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With 6 weeks left and the whole syllabus for the SAT II Math 2 Subject Test to be covered, I felt hopeless and stressed. Thanks to my tutor’s enthusiasm and positive energy, I got over the fear and managed to learn the whole syllabus in 6 weeks! The tutor explained things thoroughly and made the classes fun. He always made sure I understood everything. Thank you so much - I wouldn't have been able to do it without you!

IB Physics HL Kinematics

Subject

IB Physics HL

Question

1. The graph shows the variation with time t of the velocity v of an object.

Which one of the following graphs best represents the variation with time t of the acceleration a of the object?

(1)

2. A ball, initially at rest, takes time t to fall through a vertical distance h. If air resistance is ignored, the time taken for the ball to fall from rest through a vertical distance 9h is

A. 3t.

B. 5t.

C. 9t.

D. 10t.

(1)

3. A raindrop falling through air reaches a terminal velocity before hitting the ground. At terminal velocity, the frictional force on the raindrop is

A. zero.

B. less than the weight of the raindrop.

C. greater than the weight of the raindrop.

D. equal to the weight of the raindrop.

(1)

4. The diagram below shows the path of a projectile in the absence of air resistance.

Which one of the following diagrams best represents the path of the projectile under the same initial conditions when the air resistance is taken into account? (The path in absence of air resistance is shown for comparison as a dotted line.)

(1)

5. A sailing boat is moving with constant velocity v to the right parallel to the dock.

Sailor Hulot, up on the mast, drops his telescope at the moment he is opposite Lucie who is standing on the dock. Which one of the following best shows the path of the falling telescope as seen by Lucie?

(1)

6. This question is about forces on charged particles.

(a) A charged particle is situated in a field of force. Deduce the nature of the force-field (magnetic, electric or gravitational) when the force on the particle

(i) is along the direction of the field regardless of its charge and velocity;

...........................................................................................................................

(ii) is independent of the velocity of the particle but depends on its charge;

...........................................................................................................................

(iii) depends on the velocity of the particle and its charge.

...........................................................................................................................

(5)

(b) An electron is accelerated from rest in a vacuum through a potential difference of 2.1 kV. Deduce that the final speed of the electron is 2.7 × 107 m s–1.

.....................................................................................................................................

(3)

The electron in (b) then enters a region of uniform electric field between two conducting horizontal metal plates as shown below.

The electric field outside the region of the plates may be assumed to be zero. The potential difference between the plates is 95 V and their separation is 2.2 cm.

As the electron enters the region of the electric field, it is travelling parallel to the plates.

(c) (i) On the diagram above, draw an arrow at P to show the direction of the force due to the electric field acting on the electron.

(1)

(ii) Calculate the force on the electron due to the electric field.

...........................................................................................................................

(3)

(d) The plates in the diagram above are of length 12 cm. Determine

(i) the time of flight between the plates.

...........................................................................................................................

(1)

(ii) the vertical distance moved by the electron during its passage between the plates.

...........................................................................................................................

(3)

(e) Suggest why gravitational effects were not considered when calculating the deflection of the electron.

.....................................................................................................................................

(2)

(f) In a mass spectrometer, electric and magnetic fields are used to select charged particles of one particular speed. A uniform magnetic field is applied in the region between the plates, such that the electron passes between the plates without being deviated.

For this magnetic field,

(i) state and explain its direction;

...........................................................................................................................

(3)

(ii) determine its magnitude.

...........................................................................................................................

(2)

(g) The electric and magnetic fields in (f) remain unchanged. Giving a brief explanation in each case, compare qualitatively the deflection of the electron in (f) with that of

(i) an electron travelling at a greater initial speed;

...........................................................................................................................

(ii) a proton having the same speed;

...........................................................................................................................

(iii) an alpha particle (α-particle) having the same speed.

...........................................................................................................................

(7)

(Total 30 marks)

7. An athlete runs round a circular track at constant speed. Which one of the following graphs best represents the variation with time t of the magnitude d of the displacement of the athlete from the starting position during one lap of the track?

(1)

8. A ball is released from rest near the surface of the Moon. Which one of the following quantities increases at a constant rate?

A. Only distance fallen

B. Only speed

C. Only speed and distance fallen

D. Only speed and acceleration

(1)

9. A stone is thrown horizontally from the top of a high cliff. Assuming air resistance is negligible, what is the effect of gravitational force on the horizontal and on the vertical components of the velocity of the stone?

	Vertical component of velocity	Horizontal component of velocity
A.	increases to a constant value	stays constant
B.	increases continuously	stays constant
C.	increases to a constant value	decreases to zero
D.	increases continuously	decreases to zero

(1)

10. This question is about the kinematics of an elevator (lift).

(a) Explain the difference between the gravitational mass and the inertial mass of an object.

.....................................................................................................................................

(3)

An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s velocity with time is shown below.

(b) The mass of the elevator is 250 kg. Use this information to calculate

(i) the acceleration of the elevator during the first 0.50 s.

...........................................................................................................................

(2)

(ii) the total distance travelled by the elevator.

...........................................................................................................................

(2)

(iii) the minimum work required to raise the elevator to the higher floor.

...........................................................................................................................

(2)

(iv) the minimum average power required to raise the elevator to the higher floor.

...........................................................................................................................

(2)

(v) the efficiency of the electric motor that lifts the elevator, given that the input power to the motor is 5.0 kW.

...........................................................................................................................

(2)

(c) On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain your reasoning. (The simplified version is shown as a dotted line)

(2)

The elevator is supported by a cable. The diagram below is a free-body force diagram for when the elevator is moving upwards during the first 0.50 s.

(d) In the space below, draw free-body force diagrams for the elevator during the following time intervals.

(i) 0.5 to 11.50 s (ii) 11.50 to 12.00 s

(3)

A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on the scales is W.

(e) On the axes below, sketch a graph to show how the reading on the scales varies during the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you do not need to add any values.)

(3)

(f) The elevator now returns to the ground floor where it comes to rest. Describe and explain the energy changes that take place during the whole up and down journey.

.....................................................................................................................................

(4)

(Total 25 marks)

11. This question is about projectile motion and the use of an energy argument to find the speed with which a thrown stone lands in the sea.

Christina stands close to the edge of a vertical cliff and throws a stone. The diagram below (not drawn to scale) shows part of the trajectory of the stone. Air resistance is negligible.

Point P on the diagram is the highest point reached by the stone and point Q is at the same height above sea level as point O.

(a) At point P on the diagram above draw arrows to represent

(i) the acceleration of the stone (label this A).

(1)

(ii) the velocity of the stone (label this V).

(1)

The stone leaves Christina’s hand (point O) at a speed of 15 m s−1 in the direction shown. Her hand is at a height of 25 m above sea level. The mass of the stone is 160 g. The acceleration due to gravity g = 10 m s−2.

(b) (i) Calculate the kinetic energy of the stone immediately after it leaves Christina’s hand.

...........................................................................................................................

(1)

(ii) State the value of the kinetic energy at point Q.

...........................................................................................................................

(1)

(iii) Calculate the loss in potential energy of the stone in falling from point Q to hitting the sea.

...........................................................................................................................

(1)

(iv) Determine the speed with which the stone hits the sea.

...........................................................................................................................

(2)

(Total 7 marks)

12. A car is heading due East at a speed of 10 m s−1. A bird is flying due North at a speed of 4 m s−1, as shown below.

Answer

1. A

[1]

2. A

[1]

3. D

[1]

4. A

[1]

5. C

[1]

6. (a) (i) if independent of charge;
must be gravitational;

(ii) depends on charge so electric or magnetic;
independent of velocity so electric;

(iii) (depends on velocity and charge, so) magnetic; 5 max

(b) idea of change in electric potential energy = gain in kinetic energy;
qDV = ½ mv2;
(1.6 × 10–19 × 2.1 × 103) = (½ × 9.1 × 10–31 ×v2) / v = 7.38 × 1014; 3

Award [0] for v = 2.7 × 107 m s–1.

(ii) force = ;
=
= 6.9 × 10–16 N; 3

(d) (i) time to cross plates = = 4.44 × 10–9 s; 1

(ii) vertical acceleration = (= 7.58 × 1014 m s–2);
distance = ½ × a × t2;
= ½ × 7.58 × 1014 × (4.44 × 10–9)2 allow ecf;
= 7.5 × 10–3 m; 3

(e) gravitational force is very small;
small in comparison with electric or magnetic force; 2

(f) (i) force due to B-field must be downwards;
mention of Fleming’s left-hand rule / right-hand palm rule;
hence field into paper; 3

(ii) Bqv = 6.9 × 10–16 N allow ecf
B = ;
= 1.6 × 10–4 T; 2 max

(g) (i) electric force unchanged;
magnetic force is greater;
hence deflection downwards;

(ii) both forces reversed in direction;
but not changed in magnitude;
hence undeflected;

(iii) undeflected; 7 max

[30]

7. C

[1]

8. B

[1]

9. B

[1]

10. (a) statement that gravitational mass and inertial mass have the same numerical value;
understanding of what gravitational mass means;
eg “a quantity that determines the gravitational force on the object”
understanding of what inertial mass means;
eg “a quantity that determines the acceleration of the object” 3 max

(b) (i) the acceleration = gradient of first section of graph;
acceleration = 0.80 / 0.50 = 1.6 m s–2; 2 max

Accept bald correct answer for full marks.

(ii) the total distance travelled by the lift = area under graph;
distance = (11 × 0.80) + (0.50 × 0.80) = 8.8 + 0.4 = 9.2 m; 2 max

Accept bald correct answer for full marks.

(iii) the work done = PE gained (= force × distance);
work done = 2500 × 9.2 = 23000 J = 23 kJ; 2 max

Accept bald correct answer for full marks.

(iv)    correct substitution into power = work done / time taken
                                             = 23000 / 12;
                                             = 1916 W
                                             = 1.9 kW;                                          2 max

(v)     correct substitution into efficiency = power out / power in
                                                  = 1.9 / 5.0;
                                                  = 0.38 = 38%;                               2 max

(c) graphs should show curving or “shoulders” at the changes;
since acceleration must be finite / speed cannot change instantaneously /
OWTTE; 2 max

(d) Mark part (i) and (ii) together.
weight arrow the same in both diagrams;
magnitude of tension (size of arrow) equal to weight in (i);
magnitude of tension (size of arrow) less than weight in (ii);

(i) 0.50 to 11.50 s (ii) 11.50 to 12.00 s

3 max

(e) a constant value greater than W from 0.00 to 0.50 s;
a constant value equal to W from 0.50 to 11.50 s;
a constant value less than W from 11.50 to 12.00 s;

3 max

(f) [1] for each appropriate and valid point. Essentially [2] for journey
up and [2] for journey down. Some explanation or justification is
required for full marks eg
the law of conservation of energy does apply to round trip;
energy is all dissipated into heat and sound;
on the way up, most electrical energy converted into g.PE, initially
some electrical energy is converted into K.E;
on the way down electrical energy does work “breaking” lift some
(not all) g.PE is converted into KE; 4 max

Reject answers that imply that PE converts into KE as lift falls.

[25]

11. (a)

(i) acceleration; 1 max

(ii) velocity; 1 max

(b) (i) KE = mv2 = 0.08 × 225 = 18 J; 1 max

(ii) 18 J; 1 max

(iii) loss in PE = mgh = 40 J; 1 max

(iv) total KE = 58 J;
v = = 27 m s–1; 2 max

[7]

12. B

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