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?
The gravitational force exerted by Earth on the table
The normal force exerted by the book on the table
The gravitational force exerted by the book on Earth
The normal force exerted by the table on the book
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 block on a horizontal rough surface remains at rest when pulled by a horizontal force of to the right. The maximum possible static friction on the block is .
What is the frictional force acting on the block?
to the left
to the right
to the left
to the left
A spring obeys Hooke's law. A force of produces an extension of .
What is the spring constant?
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 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:
In a two-dimensional collision, the total initial momentum has no vertical component. After the collision, object 1 has a vertical momentum component of .
What is the vertical momentum component of object 2 after the collision, assuming the system is isolated?
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?
Its kinetic energy is unchanged but its momentum changes.
Its momentum is unchanged but its kinetic energy decreases.
Both its kinetic energy and momentum decrease.
Both its kinetic energy and momentum are unchanged.
A ball of mass is moving horizontally to the right at . It rebounds from a wall and moves to the left at . The contact time with the wall is .
Taking right as positive, what is the average force exerted by the wall on the ball?
to the right
to the left
to the left
to the left
An isolated object initially at rest explodes into three fragments. Fragment A has momentum east and fragment B has momentum north.
What is the momentum of fragment C?
southwest
northwest
southwest
northeast
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 student of mass stands on a scale in a lift. The lift accelerates upwards at .
Draw a labelled free-body diagram for the student.
Calculate the reading of the scale.
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A block of mass is pulled at constant speed along a horizontal surface by a horizontal force of .
State why the resultant horizontal force on the block is zero.
Determine the coefficient of dynamic friction between the block and the surface.
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A tennis ball of mass approaches a racket horizontally at and leaves in the opposite direction at . The contact time is .

Calculate the magnitude of the impulse exerted on the ball.
Determine the magnitude of the average force exerted by the racket on the ball.
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A car travels at constant speed around a flat circular bend of radius . The coefficient of static friction between the tyres and the road is .

State the force that provides the centripetal force.
Calculate the maximum speed at which the car can travel without skidding.
Explain why this centripetal force does no work on the car in ideal uniform circular motion.
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In a kinetic model of an ideal gas, molecules move in random directions and collide with the walls of a container.

State one assumption about molecular collisions in the ideal-gas model.
Explain how a molecule colliding elastically with a wall gives rise to a force on the wall.
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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.

Determine the vertical component of the tension in the sloping string.
Calculate the tension in the horizontal string.
The hanging mass pulls down on the ring. State the Newton's third-law partner to this force.
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A student loads and unloads a spring. The graph shows the applied force against extension for both loading and unloading.

Determine the spring constant in the region where Hooke's law is obeyed.
State the range of extension over which Hooke's law is obeyed.
Explain how the graph shows that the spring is not perfectly elastic over the full range tested.
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Puck A of mass moves initially at along the direction and collides with stationary puck B of mass . After the collision, puck A moves at at above the direction.
What is the speed of puck B after the collision?
A small steel sphere of radius falls vertically through oil at constant terminal speed. The density of steel is , the density of the oil is and the viscosity of the oil is .

Explain why the resultant force on the sphere is zero at terminal speed.
Calculate the terminal speed of the sphere.
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Two dynamics carts move on a horizontal track. Cart A has mass and speed to the right. Cart B has mass and is initially at rest. After the collision the carts stick together.
Calculate the common velocity of the carts immediately after the collision.
Show that the collision is inelastic.
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A puck of mass moves on a horizontal air table at along the positive -direction. It collides with a stationary puck of mass . After the collision, the puck moves at at above the positive -axis.

Calculate the -component of the velocity of the puck after the collision.
Calculate the -component of the velocity of the puck after the collision.
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An object initially at rest explodes into three fragments on a frictionless horizontal surface. Fragment A has momentum east. Fragment B has momentum north.

Determine the magnitude of the momentum of fragment C.
Determine the direction of the momentum of fragment C.
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A ball of mass moving horizontally strikes a smooth vertical wall and rebounds. Just before impact its velocity is at to the normal to the wall. Just after impact its velocity is at to the normal, on the other side of the normal. The contact time is .

Calculate the change in momentum of the ball perpendicular to the wall.
Determine the magnitude of the average force exerted by the wall on the ball perpendicular to the wall.
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A nucleus initially at rest emits an alpha particle and a recoiling daughter nucleus. The alpha particle has momentum at above the positive -axis. A gamma photon carries momentum along the negative -axis.

Determine the -component of the daughter nucleus momentum.
Determine the -component of the daughter nucleus momentum.
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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 .

State the maximum value of the static frictional force.
Calculate the coefficient of dynamic friction for the block and surface.
Explain why the block does not move when the applied force is .
Suggest why the frictional force is smaller after the block starts sliding.
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A puck of mass moves towards a wall with speed . The positive direction is away from the wall. The graph shows the resultant force on the puck during contact with the wall.

Determine the impulse delivered to the puck by the wall.
Calculate the speed of the puck immediately after leaving the wall.
Explain why a padded wall would reduce the maximum force on the puck for a similar rebound.
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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 | Before direction / ° | After speed / m s^-1 | After direction / ° |
|---|---|---|---|---|
| puck 1 | 1.20 | 0° | 0.958 | 37° above initial |
| puck 2 | 0.00 | — | 0.722 | 53° below initial |
Show that the measured final directions are consistent with a perfectly elastic collision of identical pucks.
Check conservation of momentum using components. The mass of each puck is .
Evaluate whether the collision is elastic using the kinetic-energy data.
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A molecule of mass collides with a vertical wall of a container. The diagram shows the velocity components immediately before and immediately after the collision.

Calculate the change in momentum of the molecule in the -direction and in the -direction.
Determine the impulse delivered to the wall by the molecule in the -direction.
Explain how collisions of this type are related to gas pressure on the wall.
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Two identical smooth discs collide on a horizontal air table. Disc A initially moves at speed along the positive -direction and disc B is initially at rest. After the collision, disc A moves at at above the original direction and disc B moves at at below the original direction.

Determine whether momentum is conserved in the direction perpendicular to the initial motion.
Suggest one experimental reason for this result.
State the expected angle between the final velocity directions for a perfectly elastic collision between identical masses when one is initially stationary.
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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 , its weight is , and the buoyancy force on it is .

Determine the terminal velocity of the sphere.
Calculate the viscosity of the oil using Stokes' law.
Explain why measurements used to calculate viscosity should be taken after the sphere has reached terminal velocity.
Suggest one condition under which the use of Stokes' law would not be valid in this experiment.
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A rubber stopper of mass is whirled in a horizontal circle. The radius is varied while the centripetal force is kept constant. The graph shows against radius , where is the period.

For the data point at , determine the angular velocity of the stopper.
Use the gradient of the graph to determine the centripetal force.
Explain why the centripetal force does no work on the stopper during uniform circular motion.
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Two pucks collide on a horizontal air table. Puck A is initially moving along the positive -direction and puck B is initially at rest. The table gives the masses and the measured velocities immediately after the collision.
| Puck | Mass / kg | Initial v_x / m s^-1 | Initial v_y / m s^-1 | Final v_x / m s^-1 | Final v_y / m s^-1 |
|---|---|---|---|---|---|
| A | 0.20 | 1.50 | 0.00 | 0.690 | 0.580 |
| B | 0.30 | 0.00 | 0.00 | unknown | unknown |
Determine the final velocity of puck B using conservation of momentum in two perpendicular directions.
Use kinetic energy to determine whether the collision is elastic.
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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 .
| Fragment | Mass / kg | Speed / m s^-1 | Direction |
|---|---|---|---|
| A | 0.200 | 12.0 | due east |
| B | 0.150 | 12.0 | 120° anticlockwise from east |
Calculate the total momentum components of fragments A and B.
Determine the velocity of fragment C immediately after the explosion.
Explain why the total kinetic energy after the explosion can be greater than before without contradicting conservation of momentum.
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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 / 10^7 m s^-1 | Angle from initial neutron direction / ° |
|---|---|---|
| neutron | 1.73 | +30 |
| proton | 1.00 | −60 |
Use the vertical components of momentum to check whether the data are consistent with conservation of momentum.
Use the horizontal components to determine the initial speed of the neutron.
Calculate the fraction of the initial kinetic energy transferred to the proton.
State one assumption about the interaction that is needed for this analysis.
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A crate of mass is at rest on a rough plane inclined at to the horizontal. A light rope pulls the crate up the plane with a tension of .

For the crate on the inclined plane:
Draw and label a free-body diagram for the crate.
Determine the magnitude and direction of the frictional force acting on the crate.
Explain why the normal force on the crate and the weight of the crate are not a Newton's third-law pair.
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A tennis ball of mass approaches a racket with speed in the negative direction. The force exerted by the racket on the ball varies during contact as shown.

The force-time graph is approximated by a triangle with a peak force of and a total contact time of .
Determine the impulse given to the ball.
Calculate the speed of the ball just after leaving the racket.
Explain why a racket with looser strings can reduce the maximum force on the ball without greatly changing the ball's change in momentum.
Suggest one reason why the triangular approximation to the force-time graph may give an inaccurate value for the impulse.
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A dynamics cart A of mass moves at along a horizontal track and collides with a stationary cart B of mass . The carts stick together after the collision.

Assume that external forces are negligible during the collision.
Calculate the common velocity of the carts immediately after the collision.
Determine the loss of kinetic energy in the collision.
Discuss why momentum can be conserved in this collision even though kinetic energy is not conserved.
Suggest one reason why an experimental value for the common velocity might be smaller than the value calculated in part (a).
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A video of two carts colliding on an air table is analysed frame by frame. Successive frames are separated by . The grid and table show the positions used to calculate velocities just before and just after the collision. The masses are for cart A and for cart B.
| Frame | t / s | Cart A x / m | Cart A y / m | Cart B x / m | Cart B y / 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 |
Calculate the velocity components of cart A immediately after the collision.
Use momentum components to assess whether momentum is conserved.
Suggest one reason why a real video analysis might give a small non-zero total momentum in the -direction before the collision.
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A small steel sphere falls vertically through oil. The radius of the sphere is and the density of steel is . The density of the oil is and its viscosity is .

Consider the forces on the sphere while it is moving at terminal speed.
Show that the weight of the sphere is about and determine the buoyancy force on the sphere.
Determine the terminal speed of the sphere using Stokes' law.
Explain two precautions or assumptions that are important if this method is used to determine the viscosity of the oil.
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A ball of mass is attached to a light string of length and moves in a vertical circle. The speed of the ball is at the top of the circle and at the bottom.

Consider the motion at the top and bottom of the circle.
Calculate the angular speed of the ball at the top of the circle.
Determine the tension in the string at the top of the circle.
Determine the tension in the string at the bottom of the circle.
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.
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A model rocket is launched vertically upward. Its initial mass is . During the first , fuel is ejected at a constant rate of with speed relative to the rocket.
Ignore air resistance.
Calculate the thrust force on the rocket.
Calculate the acceleration of the rocket after of fuel ejection.
Explain why the rocket could continue to accelerate in empty space while ejecting fuel.
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A puck P of mass moves at along a frictionless air table and collides with a stationary puck Q of mass . After the collision, P moves at at above its original direction.

Take the original direction of P as the positive -direction.
Write the momentum conservation equations for the - and -directions.
Determine the speed and direction of Q after the collision.
Evaluate whether the collision is elastic.
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An object initially at rest explodes on a smooth horizontal surface into three fragments. Fragment A has mass and moves east at . Fragment B has mass and moves north at . Fragment C has mass .

Take east as positive and north as positive .
Determine the velocity components of fragment C.
Determine the speed and direction of fragment C.
Calculate the total kinetic energy of the fragments after the explosion.
Discuss the energy and momentum changes during the explosion.
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On a horizontal air table, glider A of mass moves east at and glider B of mass moves north at . They collide and stick together.

The collision is perfectly inelastic.
Determine the velocity components of the combined gliders immediately after the collision.
Determine the speed and direction of the combined gliders.
Calculate the kinetic energy lost in the collision.
Discuss how experimental uncertainty should be considered when testing conservation of momentum in this collision.
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Two identical pucks collide on a horizontal air table. Puck A initially moves east at and puck B is initially at rest. After the collision, A moves at at north of east.

Use conservation of momentum in perpendicular directions.
Determine the velocity components of puck B after the collision.
Determine the speed and direction of puck B.
Evaluate whether the data are consistent with a perfectly elastic collision of identical pucks.
Suggest one experimental factor that could account for the result in part (b).
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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 in the positive -direction. After the collision, the neutron travels at at above the positive -direction.

Treat the neutron and hydrogen nucleus as having equal mass.
Determine the velocity components of the hydrogen nucleus after the collision.
Determine the speed of the hydrogen nucleus after the collision.
Compare the kinetic energy before and after the collision to assess whether the collision is approximately elastic.
Explain why such collisions are relevant in a nuclear reactor moderator.
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Cart A of mass travels at along the positive -direction on a horizontal air table. It collides with a stationary cart B of unknown mass. After the collision, A moves at at above the -axis, and B moves at at below the -axis.

Use the measured final directions and speeds.
Determine the mass of cart B using momentum conservation in the -direction.
Use your answer to (a)(i) to test momentum conservation in the -direction.
Evaluate whether the collision is elastic.
State one reason why momentum values from an air-table experiment may fail to agree exactly in the two directions.
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