DP Physics Questionbank

An object of weight W is falling vertically at a constant speed in a fluid. What is the magnitude of the drag force acting on the object? 

A. 0
B. $\frac{W}{2}$
C. W 
D. 2W

A mass is suspended from the ceiling of a train carriage by a string. The string makes an angle θ with the vertical when the train is accelerating along a straight horizontal track.

What is the acceleration of the train? 

A. g sin θ

B. g cos θ 

C. g tan θ 

D. $\frac{g}{\tan \theta }$

A tennis ball is released from rest at a height h above the ground. At each bounce 50 % of its kinetic energy is lost to its surroundings. What is the height reached by the ball after its second bounce?

A.  $\frac{h}{8}$

B.  $\frac{h}{4}$

C.  $\frac{h}{2}$

D.  zero

The glider reaches its launch speed of 27.0 m s^–1 after accelerating for 11.0 s. Assume that the glider moves horizontally until it leaves the ground. Calculate the total distance travelled by the glider before it leaves the ground.

Estimate the speed of the train.

Show that the acceleration of the sledge is about –2 m s^–2.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Estimate the speed of the train.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Estimate the maximum speed of the spacecraft.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

A sports car is accelerated from 0 to 100 km per hour in 3 s. What is the acceleration of the car?

A. 0.1 g

B. 0.3 g

C. 0.9 g

D. 3 g

A girl throws an object horizontally at time t = 0. Air resistance can be ignored. At t = 0.50 s the object travels horizontally a distance $x$ in metres while it falls vertically through a distance $y$ in metres.

What is the initial velocity of the object and the vertical distance fallen at t = 1.0 s?

Comment on the magnitude of the force in (b)(ii).

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

A balloon rises at a steady vertical velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. An object is dropped from the balloon at a height of $40 \mathrm{m}$ above the ground. Air resistance is negligible. What is the time taken for the object to hit the ground?

A.  $10 \mathrm{s}$

B.  $5 \mathrm{s}$

C.  $4 \mathrm{s}$

D.  $2 \mathrm{s}$

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

The minute hand of a clock hanging on a vertical wall has length $L = 30 \text{cm.}$

The minute hand is observed pointing at 12 and then again 30 minutes later when the minute hand is pointing at 6.

What is the average velocity and average speed of point P on the minute hand during this time interval?

A projectile is launched at an angle above the horizontal with a horizontal component of velocity $V_{\text{h}}$ and a vertical component of velocity $V_{\text{v}}$. Air resistance is negligible. Which graphs show the variation with time of $V_{\text{h}}$ and of $V_{\text{v}}$?

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

Determine H.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

A ball is thrown upwards at time t = 0. The graph shows the variation with time of the height of the ball. The ball returns to the initial height at time T.

What is the height h at time t ?

A.  $\frac{1}{2}g{t}^2$

B.  $\frac{1}{2}g{T}^2$

C.  $\frac{1}{2}gT\left(T-t\right)$

D.  $\frac{1}{2}gt\left(T-t\right)$

Show that a mass of about 240 kg of air moves through the fan every second.

Deduce the mass of the airboat.

Show that a mass of about 240 kg of air moves through the fan every second.

Deduce the mass of the airboat.

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

The diagram shows the stone during its motion after release.

Label the diagram to show the forces acting on the stone. Your answer should include the name, the direction and point of application of each force.

Determine the coefficient of dynamic friction between the stone and the ice during the last 14.0 s of the stone’s motion.

Two boxes in contact are pushed along a floor with a force F. The boxes move at a constant speed. Box X has a mass m and box Y has a mass 2m.

What is the resultant force acting on Y?
A.  0
B.  $\frac{F}{2}$
C.  F
D.  2F

An elevator (lift) and its load have a total mass of 750 kg and accelerate vertically downwards at 2.0 m s^–2.

What is the tension in the elevator cable?

A.  1.5 kN
B.  6.0 kN
C.  7.5 kN
D.  9.0 kN

The skier reaches point C with a speed of 8.2 m s^–1. She stops after a distance of 24 m at point D.

Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the frictional force is constant and that air resistance can be neglected.

A block of weight W is suspended by two strings of equal length. The strings are almost horizontal.

What is correct about the tension T in one string?

A.  

B.  $T=\frac{W}{2}$

C.  

D.  $T>W$

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.

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.

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

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

                                          $$F=\frac{mg}{\tan \theta }$$

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

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

Describe the effect of F on the linear speed of the wheel.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

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

                                          $$F=\frac{mg}{\tan \theta }$$

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

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

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

The graph shows the variation with time of the resultant net force acting on an object. The object has a mass of 1kg and is initially at rest.

What is the velocity of the object at a time of 200 ms?

A. 8 m s^–1

B. 16 m s^–1

C. 8 km s^–1

D. 16 km s^–1

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

A climber of mass m slides down a vertical rope with an average acceleration a. What is the average frictional force exerted by the rope on the climber?

A. mg

B. m(g + a)

C. m(g – a)

D. ma

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

Calculate the magnitude of the initial acceleration of the electron.

An object of mass $8.0 \mathrm{kg}$ is falling vertically through the air. The drag force acting on the object is $60 \mathrm{N}$. What is the best estimate of the acceleration of the object?

A.  Zero

B.  $2.5 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $7.5 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $10 \mathrm{m} {\mathrm{s}}^{-2}$

Three forces act on a block which is sliding down a slope at constant speed. $W$ is the weight, $R$ is the reaction force at the surface of the block and $F$ is the friction force acting on the block.

In this situation

A.  there must be an unbalanced force down the plane.

B.  $W=R$.

C.  $F=W$.

D.  the resultant force on the block is zero.

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

A body is held in translational equilibrium by three coplanar forces of magnitude $3 \mathrm{N}$, $4 \mathrm{N}$ and $5 \mathrm{N}$. Three statements about these forces are

I.  all forces are perpendicular to each other
II.  the forces cannot act in the same direction
III.  the vector sum of the forces is equal to zero.

Which statements are true?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

Draw and label the free-body diagram for the person.

The person must not slide down the wall. Show that the minimum angular velocity $\omega$ of the cylinder for this situation is

$\omega =\sqrt{\frac{g}{\mu R}}$

where $\mu$ is the coefficient of static friction between the person and the cylinder.

The coefficient of static friction between the person and the cylinder is $0.40$. The radius of the cylinder is $3.5 \mathrm{m}$. The cylinder makes $28$ revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

A mass is released from the top of a smooth ramp of height $h$. After leaving the ramp, the mass slides on a rough horizontal surface.

The mass comes to rest in a distance d. What is the coefficient of dynamic friction between the mass and the horizontal surface?

$\text{A. }\frac{gd}{h}$

$\text{B. }\sqrt{\frac{d}{2gh}}$

$\text{C. }\frac{d}{h}$

$\text{D. }\frac{h}{d}$

A person with a weight of $600 \text{N}$ stands on a scale in an elevator.

What is the acceleration of the elevator when the scale reads $900 \text{N}$?

A.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

B.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

C.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

D.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

A block rests on a rough horizontal plane. A force P is applied to the block and the block moves to the right.

There is a coefficient of friction ${\mu }_{\text{d}}$ giving rise to a frictional force F between the block and the plane. The force P is doubled. Will ${\mu }_{\text{d}}$ and F be unchanged or greater?

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

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

Which statement is correct in this situation?

A.  The net force on the load is zero.

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

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

D.  The elevator and its load are in translational equilibrium.

An object of mass 2.0 kg rests on a rough surface. A person pushes the object in a straight line with a force of 10 N through a distance d.

The resultant force acting on the object throughout d is 6.0 N.

What is the value of the sliding coefficient of friction $\mu$ between the surface and the object and what is the acceleration a of the object?

A book of mass m lies on top of a table of mass M that rolls freely along the ground. The coefficient of friction between the book and the table is $\mu$. A person is pushing the rolling table.

What is the maximum acceleration of the table so that the book does not slide backwards relative to the table?

A.  $\frac{g}{\mu }$

B.  $\mu g$

C.  $\frac{mg}{M \mu }$

D.  $\frac{m}{M}\mu g$

Outline why a force acts on the airboat due to the fan blade.

Deduce the mass of the airboat.

Outline why a force acts on the airboat due to the fan blade.

Deduce the mass of the airboat.

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

Which of the formulae represents Newton’s second law?

A.  $\frac{\text{mass}}{\text{volume}}$

B.  $\frac{\text{work}}{\text{displacement}}$

C.  $\frac{\text{change of momentum}}{\text{time}}$

D.  $\text{pressure}\times \text{area}$

Two masses $m_1$ and $m_2$ are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.

Mass $m_2$ accelerates downwards at $\frac{g}{2}$. What is $\frac{m_1}{m_2}$?
A.  $\frac{1}{3}$

B.  $\frac{1}{2}$

C.  2

D.  3

The vertical acceleration of the load downwards is 2.4 m s⁻².

Calculate the tension in the string.

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

A horizontal spring of spring constant k and negligible mass is compressed through a distance y from its equilibrium length. An object of mass m that moves on a frictionless surface is placed at the end of the spring. The spring is released and returns to its equilibrium length.

What is the speed of the object just after it leaves the spring?

A.  $y\sqrt{\frac{k}{m}}$

B.  $y\sqrt{\frac{m}{k}}$

C.  $y\frac{k}{m}$

D.  $y\frac{m}{k}$

From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 m s^–1.

The cable is pulled by an electric motor. The motor has an overall efficiency of 23 %. Determine the average power input to the motor.

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

When the object has fallen to height $\frac{h}{4}$ above the surface, what is

                                      $\frac{\text{kinetic energy of the object at }\frac{h}{4}}{\text{gravitational potential energy of the object at }h}$?

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

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.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

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.

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

Show that the kinetic energy of the egg just before impact is about 0.6 J.

Calculate the average power delivered to the ball during the impact.

Determine the speed of the tennis ball as it strikes the ground.

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

An object has a weight of 6.10 × 10² N. What is the change in gravitational potential energy of the object when it moves through 8.0 m vertically?

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

Outline why this force does no work on the Moon.

Outline why this force does no work on Phobos.

Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.

Calculate the average power delivered to the ball during the impact.

Determine the speed of the tennis ball as it strikes the ground.

The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension $x$ is $E$. What is the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$?

A. $\frac{E}{16}$

B. $\frac{E}{4}$

C. $\frac{3E}{4}$

D. $\frac{15E}{16}$

An object of mass m makes n revolutions per second around a circle of radius r at a constant speed. What is the kinetic energy of the object?

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

D. $4{\pi }^{2}m{n}^2{r}^2$

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

Show that the radius of the path is about 6 cm.

An object of mass $2m$ moving at velocity $3v$ collides with a stationary object of mass $4m$. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?

An object of mass $1 \mathrm{kg}$ is thrown downwards from a height of $20 \mathrm{m}$. The initial speed of the object is $6 \mathrm{m} {\mathrm{s}}^{-1}$.
The object hits the ground at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$. What is the best estimate of the energy transferred from the object to the air as it falls?

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

Calculate the power transferred to the air by the aircraft.

Determine the kinetic energy of the ball immediately after the bounce.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

A mass is released from the top of a smooth ramp of height $h$. After leaving the ramp, the mass slides on a rough horizontal surface.

The mass comes to rest in a distance d. What is the coefficient of dynamic friction between the mass and the horizontal surface?

$\text{A. }\frac{gd}{h}$

$\text{B. }\sqrt{\frac{d}{2gh}}$

$\text{C. }\frac{d}{h}$

$\text{D. }\frac{h}{d}$

The graph shows the variation with distance of a horizontal force acting on an object. The object, initially at rest, moves horizontally through a distance of $50 \text{m}$.

A constant frictional force of $2.0 \text{N}$ opposes the motion. What is the final kinetic energy of the object after it has moved $50 \text{m}$?

A. $100 \text{J}$

B. $500 \text{J}$

C. $600 \text{J}$

D. $1100 \text{J}$

A net force $F$ acts on an object of mass $m$ that is initially at rest. The object moves in a straight line. The variation of $F$ with the distance $s$ is shown.

What is the speed of the object at the distance $s_1$?

A.  $\sqrt{\frac{F_1{s}_1}{2m}}$

B.  $\sqrt{\frac{F_1{s}_1}{m}}$

C.  $\sqrt{\frac{2F_1{s}_1}{m}}$

D.  $\sqrt{\frac{4F_1{s}_1}{m}}$

Estimate the loss in the mechanical energy of the ball as a result of the collision with the floor.

Determine the average force exerted on the floor by the ball.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

Show that the kinetic energy of the object is about 0.7 mJ.

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

A ball of mass m strikes a vertical wall with a speed v at an angle of θ to the wall. The ball rebounds at the same speed and angle. What is the change in the magnitude of the momentum of the ball?

A. 2 mv sin θ
B. 2 mv cos θ
C. 2 mv 
D. zero

Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.

A stationary nucleus of polonium-210 undergoes alpha decay to form lead-206. The initial speed of the alpha particle is v. What is the speed of the lead-206 nucleus?

A.  $\frac{206}{4}$v

B.  v

C.  $\frac{206}{210}$v

D.  $\frac{4}{206}$v

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

An object is moving in a straight line. A force F and a resistive force f act on the object along the straight line.

Both forces act for a time t.

What is the rate of change of momentum with time of the object during time t ?

A.     F + f 

B.     F – f

C.     (F + f )t

D.     (F – f )t 

Determine the magnitude of the average resultant force acting on the block between B and C.

between A and B.

between B and 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.

A ball of mass m collides with a vertical wall with an initial horizontal speed u and rebounds with a horizontal speed v. The graph shows the variation of the speed of the ball with time.

What is the magnitude of the mean net force on the ball during the collision?

A.     $\frac{m(u-v)}{(t_2+t_1)}$

B.     $\frac{m(u-v)}{(t_2-t_1)}$

C.     $\frac{m(u+v)}{(t_2+t_1)}$

D.     $\frac{m(u+v)}{(t_2-t_1)}$

Determine the magnitude of the average resultant force acting on the block between B and C.

between A and B.

between B and 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.

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

Determine the initial acceleration of the spacecraft.

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Determine the initial acceleration of the spacecraft.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Calculate the average force exerted by the racquet on the ball.

Calculate the average force exerted by the racquet on the ball.

Calculate the speed of the ball as it leaves the racket.

Show that the average force exerted on the ball by the racket is about 50 N.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

An object of mass $2m$ moving at velocity $3v$ collides with a stationary object of mass $4m$. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?

An object of mass $m$ strikes a vertical wall horizontally at speed $U$. The object rebounds from the wall horizontally at speed $V$.

What is the magnitude of the change in the momentum of the object?

A.  $0$

B.  $m\left(V-U\right)$

C.  $m\left(U-V\right)$

D.  $m\left(U+V\right)$

Determine $v$. State your answer to an appropriate number of significant figures.

Determine $v$. State your answer to an appropriate number of significant figures.

Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.

Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.

The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.

Determine the average force exerted on the floor by the ball.

Outline why a force acts on the airboat due to the fan blade.

Show that the tension in the rope is about 5 kN.

Outline why a force acts on the airboat due to the fan blade.

Show that the tension in the rope is about 5 kN.