IB Physics SL A 2 Forces and Momentum Questions

Practise IB Physics SL A.2 by modelling forces, momentum and impulse with diagrams, equations and collision data.

Exam points

draw free-body diagrams, resolve forces and apply Newton’s laws to equilibrium or acceleration
calculate friction, tension, elastic, drag, buoyant or field forces from a stated model
conserve signed momentum and use impulse, collisions, explosions or centripetal relations with correct units

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

Learn this topic

Study A.2 Forces and momentum conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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: 11]

(a)

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.

[ 6 ]

(i)

State the direction of the resultant force on the ball.

[ 1 ]

(ii)

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

Figure for Question (ii) — IB Physics SL

[ 2 ]

(iii)

Show that the magnitude of the net force F on the ball is given by the following equation.

F=\frac{m g}{\tan \theta}

[ 3 ]

ALTERNATIVE 1
$\begin{aligned} & F=N \cos \theta \downarrow & m g=N \sin \theta \downarrow \end{aligned}$

dividing/substituting to get result

ALTERNATIVE 2 right angle triangle drawn with F, N and W / m g labelled

angle correctly labelled and arrows on forces in correct directions

correct use of trigonometry leading to the required relationship

eg:

Figure for Answer to Question (iii) — IB Physics SL

$\tan \theta=\frac{O}{A}=\frac{m g}{F}$ $F=\frac{m g}{\tan \theta}$

(b)

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

[ 2 ]

(c)

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.

[ 3 ]

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

«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

All question bank results loaded

Covered syllabus points

Learn this topic

Question 1

Question 2

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question 3

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)

Question (c)