surface of clay and a surface of grass.

The model assumes
- during contact with the surface the ball slides.
- the sliding time is the same for both surfaces.
- the sliding frictional force is greater for clay than grass.
- the normal reaction force is the same for both surfaces.
Predict for the student's model, without calculation, whether $\theta$ is greater for a clay surface or for a grass surface.

Exam points

For steady uphill pulling, balance tension against both friction and the downslope weight component: T = Ff + mg sinθ.
In a vertical chain of hanging blocks, the upper rope supports all weights below it; an intermediate rope supports only its lower subsystem.
For accelerating connected blocks, isolate the block without the applied pull and use tension minus its friction equal to ma.

[Maximum number: 2]

The total frictional force acting is 65 N . Determine the tension in the rope.

tension = frictional force + component of weight parallel to slope /
tension $=65+m g \sin \theta$ ;
214 / 210 N;

Exam points

For a vertically loaded spring at rest, use extension l − l0 and balance spring tension with mg to find k.

[Maximum number: 1]

A spring of negligible mass and length $l_{0}$ hangs from a fixed point. When a mass m is attached to the free end of the spring, the length of the spring increases to l. The tension in the spring is equal to $k \Delta x$ , where k is a constant and $\Delta x$ is the extension of the spring. What is k ?

$\frac{m g}{l_{0}}$

$\frac{m g}{l}$

$\frac{m g}{l-l_{0}}$

$\frac{m g}{l_{0}-l}$

Exam points

Explain why growing opposing drag reduces the resultant force as speed rises, so velocity approaches a terminal value.
For a rising oil droplet at terminal speed, balance upward buoyancy against downward weight plus drag.
Verify terminal speed from a straight section of the position–time graph with constant non-zero gradient.
For equal-density spheres in the same fluid, compare r³ weight–buoyancy with Stokes drag proportional to rv: vt ∝ r².

[Maximum number: 4]

A spherical oil droplet is released from rest at the bottom of a column of water.

The graph shows the variation with time t of the vertical velocity of the oil droplet.

(a)

Describe why the acceleration of the oil droplet changes.

[ 2 ]

(b)

Explain why the velocity of the oil droplet is constant for $t>3 \mathrm{~s}$ .

[ 2 ]

Exam points

Find buoyancy from the reduction in apparent weight: subtract the air and immersed mass readings, convert to kilograms, then multiply by g.
For a floating cylinder, equate total weight ρbodyAHg with buoyancy ρfluidADg to find the submerged fraction D/H.
Use the floating density ratio to turn iceberg freeboard into total height before calculating its mass.
For fully immersed spheres in the same liquid, buoyancy scales with displaced volume R³, not with the sphere’s material density.

[Maximum number: 4]

A cylindrical cork of height H and cross-sectional area A is floating stationary in water. Its depth below the water surface is D.

(a)

Show that

\frac{D}{H}=\frac{\rho_{\mathrm{c}}}{\rho_{\mathrm{w}}}

where $\rho_{\mathrm{c}}$ is the density of the cork and $\rho_{\mathrm{w}}$ is the density of water.

[ 2 ]

Weight $=\rho_{c} \cdot A \cdot H \cdot g$

OR

Buoyancy $=\rho_{w} \cdot A \cdot D \cdot g$ $\rho_{c} \cdot A \cdot H \cdot g=\rho_{w} \cdot A \cdot D \cdot g$

<<algebraic manipulation to show the relationship>>

(b)

An icebreaking ship is designed to withstand a collision with an iceberg, a large partially submerged body of ice freely floating in water. The designers model the shape of the iceberg as a cylinder with an approximate cross-sectional area of $4200 \mathrm{~m}^{2}$ and height above sea level of 32 m .

The following data are available:

\begin{aligned} \rho_{\text {ice }} & =920 \mathrm{~kg} \mathrm{~m}^{-3} \\ \rho_{\text {seawater }} & =1030 \mathrm{~kg} \mathrm{~m}^{-3} \end{aligned}

[ 2 ]

(i)

Show that the mass of the iceberg is about $1.2 \times 10^{9} \mathrm{~kg}$ .

The designers assume that the mass of the ship is about $\frac{1}{40}$ the mass of the iceberg and is moving at $12 \mathrm{~m} \mathrm{~s}^{-1}$ when it collides with the iceberg. They stick together after the collision.

[ 2 ]

$\begin{aligned} \text { «(H -32) /H = 920 / } 1030 \text { so } \text { » } \mathrm{H}=300 \text { 《m》 } \text { OR } \mathrm{D}=268 \text { "m" } \mathrm{m}=920 \times 300 \times 4200 \text { OR } 1.16 \times 10^{9} \text { "kg" } \end{aligned}$

Must see either full substitution or answer to 3 or more significant
figures.

Exam points

For a charged massive particle moving parallel to a field, distinguish electric and gravitational forces from zero magnetic force.
Name gravity as the actual interaction providing a planet’s centripetal force around its star.

[Maximum number: 1]

A planet is in a circular orbit around a star. The speed of the planet is constant.

State the nature of this centripetal force.

Exam points

Calculate weight from mg using the stated local gravitational field strength, rather than automatically substituting Earth’s g.
For an incline at θ to the horizontal, calculate full weight mg before taking its downslope component mg sinθ.
Construct weight vertically down with a length matching the balancing vertical component of the supplied normal force.

[Maximum number: 2]

A small ball of mass m is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.

The normal reaction force N makes an angle $\theta$ to the horizontal.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

Exam points

Use tension components in equilibrium to find Fe = mg tanθ for an angle to the vertical; distinguish this force from the zero resultant.

[Maximum number: 3]

A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.

The thread makes an angle of $30^{\circ}$ with the vertical wall. The ball has a mass of 0.025 kg .

Determine the horizontal force that acts on the ball.

Horizontal force on ball $F=T\sin30^\circ$ .
$T=mg/\cos30^\circ$ .
$F=mg\tan30^\circ=0.025\times9.8\times\tan30^\circ=0.14\ \mathrm{N}$ .

Allow $g=10\ \mathrm{N\ kg^{-1}}$ . Award [3] for a bald correct answer. Award [1 max] for an answer of zero, interpreting the horizontal force as the horizontal component of the net force.

Exam points

Define momentum as mass × velocity; equal speeds do not give equal momenta when masses or directions differ.
State that total system momentum remains constant when the resultant external force is zero; naming conservation alone is insufficient.
Choose the system explicitly: a ball may exchange momentum with a floor while a larger system including its surroundings conserves the total.
For a sticking collision, add signed initial momenta and divide by the full combined mass immediately after impact.
When outgoing bodies separate, conserve the signed momentum sum to find an unknown velocity; keep rebound direction distinct from speed.
Zero total momentum does not require each body to stop; opposite individual momenta can remain after a collision or recoil.
For an isolated throw or recoil, relate equal opposite momentum changes and use the stated ground-frame launch speed.
Keep momentum conservation separate from kinetic-energy conservation: inelastic capture loses KE, while an internal throw can increase it.
For a nucleus decaying from rest, use equal opposite recoil momenta and KE = p²/(2m) to compare the product energies.
Explain why an incoming reaction particle must provide kinetic energy as well as the rest-mass increase when products must carry its momentum.
In the given ion-engine estimate, reserve half the fuel for braking before using the remaining fuel’s momentum to estimate top speed.

[Maximum number: 2]

Assuming that the lithium-7 nucleus in (b) is at rest, suggest why, in terms of conservation of momentum, the neutron initiating the reaction must have an energy greater than 2.5 MeV .

Exam points

Identify impulse as change in momentum, with units N s or kg m/s; distinguish it from force and energy.
Use signed velocities in Δp = m(v − u): a reversal adds speed magnitudes, while a same-direction slowdown subtracts them.
Use the actual contact duration in Favg = Δp/Δt and convert milliseconds or microseconds before substituting.
Find impulse from force–time area; use triangular area to connect peak force, duration, momentum change and final speed.
Distinguish net stopping force from the support or thrust force; include weight in the vertical force balance when required.
Explain cushioning through the same momentum change over a longer stopping time, producing a smaller average force.
Connect impulse from rest to kinetic energy with K = J²/(2m), rather than treating impulse as an energy.
If rebound energy is given, obtain speed using the square-root energy relation before calculating the signed momentum change.
Sketch momentum with gradient following the force: reverse its sign during the rebound and keep the gradient’s sign consistent.
For a symmetric oblique wall rebound, identify the impulse qualitatively as perpendicular to the wall, away from it.
Carry the actual pre-impact speed into the contact stage; a drag-affected fall need not have the free-fall speed from the same height.
Use the height gained after takeoff to find v = √(2gh), then calculate the athlete’s net contact impulse Mv from rest.

[Maximum number: 2]

Calculate the

average force exerted by the racquet on the ball.

$\begin{aligned} F=\frac{\Delta m v}{\Delta t} / m \frac{\Delta v}{\Delta t} / \frac{0.058 \times 64.0}{25 \times 10^{-3}} F=148 \text { «N» } \approx 150 \text { «N» } \end{aligned}$

Exam points

Calculate rebound impulse using signed velocities; opposite directions give |Δp| = m(u + v).
Estimate landing impulse from a drop height by finding the impact speed and momentum lost on stopping.
Use force–time area as impulse, then divide by mass to find the speed from rest.
Find average rebound force from Δp/Δt; add weight when the question asks for the ground reaction.

[Maximum number: 5]

A toy rocket is made from a plastic bottle that contains some water.

Air is pumped into the vertical bottle until the pressure inside forces water and air out of the bottle. The bottle then travels vertically upwards.

The air-water mixture is called the propellant.
The variation with time of the vertical velocity of the bottle is shown.

The bottle reaches its highest point at time $T_{1}$ on the graph and returns to the ground at time $T_{2}$ . The bottle then bounces. The motion of the bottle after the bounce is shown as a dashed line.

(a)

The bottle bounces when it returns to the ground.

[ 3 ]

(i)

The mass of the bottle is 27 g and it is in contact with the ground for 85 ms .

Determine the average force exerted by the ground on the bottle. Give your answer to an appropriate number of significant figures.

[ 3 ]

Attempt to use force = momentum change ÷ time $\ll=\frac{(4.5+10) \times 0.027}{85 \times 10^{-3}}=4.6 \gg$

Force = «4.6 + 0.3» 4.9 «N»

Any answer to 2 sf

Marking guidance:

Accept ± 0.5 velocity values from graph

(b)

The maximum height reached by the bottle is greater with an air-water mixture than with only high-pressure air in the bottle.

Assume that the speed at which the propellant leaves the bottle is the same in both cases.

Explain why the bottle reaches a greater maximum height with an air-water mixture.

[ 2 ]

Exam points

State Newton’s second law using resultant force and vector momentum rate; distinguish a force from its impulse or a change in speed alone.
Subtract resistance or other opposing forces before applying Fnet = ma; an applied pull need not equal the resultant.
For connected bodies, use total external drive over total moving mass for acceleration, then isolate one body to find tension.
For lifts and descending loads, distinguish support or cable force from weight: use N = m(g ± a) with the sign set by acceleration.
Immediately after cutting a thread or releasing a load, keep unchanged forces fixed but update the body’s mass and force balance.
Resolve forces with the stated angle reference; combine vertical balance with horizontal acceleration for a suspended accelerating ball.
Read acceleration from the relevant velocity–time gradient; use an initial tangent when the force is specified at the start.
Use a supplied acceleration graph directly: multiply its peak or its time-averaged acceleration by mass, according to the question.
For a steady stream, calculate force from mass flow rate × velocity change, then relate it to acceleration or supported weight.
For gravel accumulating on a belt, add the accumulated weight to the force from stopping the incoming momentum flow.
Distinguish post-ejection ion repulsion from forces on the spacecraft; the given mutual spreading does not change its acceleration.
For a triangular driving-force pulse, relate its area to momentum change and distinguish the peak from the interval-average force.
Use the vector range of a resultant before dividing by mass; equal opposite rocket forces can leave centre-of-mass acceleration zero.
Sum the actual forces before finding acceleration in spring or charged-particle systems; do not import a separate SHM or relativity formula.
For a stopping stage, identify momentum rate as net force and derive it from the stage’s speed, distance and combined mass.
With no horizontal force, use Newton’s second law to explain constant horizontal momentum even while gravity changes vertical motion.

[Maximum number: 1]

This question is in two parts. Part 1 is about simple harmonic motion and forced oscillations. Part 2 is about electric and magnetic force fields.

Part 1 Simple harmonic motion and forced oscillations
The graph shows the variation with time of the displacement of an object undergoing simple harmonic motion.
displacement / mm

time / ms

Part 2 Electric and magnetic force fields

The diagram shows two isolated electrons, X and Y , initially at rest in a vacuum. The initial separation of the electrons is 5.0 mm . The electrons subsequently move apart in the directions shown.

Calculate the initial acceleration of one electron due to the force in (c)(i).

$1.0 \times 10^{7} \mathrm{~ms}^{-2}\left(9.9 \times 10^{6} \mathrm{~ms}^{-2}\right.$ if $9 \times 10^{-24} \mathrm{~N}$ used );

Exam points

Classify elasticity using total kinetic energy; an isolated inelastic collision still conserves total momentum.
To show a collision is elastic, compare the sum of both bodies’ kinetic energies before and after; momentum conservation alone is insufficient.
In a one-dimensional elastic collision of equal masses with one initially at rest, select transfer of the incident speed to the target.
For an elastic wall rebound, distinguish unchanged momentum magnitude from a non-zero vector change and impulse.
For a fall–sticking-impact–rise sequence, conserve energy on each smooth travel stage and momentum across the impact.
Use a lower rebound height as evidence of inelastic impact when air resistance is negligible.
Do not infer elasticity just because bodies separate; use kinetic-energy evidence or the specified elastic molecular-scattering model.

[Maximum number: 3]

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m .

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m , the maximum height reached by the two balls.

$\text { speed before collision } v=\ll \sqrt{2 g R}=>12.5<\mathrm{ms}^{-1} \gg$

«from conservation of momentum» common speed after collision is $\frac{1}{2}$ initial
$\begin{aligned} & \text { speed }<v_{c}=\frac{12.5}{2}=6.25 \mathrm{~ms}^{-1} \gg & h=<\frac{v_{c}^{2}}{2 g}=\frac{6.25^{2}}{2 \times 9.81}>2.0<\mathrm{m} \gg \end{aligned}$

Allow 12.5 from incorrect use of kinematics equations

Award [3] for a bald correct answer Award [0] for m g(8)=2 m g h leading to h=4 m if done in one step.

Allow ECF from MP1

Allow ECF from MP2

Exam points

Add both bodies’ kinetic energies as positive scalars; opposite momentum directions do not make their total kinetic energy zero.
For sticking collisions, first find the shared speed from momentum, then calculate total final kinetic energy with the combined mass.
Read rebound speeds just before and after impact, then calculate mechanical-energy loss from ½m(u² − v²).
Explain impact energy loss through contact work and deformation, and name the receiving energy store required by the question.
For an isolated internal explosion, distinguish unchanged total momentum from increased total kinetic energy.
When the final angular speed of two point masses is supplied, use speed ωR and sum their ordinary kinetic energies before finding the loss.

[Maximum number: 3]

A horizontal rigid bar of length 2 R is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass M is attached to one end of the bar and a container is attached to the other end of the bar.

A point particle of mass $\frac{M}{3}$ moving with speed v at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis.

The mass of the rod and the container can be neglected.

Determine in terms of M and v the energy lost during the collision.

$\begin{aligned} \text { initial } K E=\frac{M v^{2}}{6} \text { final } K E=\frac{M v^{2}}{24} \end{aligned}$

Exam points

Give centripetal acceleration v²/r towards the centre, and explain why changing velocity direction produces acceleration at constant speed.
Convert revolutions per minute to angular speed or period before using a = ω²r or v²/r.
On one rigid disc at fixed angular speed, both linear speed and centripetal acceleration are proportional to radius.
If a rider moves to a new radius, find that rider’s new linear speed from the shared period before calculating v²/r.
For unequal wheels rolling at the same constant bicycle speed, compare rim centripetal accelerations using a ∝ 1/r.
For a conical pendulum, divide horizontal tension balance by vertical balance to obtain a = g tanθ for θ to vertical.

[Maximum number: 3]

This question is in two parts. Part 1 is about two children on a merry-go-round. Part 2 is about electric circuits.

Part 1 Two children on a merry-go-round
Aibhe and Euan are sitting on opposite sides of a merry-go-round, which is rotating at constant speed around a fixed centre. The diagram below shows the view from above.

Aibhe is moving at speed $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

(a)

Draw an arrow on the diagram on page 22 to show the direction in which Aibhe is accelerating.

[ 1 ]

(b)

Aibhe moves so that she is sitting at a distance of 0.75 m from the centre of the merry-go-round, as shown below.

Euan pushes the merry-go-round so that he is again moving at $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

[ 2 ]

(i)

Calculate the magnitude of Aibhe's acceleration.
Part 2 Electric circuits

[ 2 ]

$\quad a\left(=\frac{v^{2}}{r}\right)=\frac{0.5^{2}}{0.75}$ ;
$a=0.33\left(\mathrm{~ms}^{-2}\right)$ ;

Marking guidance:

Allow ECF from (d)(i).
Award [2] for a bald correct answer.

Part 2 Electric circuits

(c)

Outline why Aibhe is accelerating even though she is moving at constant speed.

[ 2 ]

(d)

The diagram below shows a side view of Aibhe and Euan on the merry-go-round.

Explain why Aibhe feels as if her upper body is being "thrown outwards", away from the centre of the merry-go-round.

[ 2 ]

Exam points

Identify the actual interaction supplying the inward resultant: friction, a contact force, tension components or gravitational attraction.
Explain uniform circular motion using an inward force perpendicular to the changing velocity; constant speed does not mean zero resultant.
Resolve a conical or bowl contact: vertical components balance weight while the horizontal component provides the inward force.
At the bottom of a vertical circle, subtract weight from support tension to obtain mv²/r; tension itself exceeds weight.
For the specified uniform-speed rod models, compare the individual rod force at the top and bottom rather than treating it as constant.
At a loop’s top, state the contact condition N > 0 or compare actual speed with √(gr); quoting a numerical normal force alone is insufficient.
For friction-limited motion on a horizontal bend, set maximum static friction equal to mv²/r; at fixed conditions vmax ∝ √r.
For the same rope-breaking limit, keep mv²/r or mω²r constant when mass, speed or radius changes.
Combine force scalings carefully: F = 2K/r and F ∝ ω² at fixed mass and radius; √F versus ω is linear.
In orbital-speed calculations, equate v²/r to the local gravitational acceleration and use distance from the planet’s centre.
For a rotating asteroid surface, subtract outward normal force from inward gravity, and draw the normal arrow shorter than the weight.
For qualitative banked-corner comparisons, a larger banking angle and greater tyre–road friction allow a higher speed in the given model.
Convert diameter to radius before using mω²r, and keep the force direction inward.
Explain why an inward force does no work in uniform circular motion: it stays perpendicular to each instantaneous displacement.
In circular-motion experiments, justify a friction-bias conclusion from the force balance or an explicit graph-error model.

[Maximum number: 1]

Aibhe is moving at speed $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

Identify the force that is causing Aibhe to move in a circle.

Exam points

Explain that constant speed can accompany acceleration because the velocity direction changes during circular motion.
Explain an apparent outward sensation by the upper body’s tangential tendency when it lacks the inward force needed to follow the circle.

[Maximum number: 3]

Aibhe is moving at speed $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

(a)

Draw an arrow on the diagram on page 22 to show the direction in which Aibhe is accelerating.

[ 1 ]

(b)

Aibhe moves so that she is sitting at a distance of 0.75 m from the centre of the merry-go-round, as shown below.

Euan pushes the merry-go-round so that he is again moving at $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

[ 2 ]

(i)

Calculate the magnitude of Aibhe's acceleration.
Part 2 Electric circuits

[ 2 ]

$\quad a\left(=\frac{v^{2}}{r}\right)=\frac{0.5^{2}}{0.75}$ ;
$a=0.33\left(\mathrm{~ms}^{-2}\right)$ ;

Marking guidance:

Allow ECF from (d)(i).
Award [2] for a bald correct answer.

Part 2 Electric circuits

(c)

Outline why Aibhe is accelerating even though she is moving at constant speed.

[ 2 ]

(d)

The diagram below shows a side view of Aibhe and Euan on the merry-go-round.

Explain why Aibhe feels as if her upper body is being "thrown outwards", away from the centre of the merry-go-round.

[ 2 ]

Exam points

Use ω = v/r with radius in metres, and give angular speed in rad/s rather than Hz.
Use one circumference per period, v = 2πr/T, converting orbital radii, hours and seconds consistently.
For points sharing angular speed or period, make linear speed proportional to distance from the axis; centripetal acceleration also scales with r.
For rotation about a stationary centre of mass, measure the point’s radius from that centre and convert revolutions per second with ω = 2πf.
Apply v = ωr to rolling only when the source states no sliding; the ball’s translation and surface rotation then give ω = v/r.

[Maximum number: 3]

Aibhe is moving at speed $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

Aibhe moves so that she is sitting at a distance of 0.75 m from the centre of the merry-go-round, as shown below.

Euan pushes the merry-go-round so that he is again moving at $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

Determine Aibhe's speed relative to the ground.

Aibhe's period of revolution is the same as before;
from $v=\frac{2 \pi r}{T}$ , since r is halved, v is halved;
$v=0.5\left(\mathrm{~ms}^{-1}\right) ;$

Marking guidance:

Award [3] for a bald correct answer.

More syllabus points

A.2.5—Contact forcesNo questions yet

No public sample questions are available for this syllabus point yet.

A.2.15—Magnetic force FmNo questions yet

No public sample questions are available for this syllabus point yet.

A.2.21—ExplosionsNo questions yet

No public sample questions are available for this syllabus point yet.

Question 1

Question 1

Question 1

Question 1

Question 1

Question 1

Question 1

Question 1

Question 1

Question (a)

Question (b)

Question 1

Question (a)

Question (b)

Question (i)

Question 1

Question 1

Question 1

Question 1

Question 1

Question 1

Question (a)

Question (i)

Question (b)

Question 1

Question 1

Question 1

Question 1

Question (a)

Question (b)

Question (i)

Question (c)

Question (d)

Question 1

Question 1

Question (a)

Question (b)

Question (i)

Question (c)

Question (d)

Question 1

More syllabus points