IB Physics SL A 2 Forces and Momentum Questions

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

Exam points

Resolve free-body diagrams to identify forces and apply Newton’s laws to equilibrium or acceleration.
Identify action–reaction pairs on different bodies rather than balancing forces on one body.
Apply static and kinetic friction models to find a coefficient or decide whether a body will slip.
Use F = kΔx with a hanging mass and spring extension to determine the spring constant.
Explain terminal motion in a fluid by balancing drag, buoyancy and weight.
Use buoyancy and weight balance to relate a floating object’s submerged fraction to relative density.
Distinguish electric, gravitational and magnetic field effects on charged particles in different frames.
Apply momentum conservation when external resultant force is zero to calculate post-collision speed.
Use impulse, J = Δp, and force–time data to calculate momentum change or mean impact force.
Compare elastic and inelastic collisions using momentum and kinetic-energy conservation or loss.
Use a_c = v²/r and F_c = mv²/r, linking v = ωr to speed, radius and period in circular motion.

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

[Maximum number: 9]

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.

(a)

The glider and pilot have a total mass of 492 kg . During the acceleration the glider is subject to an average resistive force of 160 N . Determine the average tension in the cable as the glider accelerates.

[ 3 ]

$a=\frac{27}{11}=2.45\,\mathrm{m\,s^{-2}}$ $F-160\,\mathrm{N}=492\,\mathrm{kg}\times2.45\,\mathrm{m\,s^{-2}}$ $F=1370\,\mathrm{N}$

This calculation could also be shown in part (a).

Award [0] for a solution that uses $a=9.81\,\mathrm{m\,s^{-2}}$ .

(b)

The cable is wound onto a cylinder of diameter 1.2 m . Calculate the angular velocity of the cylinder at the instant when the glider has a speed of $27 \mathrm{~m} \mathrm{~s}^{-1}$ . Include an appropriate unit for your answer.

[ 2 ]

\omega=\frac{v}{r}=\frac{27\,\mathrm{m\,s^{-1}}}{0.6\,\mathrm{m}}=45\,\mathrm{rad\,s^{-1}}

Do not accept Hz.

Award [1 max] if the unit is missing.

(c)

After takeoff the cable is released and the unpowered glider moves horizontally at constant speed. The wings of the glider provide a lift force. The diagram shows the lift force acting on the glider and the direction of motion of the glider.

Draw the forces acting on the glider to complete the free-body diagram. The dotted lines show the horizontal and vertical directions.

[ 2 ]

(d)

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

[ 2 ]

[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.

[Maximum number: 7]

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)

Draw and label the forces acting on the cork.

[ 1 ]

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.

(b)

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>>

(c)

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}

[ 4 ]

(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.

(ii)

Calculate the speed of the ship after the collision.

Ice in a still lake will usually form in a single layer on the surface.

[ 2 ]

$\begin{aligned} \frac{1}{40} m 12=\left(\frac{1}{40} m+m\right) v v=0.29\left\langle\mathrm{~m} \mathrm{~s}^{-1}\right\rangle \end{aligned}$

[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.

[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.

[Maximum number: 2]

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

[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} ;

[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.

[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;

[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 ?

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

$\frac{m g}{l}$

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

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

[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 ]

[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.

[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.

[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.

[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 .

[Maximum number: 2]

Calculate the

average force exerted by the racquet on the ball.

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

[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 ]

[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 );

[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

[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.

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

[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 ]

[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.

[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.

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question (d)

Question 2

Question 3

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question (a)

Question (b)

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question (a)

Question (i)

Question (b)

Question 18

Question 19

Question 20

Question 21

Question (a)

Question (b)

Question (i)

Question (c)

Question (d)

Question 22

Question 23