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A.2 Forces and momentum

Practice exam-style IB Physics questions for Forces and momentum, aligned with the syllabus and grouped by topic.

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Question 1
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A book rests on a horizontal table. The weight of the book is the gravitational force exerted by Earth on the book.

What is the Newton's third-law partner of the weight of the book?

A.

The gravitational force exerted by Earth on the table

B.

The normal force exerted by the book on the table

C.

The gravitational force exerted by the book on Earth

D.

The normal force exerted by the table on the book

Question 2
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
Calculator Permitted

Two identical smooth spheres collide elastically on a horizontal air table. One sphere is initially at rest and the collision is not head-on.

What is the angle between the two final velocity directions?

A.

180∘180^\circ

B.

90∘90^\circ

C.

45∘45^\circ

D.

0∘0^\circ

Question 3
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A block on a horizontal rough surface remains at rest when pulled by a horizontal force of 12 N12\ \text{N} to the right. The maximum possible static friction on the block is 20 N20\ \text{N}.

What is the frictional force acting on the block?

A.

12 N12\ \text{N} to the left

B.

12 N12\ \text{N} to the right

C.

32 N32\ \text{N} to the left

D.

20 N20\ \text{N} to the left

Question 4
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A spring obeys Hooke's law. A force of 2.0 N2.0\ \text{N} produces an extension of 4.0 cm4.0\ \text{cm}.

What is the spring constant?

A.

0.080 N m−10.080\ \text{N m}^{-1}

B.

50 N m−150\ \text{N m}^{-1}

C.

500 N m−1500\ \text{N m}^{-1}

D.

8.0 N m−18.0\ \text{N m}^{-1}

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Question 5
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A small smooth sphere moves slowly through a uniform fluid so that Stokes' law applies. The sphere is replaced by another sphere of twice the radius moving at three times the speed in the same fluid.

By what factor does the viscous drag force change?

A.

55

B.

23\frac{2}{3}

C.

66

D.

32\frac{3}{2}

Question 6
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A car travels at constant speed around a flat horizontal circular bend. At the instant shown, the centre of the circular path is to the left of the car.

The correct free-body diagram for the car is:

A.
A simple free-body diagram of a car represented by a dot or small rectangle on a plain background. Show a vertical arrow downward labelled $F_g$, a vertical arrow upward labelled $F_N$, a horizontal arrow to the left labelled $F_f$, and an additional horizontal arrow to the left labelled $F_c$. The two horizontal arrows are visually similar and both point toward the centre.
B.
A simple free-body diagram of a car represented by a dot or small rectangle on a plain background. Show a vertical arrow downward labelled $F_g$, a horizontal arrow to the left labelled $F_N$, and a second horizontal arrow to the left labelled $F_f$. The two horizontal arrows are drawn separately but in the same inward direction.
C.
A simple free-body diagram of a car represented by a dot or small rectangle on a plain background. Show a vertical arrow downward labelled $F_g$, a vertical arrow upward labelled $F_N$ of comparable length, and a horizontal arrow to the left labelled $F_f$. The leftward arrow is parallel to the road surface and points toward the centre of the circular path. No separate arrow labelled centripetal force is shown.
D.
A simple free-body diagram of a car represented by a dot or small rectangle on a plain background. Show a vertical arrow downward labelled $F_g$, a vertical arrow upward labelled $F_N$, and a horizontal arrow to the right labelled $F_f$. The horizontal arrow is parallel to the road surface and points away from the stated centre of the circular path.
Question 7
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
Calculator Permitted

In a two-dimensional collision, the total initial momentum has no vertical component. After the collision, object 1 has a vertical momentum component of +0.80 kg m s−1+0.80\ \text{kg m s}^{-1}.

What is the vertical momentum component of object 2 after the collision, assuming the system is isolated?

A.

0 kg m s−10\ \text{kg m s}^{-1}

B.

−1.60 kg m s−1-1.60\ \text{kg m s}^{-1}

C.

+0.80 kg m s−1+0.80\ \text{kg m s}^{-1}

D.

−0.80 kg m s−1-0.80\ \text{kg m s}^{-1}

Question 8
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
Calculator Permitted

In the kinetic model of an ideal gas, collisions between gas molecules and the container walls are modelled as elastic.

What does this imply for a molecule during a collision with a stationary wall?

A.

Its kinetic energy is unchanged but its momentum changes.

B.

Its momentum is unchanged but its kinetic energy decreases.

C.

Both its kinetic energy and momentum decrease.

D.

Both its kinetic energy and momentum are unchanged.

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Question 9
SL • Paper 1A
Medium
Calculator Permitted
SL • Paper 1A
Medium
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A ball of mass 0.15 kg0.15\ \text{kg} is moving horizontally to the right at 18 m s−118\ \text{m s}^{-1}. It rebounds from a wall and moves to the left at 12 m s−112\ \text{m s}^{-1}. The contact time with the wall is 0.030 s0.030\ \text{s}.

Taking right as positive, what is the average force exerted by the wall on the ball?

A.

150 N150\ \text{N} to the right

B.

30 N30\ \text{N} to the left

C.

90 N90\ \text{N} to the left

D.

150 N150\ \text{N} to the left

Question 10
HL • Paper 1A
Medium
Calculator Permitted
HL • Paper 1A
Medium
Calculator Permitted

An isolated object initially at rest explodes into three fragments. Fragment A has momentum 6.0 kg m s−16.0\ \text{kg m s}^{-1} east and fragment B has momentum 8.0 kg m s−18.0\ \text{kg m s}^{-1} north.

What is the momentum of fragment C?

A.

14 kg m s−114\ \text{kg m s}^{-1} southwest

B.

2.0 kg m s−12.0\ \text{kg m s}^{-1} northwest

C.

10 kg m s−110\ \text{kg m s}^{-1} southwest

D.

10 kg m s−110\ \text{kg m s}^{-1} northeast

Question 11
HL • Paper 1A
Medium
Calculator Permitted
HL • Paper 1A
Medium
Calculator Permitted

A moving puck collides with an identical puck initially at rest on a horizontal air table. After the collision, one puck moves above the original line of motion and the other moves below it. The system is isolated.

The vector diagram that represents conservation of momentum is:

A.
A clean vector diagram on a plain background. Draw an initial momentum arrow labelled $p_i$ horizontally to the right. From the tail of a separate common origin, draw $p_1$ angled upward to the right and $p_2$ angled downward to the right. Do not include a resultant arrow connecting the vector sum to $p_i$. Use the same style and size scale as the other options.
B.
A clean vector diagram on a plain background. Draw an initial momentum arrow labelled $p_i$ horizontally to the right. Beside it, draw a head-to-tail vector addition in which $p_1$ is angled upward to the right and $p_2$ begins at the head of $p_1$ and is angled downward to the right so that the resultant from the tail of $p_1$ to the head of $p_2$ is horizontal to the right and labelled $p_i$. The vertical components of $p_1$ and $p_2$ visually cancel.
C.
A clean vector diagram on a plain background. Draw an initial momentum arrow labelled $p_i$ horizontally to the right. Separately, draw two final momentum arrows labelled $p_1$ and $p_2$ both angled above the horizontal to the right. Their head-to-tail resultant is not horizontal. Use the same line style and arrow thickness as the other options.
D.
A clean vector diagram on a plain background. Draw an initial momentum arrow labelled $p_i$ horizontally to the right. Separately, draw a head-to-tail pair where $p_1$ is angled upward to the right but $p_2$ is angled downward to the left from the head of $p_1$, so the resultant is shorter and not aligned with the required original momentum. Use the same line style and arrow thickness as the other options.
Question 12
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

A student of mass 62 kg62\ \text{kg} stands on a scale in a lift. The lift accelerates upwards at 1.8 m s−21.8\ \text{m s}^{-2}.

A

Draw a labelled free-body diagram for the student.

[2]
B

Calculate the reading of the scale.

[2]

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Question 13
SL • Paper 2
Medium
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SL • Paper 2
Medium
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A block of mass 4.0 kg4.0\ \text{kg} is pulled at constant speed along a horizontal surface by a horizontal force of 11 N11\ \text{N}.

A

State why the resultant horizontal force on the block is zero.

[1]
B

Determine the coefficient of dynamic friction between the block and the surface.

[3]
Question 14
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

A tennis ball of mass 0.058 kg0.058\ \text{kg} approaches a racket horizontally at 18 m s−118\ \text{m s}^{-1} and leaves in the opposite direction at 24 m s−124\ \text{m s}^{-1}. The contact time is 5.0 ms5.0\ \text{ms}.

A horizontal before-and-after diagram of a tennis ball colliding with a racket. The incoming ball is labelled with speed toward the racket and the outgoing ball is labelled with speed away from the racket in the opposite direction. The positive direction should be indicated along the outgoing velocity.
A

Calculate the magnitude of the impulse exerted on the ball.

[2]
B

Determine the magnitude of the average force exerted by the racket on the ball.

[2]
Question 15
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

A car travels at constant speed around a flat circular bend of radius 48 m48\ \text{m}. The coefficient of static friction between the tyres and the road is 0.620.62.

A top-view diagram of a car on a flat circular bend. The centre of the circular path is marked, the radius from the centre to the car is shown, and the car velocity is tangent to the path. The diagram should not show the required friction force.
A

State the force that provides the centripetal force.

[1]
B

Calculate the maximum speed at which the car can travel without skidding.

[2]
C

Explain why this centripetal force does no work on the car in ideal uniform circular motion.

[1]
Question 16
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

In a kinetic model of an ideal gas, molecules move in random directions and collide with the walls of a container.

A simple container diagram with several gas molecules represented as small dots with velocity arrows in random directions. One molecule is shown approaching and rebounding from a wall, with velocity components perpendicular and parallel to the wall indicated qualitatively.
A

State one assumption about molecular collisions in the ideal-gas model.

[1]
B

Explain how a molecule colliding elastically with a wall gives rise to a force on the wall.

[3]

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Question 17
SL • Paper 1B
Medium
Calculator Permitted
SL • Paper 1B
Medium
Calculator Permitted

A small ring is held at rest by three light strings. One string is attached to a force sensor, one is horizontal, and one supports a hanging mass. The annotated diagram shows the forces acting on the ring and the angle of the force-sensor string to the horizontal.

An annotated free-body diagram of a ring represented by a small circle with three labelled force arrows from its centre: a sloping tension up and to the left from a force sensor, a horizontal tension to the right, and a vertical downward weight from a hanging mass. The diagram shows the angle between the sloping tension and the horizontal and gives the relevant force magnitudes or sensor reading needed for equilibrium analysis.
A

Determine the vertical component of the tension in the sloping string.

[1]
B

Calculate the tension in the horizontal string.

[2]
C

The hanging mass pulls down on the ring. State the Newton's third-law partner to this force.

[1]
Question 18
SL • Paper 1B
Medium
Calculator Permitted
SL • Paper 1B
Medium
Calculator Permitted

A student loads and unloads a spring. The graph shows the applied force against extension for both loading and unloading.

Applied force during loading and unloading of a spring.
A

Determine the spring constant in the region where Hooke's law is obeyed.

[2]
B

State the range of extension over which Hooke's law is obeyed.

[1]
C

Explain how the graph shows that the spring is not perfectly elastic over the full range tested.

[1]
Question 19
HL • Paper 1A
Medium
Calculator Permitted
HL • Paper 1A
Medium
Calculator Permitted

Puck A of mass 0.20 kg0.20\ \text{kg} moves initially at 3.0 m s−13.0\ \text{m s}^{-1} along the +x+x direction and collides with stationary puck B of mass 0.30 kg0.30\ \text{kg}. After the collision, puck A moves at 2.0 m s−12.0\ \text{m s}^{-1} at 30∘30^\circ above the +x+x direction.

What is the speed of puck B after the collision?

A.

1.5 m s−11.5\ \text{m s}^{-1}

B.

2.0 m s−12.0\ \text{m s}^{-1}

C.

1.1 m s−11.1\ \text{m s}^{-1}

D.

0.67 m s−10.67\ \text{m s}^{-1}

Question 20
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

A small steel sphere of radius 1.2 mm1.2\ \text{mm} falls vertically through oil at constant terminal speed. The density of steel is 7.8×103 kg m−37.8\times10^3\ \text{kg m}^{-3}, the density of the oil is 9.0×102 kg m−39.0\times10^2\ \text{kg m}^{-3} and the viscosity of the oil is 0.65 Pa s0.65\ \text{Pa s}.

A simple labelled free-body diagram of a sphere falling downward through a liquid at terminal speed. The diagram should show the sphere in a container of liquid, with weight downward and buoyancy and viscous drag upward. No numerical force values are shown.
A

Explain why the resultant force on the sphere is zero at terminal speed.

[2]
B

Calculate the terminal speed of the sphere.

[2]

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Question 21
SL • Paper 2
Medium
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SL • Paper 2
Medium
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Two dynamics carts move on a horizontal track. Cart A has mass 0.35 kg0.35\ \text{kg} and speed 1.6 m s−11.6\ \text{m s}^{-1} to the right. Cart B has mass 0.55 kg0.55\ \text{kg} and is initially at rest. After the collision the carts stick together.

A

Calculate the common velocity of the carts immediately after the collision.

[2]
B

Show that the collision is inelastic.

[2]
Question 22
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

A puck of mass 0.20 kg0.20\ \text{kg} moves on a horizontal air table at 3.0 m s−13.0\ \text{m s}^{-1} along the positive xx-direction. It collides with a stationary puck of mass 0.30 kg0.30\ \text{kg}. After the collision, the 0.20 kg0.20\ \text{kg} puck moves at 1.5 m s−11.5\ \text{m s}^{-1} at 40∘40^\circ above the positive xx-axis.

A plan-view vector diagram for an off-centre collision on an air table. The incident puck velocity is along the positive x-axis. After collision one puck has a labelled velocity above the x-axis, while the second puck leaves below the x-axis with unknown speed and direction.
A

Calculate the xx-component of the velocity of the 0.30 kg0.30\ \text{kg} puck after the collision.

[2]
B

Calculate the yy-component of the velocity of the 0.30 kg0.30\ \text{kg} puck after the collision.

[2]
Question 23
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

An object initially at rest explodes into three fragments on a frictionless horizontal surface. Fragment A has momentum 0.80 kg m s−10.80\ \text{kg m s}^{-1} east. Fragment B has momentum 0.60 kg m s−10.60\ \text{kg m s}^{-1} north.

A vector diagram in plan view showing two perpendicular momentum vectors from an explosion: fragment A east and fragment B north. A third fragment C has an unknown momentum directed generally southwest. Axes north and east are shown.
A

Determine the magnitude of the momentum of fragment C.

[2]
B

Determine the direction of the momentum of fragment C.

[2]
Question 24
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

A ball of mass 0.16 kg0.16\ \text{kg} moving horizontally strikes a smooth vertical wall and rebounds. Just before impact its velocity is 7.0 m s−17.0\ \text{m s}^{-1} at 30∘30^\circ to the normal to the wall. Just after impact its velocity is 6.0 m s−16.0\ \text{m s}^{-1} at 30∘30^\circ to the normal, on the other side of the normal. The contact time is 0.012 s0.012\ \text{s}.

A top-view diagram of a ball striking a vertical wall. The wall is a vertical line, the normal to the wall is horizontal, and incident and rebound velocity vectors make equal labelled angles to the normal. The tangential direction along the wall is also indicated.
A

Calculate the change in momentum of the ball perpendicular to the wall.

[2]
B

Determine the magnitude of the average force exerted by the wall on the ball perpendicular to the wall.

[2]

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Question 25
HL • Paper 2
Medium
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HL • Paper 2
Medium
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A nucleus initially at rest emits an alpha particle and a recoiling daughter nucleus. The alpha particle has momentum 3.6×10−20 kg m s−13.6\times10^{-20}\ \text{kg m s}^{-1} at 25∘25^\circ above the positive xx-axis. A gamma photon carries momentum 1.1×10−20 kg m s−11.1\times10^{-20}\ \text{kg m s}^{-1} along the negative yy-axis.

A two-dimensional momentum-vector diagram for a nuclear decay. The alpha particle momentum is shown in the first quadrant, the gamma photon momentum is shown along the negative y-axis, and the daughter nucleus has an unknown recoil momentum.
A

Determine the xx-component of the daughter nucleus momentum.

[2]
B

Determine the yy-component of the daughter nucleus momentum.

[2]
Question 26
SL • Paper 1B
Medium
Calculator Permitted
SL • Paper 1B
Medium
Calculator Permitted

A block is pulled across a horizontal surface by a steadily increasing horizontal force. The graph shows the frictional force on the block against the applied force. The normal force on the block is 40 N40\ \text{N}.

Frictional force on the block as the applied force increases.
A

State the maximum value of the static frictional force.

[1]
B

Calculate the coefficient of dynamic friction for the block and surface.

[1]
C

Explain why the block does not move when the applied force is 10 N10\ \text{N}.

[2]
D

Suggest why the frictional force is smaller after the block starts sliding.

[1]
Question 27
SL • Paper 1B
Medium
Calculator Permitted
SL • Paper 1B
Medium
Calculator Permitted

A puck of mass 0.160 kg0.160\ \text{kg} moves towards a wall with speed 6.0 m s−16.0\ \text{m s}^{-1}. The positive direction is away from the wall. The graph shows the resultant force on the puck during contact with the wall.

Resultant force on the puck as a function of time during contact with the wall.
A

Determine the impulse delivered to the puck by the wall.

[1]
B

Calculate the speed of the puck immediately after leaving the wall.

[2]
C

Explain why a padded wall would reduce the maximum force on the puck for a similar rebound.

[1]
Question 28
HL • Paper 1B
Medium
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HL • Paper 1B
Medium
Calculator Permitted

Two identical pucks collide on a low-friction table. One puck is initially at rest. The vector diagram and table show the measured speeds and directions after the collision.

Puck

Before speed / m s−1^{-1}

Before direction / ∘^\circ

After speed / m s−1^{-1}

After direction / ∘^\circ

puck 1

1.20

0∘0^\circ

0.958

37∘37^\circ above initial

puck 2

0.00

—

0.722

53∘53^\circ below initial

A

Show that the measured final directions are consistent with a perfectly elastic collision of identical pucks.

[1]
B

Check conservation of momentum using components. The mass of each puck is 0.100 kg0.100\ \text{kg}.

[2]
C

Evaluate whether the collision is elastic using the kinetic-energy data.

[2]

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Question 29
HL • Paper 1B
Medium
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HL • Paper 1B
Medium
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A molecule of mass 4.65×10−26 kg4.65\times10^{-26}\ \text{kg} collides with a vertical wall of a container. The diagram shows the velocity components immediately before and immediately after the collision.

A molecular collision diagram at a vertical wall. The molecule approaches the wall with labelled horizontal and vertical velocity components and leaves with its horizontal component reversed in direction while its vertical component is unchanged. A small table beside the diagram lists the before-and-after velocity components. The wall is labelled and the positive $x$-direction is defined.
A

Calculate the change in momentum of the molecule in the xx-direction and in the yy-direction.

[2]
B

Determine the impulse delivered to the wall by the molecule in the xx-direction.

[1]
C

Explain how collisions of this type are related to gas pressure on the wall.

[1]
Question 30
HL • Paper 2
Medium
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HL • Paper 2
Medium
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Two identical smooth discs collide on a horizontal air table. Disc A initially moves at speed 2.4 m s−12.4\ \text{m s}^{-1} along the positive xx-direction and disc B is initially at rest. After the collision, disc A moves at 1.4 m s−11.4\ \text{m s}^{-1} at 35∘35^\circ above the original direction and disc B moves at 1.9 m s−11.9\ \text{m s}^{-1} at 50∘50^\circ below the original direction.

A plan-view collision diagram for two identical discs. Initial velocity of disc A is along the positive x-axis and disc B is at rest. Final velocity vectors are shown above and below the x-axis with labelled speeds and angles.
A

Determine whether momentum is conserved in the direction perpendicular to the initial motion.

[2]
B

Suggest one experimental reason for this result.

[1]
C

State the expected angle between the final velocity directions for a perfectly elastic collision between identical masses when one is initially stationary.

[1]
Question 31
SL • Paper 1B
Hard
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SL • Paper 1B
Hard
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A small smooth sphere falls through oil. Its speed is measured using light gates after release. The graph shows speed against time. The radius of the sphere is 1.20×10−3 m1.20\times10^{-3}\ \text{m}, its weight is 1.20×10−4 N1.20\times10^{-4}\ \text{N}, and the buoyancy force on it is 3.0×10−5 N3.0\times10^{-5}\ \text{N}.

Speed of a sphere falling through oil as a function of time, showing a rise to a constant terminal speed.
A

Determine the terminal velocity of the sphere.

[1]
B

Calculate the viscosity of the oil using Stokes' law.

[2]
C

Explain why measurements used to calculate viscosity should be taken after the sphere has reached terminal velocity.

[1]
D

Suggest one condition under which the use of Stokes' law would not be valid in this experiment.

[1]
Question 32
SL • Paper 1B
Hard
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SL • Paper 1B
Hard
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A rubber stopper of mass 0.080 kg0.080\ \text{kg} is whirled in a horizontal circle. The radius is varied while the centripetal force is kept constant. The graph shows T2T^2 against radius rr, where TT is the period.

$\text{T}^{2}$ vs radius for a stopper in circular motion.
A

For the data point at r=0.50 mr=0.50\ \text{m}, determine the angular velocity of the stopper.

[1]
B

Use the gradient of the graph to determine the centripetal force.

[2]
C

Explain why the centripetal force does no work on the stopper during uniform circular motion.

[1]

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Question 33
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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Two pucks collide on a horizontal air table. Puck A is initially moving along the positive xx-direction and puck B is initially at rest. The table gives the masses and the measured velocities immediately after the collision.

Puck

Mass / kg

vxv_x / m s−1^{-1}

vyv_y / m s−1^{-1}

vxv_x / m s−1^{-1}

vyv_y / m s−1^{-1}

A

0.20

1.50

0.00

0.690

0.580

B

0.30

0.00

0.00

unknown

unknown

A

Determine the final velocity of puck B using conservation of momentum in two perpendicular directions.

[3]
B

Use kinetic energy to determine whether the collision is elastic.

[2]
Question 34
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
Calculator Permitted

A small object initially at rest explodes on a smooth horizontal surface into three fragments A, B and C. The table gives the masses and velocities of fragments A and B immediately after the explosion. Fragment C has mass 0.200 kg0.200\ \text{kg}.

Fragment

Mass / kg

Speed / m s−1^{-1}

Direction

A

0.200

12.0

due east

B

0.150

12.0

120∘120^\circ anticlockwise from east

A

Calculate the total momentum components of fragments A and B.

[2]
B

Determine the velocity of fragment C immediately after the explosion.

[2]
C

Explain why the total kinetic energy after the explosion can be greater than before without contradicting conservation of momentum.

[1]
Question 35
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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A neutron collides elastically with a stationary proton in a cloud chamber. The masses of the neutron and proton may be taken as equal. The diagram shows the measured directions and speeds after the collision.

Particle

Speed / 10710^{7} m s−1^{-1}

Angle from initial neutron direction / ∘^\circ

neutron

1.73

+30+30

proton

1.00

−60-60

A

Use the vertical components of momentum to check whether the data are consistent with conservation of momentum.

[1]
B

Use the horizontal components to determine the initial speed of the neutron.

[1]
C

Calculate the fraction of the initial kinetic energy transferred to the proton.

[1]
D

State one assumption about the interaction that is needed for this analysis.

[1]
Question 36
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
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A crate of mass 12 kg12\ \text{kg} is at rest on a rough plane inclined at 28∘28^\circ to the horizontal. A light rope pulls the crate up the plane with a tension of 35 N35\ \text{N}.

Side-view diagram of a crate on a rough inclined plane. The plane is labelled with an angle to the horizontal. A rope attached to the crate is parallel to the plane and directed up the slope. No force arrows are shown on the crate.
A

For the crate on the inclined plane:

I.

Draw and label a free-body diagram for the crate.

[2]
II.

Determine the magnitude and direction of the frictional force acting on the crate.

[3]
B

Explain why the normal force on the crate and the weight of the crate are not a Newton's third-law pair.

[2]

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Question 37
SL • Paper 2
Hard
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SL • Paper 2
Hard
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A tennis ball of mass 0.058 kg0.058\ \text{kg} approaches a racket with speed 12 m s−112\ \text{m s}^{-1} in the negative direction. The force exerted by the racket on the ball varies during contact as shown.

Force-time graph for a tennis ball in contact with a racket.
A

The force-time graph is approximated by a triangle with a peak force of 900 N900\ \text{N} and a total contact time of 8.0 ms8.0\ \text{ms}.

I.

Determine the impulse given to the ball.

[2]
II.

Calculate the speed of the ball just after leaving the racket.

[2]
B

Explain why a racket with looser strings can reduce the maximum force on the ball without greatly changing the ball's change in momentum.

[2]
C

Suggest one reason why the triangular approximation to the force-time graph may give an inaccurate value for the impulse.

[1]
Question 38
SL • Paper 2
Hard
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SL • Paper 2
Hard
Calculator Permitted

A dynamics cart A of mass 0.60 kg0.60\ \text{kg} moves at 2.4 m s−12.4\ \text{m s}^{-1} along a horizontal track and collides with a stationary cart B of mass 0.90 kg0.90\ \text{kg}. The carts stick together after the collision.

Two dynamics carts on a horizontal track before collision. Cart A is to the left moving toward cart B, which is stationary. A second small panel shows the two carts joined after collision moving to the right. No numerical working is shown.
A

Assume that external forces are negligible during the collision.

I.

Calculate the common velocity of the carts immediately after the collision.

[2]
II.

Determine the loss of kinetic energy in the collision.

[3]
B

Discuss why momentum can be conserved in this collision even though kinetic energy is not conserved.

[2]
C

Suggest one reason why an experimental value for the common velocity might be smaller than the value calculated in part (a).

[1]
Question 39
HL • Paper 1B
Hard
Calculator Permitted
HL • Paper 1B
Hard
Calculator Permitted

A video of two carts colliding on an air table is analysed frame by frame. Successive frames are separated by 0.040 s0.040\ \text{s}. The grid and table show the positions used to calculate velocities just before and just after the collision. The masses are 0.200 kg0.200\ \text{kg} for cart A and 0.300 kg0.300\ \text{kg} for cart B.

Frame

tt / s

Cart A xx / m

Cart A yy / m

Cart B xx / m

Cart B yy / m

1

0.000

0.0600

0.0000

0.0920

0.0000

2

0.040

0.0920

0.0000

0.0920

0.0000

3

0.080

0.1040

0.0240

0.1053

-0.0040

4

0.120

0.1160

0.0480

0.1186

-0.0200

A

Calculate the velocity components of cart A immediately after the collision.

[1]
B

Use momentum components to assess whether momentum is conserved.

[2]
C

Suggest one reason why a real video analysis might give a small non-zero total momentum in the yy-direction before the collision.

[1]
Question 40
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A small steel sphere falls vertically through oil. The radius of the sphere is 1.5×10−3 m1.5\times10^{-3}\ \text{m} and the density of steel is 7.8×103 kg m−37.8\times10^3\ \text{kg m}^{-3}. The density of the oil is 9.0×102 kg m−39.0\times10^2\ \text{kg m}^{-3} and its viscosity is 0.85 Pa s0.85\ \text{Pa s}.

Vertical column of oil with a small sphere moving downward between two horizontal timing marks. The sphere is shown below the upper mark and above the lower mark. No force arrows are shown.
A

Consider the forces on the sphere while it is moving at terminal speed.

I.

Show that the weight of the sphere is about 1.1×10−3 N1.1\times10^{-3}\ \text{N} and determine the buoyancy force on the sphere.

[3]
II.

Determine the terminal speed of the sphere using Stokes' law.

[3]
B

Explain two precautions or assumptions that are important if this method is used to determine the viscosity of the oil.

[2]

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Question 41
SL • Paper 2
Hard
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SL • Paper 2
Hard
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A ball of mass 0.25 kg0.25\ \text{kg} is attached to a light string of length 0.80 m0.80\ \text{m} and moves in a vertical circle. The speed of the ball is 3.4 m s−13.4\ \text{m s}^{-1} at the top of the circle and 6.0 m s−16.0\ \text{m s}^{-1} at the bottom.

Vertical circle traced by a small ball on a string. The centre of the circle and the top and bottom positions are marked. Tangential velocity arrows are shown at the top and bottom, but no force arrows are shown.
A

Consider the motion at the top and bottom of the circle.

I.

Calculate the angular speed of the ball at the top of the circle.

[1]
II.

Determine the tension in the string at the top of the circle.

[2]
III.

Determine the tension in the string at the bottom of the circle.

[2]
B

Explain why the string is more likely to break at the bottom of the circle, and why the centripetal force does no work in uniform circular motion.

[3]
Question 42
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A model rocket is launched vertically upward. Its initial mass is 0.75 kg0.75\ \text{kg}. During the first 2.0 s2.0\ \text{s}, fuel is ejected at a constant rate of 0.080 kg s−10.080\ \text{kg s}^{-1} with speed 620 m s−1620\ \text{m s}^{-1} relative to the rocket.

A

Ignore air resistance.

I.

Calculate the thrust force on the rocket.

[2]
II.

Calculate the acceleration of the rocket after 1.5 s1.5\ \text{s} of fuel ejection.

[3]
B

Explain why the rocket could continue to accelerate in empty space while ejecting fuel.

[2]
Question 43
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A puck P of mass 0.20 kg0.20\ \text{kg} moves at 5.0 m s−15.0\ \text{m s}^{-1} along a frictionless air table and collides with a stationary puck Q of mass 0.30 kg0.30\ \text{kg}. After the collision, P moves at 3.0 m s−13.0\ \text{m s}^{-1} at 40∘40^\circ above its original direction.

Top-view air-table diagram showing puck P approaching puck Q along a horizontal line. After collision, puck P is shown moving above the original direction at a labelled angle. Puck Q's final direction is not labelled with a value. Coordinate axes are shown with x along the original direction and y perpendicular.
A

Take the original direction of P as the positive xx-direction.

I.

Write the momentum conservation equations for the xx- and yy-directions.

[2]
II.

Determine the speed and direction of Q after the collision.

[3]
B

Evaluate whether the collision is elastic.

[3]
Question 44
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

An object initially at rest explodes on a smooth horizontal surface into three fragments. Fragment A has mass 0.40 kg0.40\ \text{kg} and moves east at 6.0 m s−16.0\ \text{m s}^{-1}. Fragment B has mass 0.30 kg0.30\ \text{kg} and moves north at 5.0 m s−15.0\ \text{m s}^{-1}. Fragment C has mass 0.50 kg0.50\ \text{kg}.

Top-view diagram of an explosion point on a horizontal surface. Fragment A is shown moving to the right and fragment B upward from the point. Fragment C's direction is left unspecified. North and east reference directions are shown.
A

Take east as positive xx and north as positive yy.

I.

Determine the velocity components of fragment C.

[3]
II.

Determine the speed and direction of fragment C.

[2]
III.

Calculate the total kinetic energy of the fragments after the explosion.

[1]
B

Discuss the energy and momentum changes during the explosion.

[2]

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Question 45
HL • Paper 2
Hard
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HL • Paper 2
Hard
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On a horizontal air table, glider A of mass 0.50 kg0.50\ \text{kg} moves east at 1.6 m s−11.6\ \text{m s}^{-1} and glider B of mass 0.40 kg0.40\ \text{kg} moves north at 1.2 m s−11.2\ \text{m s}^{-1}. They collide and stick together.

Top-view diagram of two gliders approaching a collision point at right angles, one from the west moving east and one from the south moving north. A combined glider leaves the collision point in a northeast direction. East and north axes are shown.
A

The collision is perfectly inelastic.

I.

Determine the velocity components of the combined gliders immediately after the collision.

[2]
II.

Determine the speed and direction of the combined gliders.

[2]
B

Calculate the kinetic energy lost in the collision.

[2]
C

Discuss how experimental uncertainty should be considered when testing conservation of momentum in this collision.

[2]
Question 46
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

Two identical pucks collide on a horizontal air table. Puck A initially moves east at 1.8 m s−11.8\ \text{m s}^{-1} and puck B is initially at rest. After the collision, A moves at 1.1 m s−11.1\ \text{m s}^{-1} at 35∘35^\circ north of east.

Top-view diagram of two identical pucks before and after collision. Before collision, puck A moves east toward stationary puck B. After collision, puck A moves north of east at a labelled angle, while puck B's final path is to be determined. Axes east and north are shown.
A

Use conservation of momentum in perpendicular directions.

I.

Determine the velocity components of puck B after the collision.

[2]
II.

Determine the speed and direction of puck B.

[2]
B

Evaluate whether the data are consistent with a perfectly elastic collision of identical pucks.

[3]
C

Suggest one experimental factor that could account for the result in part (b).

[1]
Question 47
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A neutron in a moderator is modelled as colliding with a stationary hydrogen nucleus of approximately the same mass. Before the collision, the neutron travels at 2.0×106 m s−12.0\times10^6\ \text{m s}^{-1} in the positive xx-direction. After the collision, the neutron travels at 1.2×106 m s−11.2\times10^6\ \text{m s}^{-1} at 50∘50^\circ above the positive xx-direction.

Two-dimensional scattering diagram. An incoming neutron travels along the positive x-axis toward a stationary hydrogen nucleus. After collision, the neutron path is above the x-axis at a labelled angle. The hydrogen nucleus final path is not labelled with a value. Axes are shown.
A

Treat the neutron and hydrogen nucleus as having equal mass.

I.

Determine the velocity components of the hydrogen nucleus after the collision.

[2]
II.

Determine the speed of the hydrogen nucleus after the collision.

[1]
B

Compare the kinetic energy before and after the collision to assess whether the collision is approximately elastic.

[2]
C

Explain why such collisions are relevant in a nuclear reactor moderator.

[2]
Question 48
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

Cart A of mass 0.25 kg0.25\ \text{kg} travels at 1.09 m s−11.09\ \text{m s}^{-1} along the positive xx-direction on a horizontal air table. It collides with a stationary cart B of unknown mass. After the collision, A moves at 0.80 m s−10.80\ \text{m s}^{-1} at 30∘30^\circ above the xx-axis, and B moves at 0.60 m s−10.60\ \text{m s}^{-1} at 45∘45^\circ below the xx-axis.

Top-view collision diagram with cart A initially moving along the positive x-axis toward stationary cart B. After the collision, A is shown above the x-axis at a labelled angle and B below the x-axis at a labelled angle. Cart B is shown with unknown mass (for example, labelled with a question mark), and the axes and final speeds are indicated, but no calculations are shown.
A

Use the measured final directions and speeds.

I.

Determine the mass of cart B using momentum conservation in the yy-direction.

[3]
II.

Use your answer to (a)(i) to test momentum conservation in the xx-direction.

[2]
B

Evaluate whether the collision is elastic.

[2]
C

State one reason why momentum values from an air-table experiment may fail to agree exactly in the two directions.

[1]

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A.1 Kinematics

A.3 Work, energy and power