Topic 2 P2 [172 marks]

1a.

An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The otherend of the rope is connected to a block which is initially at position A. The block is released fromrest. The mass of the rope is negligible.

The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.

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

1b.

At position C the speed of the block reaches zero. The time taken for the block to fall between Band C is 0.759 s. The mass of the block is 80.0 kg.

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

Sketch on the diagram the average resultant force acting on the block between B and

[2 marks]

[2 marks]

1c. Sketch on the diagram the average resultant force acting on the block between B andC. The arrow on the diagram represents the weight of the block.

1d. Calculate the magnitude of the average force exerted by the rope on the blockbetween B and C.

1e.

For the rope and block, describe the energy changes that take place

between A and B.

between B and C.

[2 marks]

[2 marks]

[1 mark]

1f. between B and C.

1g. The length reached by the rope at C is 77.4 m. Suggest how energy considerationscould be used to determine the elastic constant of the rope.

2a.

A small ball of mass m is moving in a horizontal circle on the inside surface of a frictionlesshemispherical bowl.

The normal reaction force N makes an angle θ to the horizontal.

State the direction of the resultant force on the ball.

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

[1 mark]

[2 marks]

[1 mark]

2b. On the diagram, construct an arrow of the correct length to represent the weight of theball.

2c. Show that the magnitude of the net force F on the ball is given by thefollowing equation.

F =mg

tanθ

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

[2 marks]

[3 marks]

2d. The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

2e. Outline whether this ball can move on a horizontal circular path of radius equal tothe radius of the bowl.

A second identical ball is placed at the bottom of the bowl and the first ball is

[4 marks]

[2 marks]

2f. A second identical ball is placed at the bottom of the bowl and the first ball isdisplaced 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.

3a. At position B the rope starts to extend. Calculate the speed of the block at position B.

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

[3 marks]

[2 marks]

3b. Determine the magnitude of the average resultant force acting on the block between Band C.

3c. Sketch on the diagram the average resultant force acting on the block between B andC. The arrow on the diagram represents the weight of the block.

3d. Calculate the magnitude of the average force exerted by the rope on the blockbetween B and C.

between A and B.

[2 marks]

[2 marks]

[2 marks]

3e. between A and B.

3f. between B and C.

3g. The length reached by the rope at C is 77.4 m. Suggest how energy considerationscould be used to determine the elastic constant of the rope.

An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other

[1 mark]

[1 mark]

[2 marks]

3h.

An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The otherend of the rope is connected to a block which is initially at position A. The block is released fromrest. The mass of the rope is negligible.

The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.

In another test, the block hangs in equilibrium at the end of the same elastic rope. The elasticconstant of the rope is 400 Nm . The block is pulled 3.50 m vertically below the equilibriumposition and is then released from rest.

Calculate the time taken for the block to return to the equilibrium position for the firsttime.

–1

3i. Calculate the speed of the block as it passes the equilibrium position.

Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to the

[2 marks]

[2 marks]

4a.

Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to theground state. Photons are emitted and are incident on a photoelectric surface as shown.

Show that the energy of photons from the UV lamp is about 10 eV.

4b.

The photons cause the emission of electrons from the photoelectric surface. The work functionof the photoelectric surface is 5.1 eV.

Calculate, in J, the maximum kinetic energy of the emitted electrons.

Suggest, with reference to conservation of energy, how the variable voltage source

[2 marks]

[2 marks]

4c. Suggest, with reference to conservation of energy, how the variable voltage sourcecan be used to stop all emitted electrons from reaching the collecting plate.

4d. The variable voltage can be adjusted so that no electrons reach the collecting plate.Write down the minimum value of the voltage for which no electrons reach the collectingplate.

4e.

The electric potential of the photoelectric surface is 0 V. The variable voltage is adjusted so thatthe collecting plate is at –1.2 V.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV.

[2 marks]

[1 mark]

[2 marks]

4f. An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV.Calculate the speed of the electron at the collecting plate.

5a. State the direction of the resultant force on the ball.

5b. On the diagram, construct an arrow of the correct length to represent the weight of theball.

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

[2 marks]

[1 mark]

[2 marks]

5c. Show that the magnitude of the net force F on the ball is given by thefollowing equation.

F =mg

tanθ

5d. 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

[3 marks]

[4 marks]

5e. Outline whether this ball can move on a horizontal circular path of radius equal tothe radius of the bowl.

5f. A second identical ball is placed at the bottom of the bowl and the first ball isdisplaced 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.

The ball is now displaced through a small distance x from the bottom of the bowl and is then

[2 marks]

[3 marks]

5g.

The ball is now displaced through a small distance x from the bottom of the bowl and is thenreleased from rest.

The magnitude of the force on the ball towards the equilibrium position is given by

where R is the radius of the bowl.

Outline why the ball will perform simple harmonic oscillations about the equilibriumposition.

mgx

R

5h. Show that the period of oscillation of the ball is about 6 s.

The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation

[1 mark]

[2 marks]

5i. The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variationwith time t of the velocity v of the ball during one period.

6a.

A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has aradius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with thecylinder able to spin freely between the rails.

The stationary wheel is released from rest and rolls down a slope with the shaft rolling on therails without slipping from point A to point B.

The moment of inertia of the wheel is 1.3 × 10 kg m . Outline what is meant by themoment of inertia.

–4 2

[3 marks]

[1 mark]

6b. In moving from point A to point B, the centre of mass of the wheel falls through avertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 ms after its displacement.–1

6c. Determine the angular velocity of the wheel at B.

6d.

The wheel leaves the rails at point B and travels along the flat track to point C. For a short timethe wheel slips and a frictional force F exists on the edge of the wheel as shown.

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

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

[3 marks]

[1 mark]

[2 marks]

6e. Describe the effect of F on the angular speed of the wheel.

7a.

A girl on a sledge is moving down a snow slope at a uniform speed.

Draw the free-body diagram for the sledge at the position shown on the snow slope.

After leaving the snow slope, the girl on the sledge moves over a horizontal region

[2 marks]

[2 marks]

7b. After leaving the snow slope, the girl on the sledge moves over a horizontal regionof snow. Explain, with reference to the physical origin of the forces, why the verticalforces on the girl must be in equilibrium as she moves over the horizontal region.

7c. When the sledge is moving on the horizontal region of the snow, the girl jumps off thesledge. The girl has no horizontal velocity after the jump. The velocity of the sledgeimmediately after the girl jumps off is 4.2 m s . The mass of the girl is 55 kg and the mass ofthe sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

–1

7d. The girl chooses to jump so that she lands on loosely-packed snow rather than frozenice. Outline why she chooses to land on the snow.

The sledge, without the girl on it, now travels up a snow slope that makes an angle of 6.5˚ to the

[3 marks]

[2 marks]

[3 marks]

7e.

The sledge, without the girl on it, now travels up a snow slope that makes an angle of 6.5˚ to thehorizontal. At the start of the slope, the speed of the sledge is 4.2 m s . The coefficient ofdynamic friction of the sledge on the snow is 0.11.

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

–1

–2

7f. Calculate the distance along the slope at which the sledge stops moving. Assume thatthe coefficient of dynamic friction is constant.

7g. The coefficient of static friction between the sledge and the snow is 0.14. Outline,with a calculation, the subsequent motion of the sledge.

A non-uniform electric field, with field lines as shown, exists in a region where there is no

[3 marks]

[2 marks]

[2 marks]

8a.

A non-uniform electric field, with field lines as shown, exists in a region where there is nogravitational field. X is a point in the electric field. The field lines and X lie in the plane of thepaper.

Outline what is meant by electric field strength.

8b. An electron is placed at X and released from rest. Draw, on the diagram, the direction ofthe force acting on the electron due to the field.

The electron is replaced by a proton which is also released from rest at X. Compare,

[2 marks]

[1 mark]

8c. 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 afterrelease. You may assume that no frictional forces act on the electron or the proton.

9a.

The diagram below shows part of a downhill ski course which starts at point A, 50 m above levelground. Point B is 20 m above level ground.

A skier of mass 65 kg starts from rest at point A and during the ski course some of thegravitational potential energy transferred to kinetic energy.

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

[4 marks]

[2 marks]

9b. Some of the gravitational potential energy transferred into internal energy of the skis,slightly increasing their temperature. Distinguish between internal energy andtemperature.

9c. The dot on the following diagram represents the skier as she passes point B.Draw and label the vertical forces acting on the skier.

9d. The hill at point B has a circular shape with a radius of 20 m. Determine whether theskier will lose contact with the ground at point B.

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

[2 marks]

[2 marks]

[3 marks]

9e. The skier reaches point C with a speed of 8.2 m s . She stops after a distance of 24m 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.

–1

9f.

At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normallyinto the safety net with speed 9.6 m s .

Calculate the impulse required from the net to stop the skier and state an appropriateunit for your answer.

–1

9g. Explain, with reference to change in momentum, why a flexible safety net is less likelyto harm the skier than a rigid barrier.

A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest

[3 marks]

[2 marks]

[2 marks]

10a.

A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from restby a cable pulled by a motor that exerts a horizontal force on the glider throughout the launch.

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

–1

10b. The glider and pilot have a total mass of 492 kg. During the acceleration the glider issubject to an average resistive force of 160 N. Determine the average tension in thecable as the glider accelerates.

The cable is pulled by an electric motor. The motor has an overall efficiency of 23 %.

[2 marks]

[3 marks]

10c. The cable is pulled by an electric motor. The motor has an overall efficiency of 23 %.Determine the average power input to the motor.

10d. The cable is wound onto a cylinder of diameter 1.2 m. Calculate the angular velocity ofthe cylinder at the instant when the glider has a speed of 27 m s . Includean appropriate unit for your answer.

–1

After takeoff the cable is released and the unpowered glider moves horizontally

[3 marks]

[2 marks]

10e. After takeoff the cable is released and the unpowered glider moves horizontallyat constant speed. The wings of the glider provide a lift force. The diagram showsthe 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 showthe horizontal and vertical directions.

10f. Explain, using appropriate laws of motion, how the forces acting on the glidermaintain it in level flight.

10g. At a particular instant in the flight the glider is losing 1.00 m of vertical height for every6.00 m that it goes forward horizontally. At this instant, the horizontal speed of theglider is 12.5 m s . Calculate the velocity of the glider. Give your answer to an appropriatenumber of significant figures.

–1

[2 marks]

[2 marks]

[3 marks]

11a.

A student investigates how light can be used to measure the speed of a toy train.

Light from a laser is incident on a double slit. The light from the slits is detected by a lightsensor attached to the train.

The graph shows the variation with time of the output voltage from the light sensor as the trainmoves parallel to the slits. The output voltage is proportional to the intensity of light incident onthe sensor.

Explain, with reference to the light passing through the slits, why a series of voltagepeaks occurs.

The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10 m.–7

[3 marks]

11b. The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10 m.The slits are 5.0 m from the train track. Calculate the separation between two adjacentpositions of the train when the output voltage is at a maximum.

–7

11c. Estimate the speed of the train.

11d. In another experiment the student replaces the light sensor with a sound sensor. Thetrain travels away from a loudspeaker that is emitting sound waves ofconstant amplitude and frequency towards a reflecting barrier.

The sound sensor gives a graph of the variation of output voltage with time along the track thatis similar in shape to the graph shown in the resource. Explain how this effect arises.

A mass is suspended from the ceiling of a train carriage by a string. The string makes

[1 mark]

[2 marks]

[2 marks]

12. A mass is suspended from the ceiling of a train carriage by a string. The string makesan angle θ with the vertical when the train is accelerating along a straight horizontaltrack.

What is the acceleration of the train?

A. g sin θB. g cos θ

C. g tan θ

D. g

tanθ

13a.

Curling is a game played on a horizontal ice surface. A player pushes a large smooth stoneacross the ice for several seconds and then releases it. The stone moves until friction brings it torest. The graph shows the variation of speed of the stone with time.

The total distance travelled by the stone in 17.5 s is 29.8 m.

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

The diagram shows the stone during its motion after release.

[4 marks]

[3 marks]

13b. 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 thename, the direction and point of application of each force.

14a.

A company designs a spring system for loading ice blocks onto a truck. The ice block is placedin a holder H in front of the spring and an electric motor compresses the spring by pushing H tothe left. When the spring is released the ice block is accelerated towards aramp ABC. When the spring is fully decompressed, the ice block loses contact with the spring atA. The mass of the ice block is 55 kg.

Assume that the surface of the ramp is frictionless and that the masses of the spring and theholder are negligible compared to the mass of the ice block.

(i) The block arrives at C with a speed of 0.90ms . Show that the elastic energystored in the spring is 670J.

(ii) Calculate the speed of the block at A.

−1

Describe the motion of the block

[3 marks]

[4 marks]

14b. Describe the motion of the block

(i) from A to B with reference to Newton's first law.

(ii) from B to C with reference to Newton's second law.

14c. On the axes, sketch a graph to show how the displacement of the block varies withtime from A to C. (You do not have to put numbers on the axes.)

14d. The spring decompression takes 0.42s. Determine the average force that the springexerts on the block.

The electric motor is connected to a source of potential difference 120V and draws a

[3 marks]

[2 marks]

[2 marks]

Printed for Jyvaskylan Lyseon lukio

© International Baccalaureate Organization 2019 International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®

14e. The electric motor is connected to a source of potential difference 120V and draws acurrent of 6.8A. The motor takes 1.5s to compress the spring.

Estimate the efficiency of the motor.

[2 marks]