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Examples & Past Paper for AL Physics
Chapter 1: Statics
 1.2
Different Types of Forces (Weight, Normal Reaction & Tension)
Question 1 (85/I/1)
B
P
A
Q
Two bodies P and Q are connected by a light string A. The weights of P and Q are 4 N and 10 N respectively. P
is connected to the roof by another light string B. If string B is cut and the bodies allowed to fall, the net force
acting on P during free fall is
A.
D.
0N
10 N
B.
E.
4N
14 N
C.
6N
Question 2 (87/I/4)
axle
2 kg
3 kg
An object of mass 3 kg is tied to another object of mass 2 kg with a string passing over a fixed smooth pulley.
The weight of the pulley is negligible. When the objects move under the action of gravity, the vertical upward
force acting on the axle of the pulley is
A.
D.
zero
48 N
B.
E.
10 N
50 N
C.
24 N
Question 3 (86/I/1)
3 kg
30
o
2 kg
An object of mass 3 kg is placed on a smooth plane inclined at 30º to the horizontal. It is connected by a light
string passing over a frictionless pulley to another object of mass 2 kg, as shown above. Given that g = 10 ms-2,
when the system is released, the tension in the string will be
A.
D.
18 N
25 N
B.
E.
20 N
30 N
C.
24 N
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 1
Question 4 (92/I/3)
A simple pendulum is swinging in a vertical plane. When it is at the position shown, which of the following
diagrams best represents the forces acting on the bob? Neglect air friction.
A.
B.
D.
E.
C.
Question 5 (94/II/1; 94AS/II/1)
P
rod
motor
propeller
The above figure shows a propeller-motor system connected by a light, rigid rod to a fixed point P on the
ceiling. The system remains stationary when the motor is on. Which of the following diagrams correctly
represents the forces acting on the propeller-motor system?
A.
B.
D.
E.
C.
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 2
Question 6 (88/I/2)
A smooth block of mass 2 kg slides down a wedge. The wedge, of mass 10 kg, is placed on a horizontal table,
and its inclined plane makes an angle of 30º with the horizontal. If the wedge remains stationary all the time, the
normal reaction of the table acting on the wedge is
A.
D.
15 N
115 N
B.
E.
85 N
120 N
C.
100 N
Question 7 (89/I/5)
P
S
X
Y
30o
30o
In the figure above, X and Y are blocks of mass 1 kg and 2 kg respectively. S is a spring balance of negligible
mass and P is a smooth pulley fixed at the top of two smooth inclined planes. What is the reading of S when X
is held stationary?
A.
D.
5N
20 N
B.
E.
10 N
30 N
C.
15 N
Question 8 (93/I/1)
F1
F2
The resultant of two forces F1 and F2 acting at a point can have a minimum value of 1 N and a maximum value
of 7 N. When the two forces act at right angles to each other, the magnitude of their resultant is
A.
D.
3N
50 N
B.
E.
5N
8N
C.
6N
Question 9 (99/II/2; 99AS/II/3)
A block of mass 5 kg is placed on the inclined surface of the wedge shown above. All contact surfaces are
assumed to be smooth. What is the magnitude of the horizontal force F exerted on the wedge so that it remains
stationary while the block is sliding down the inclined surface with acceleration?
A.
D.
0N
30 N
B.
E.
18 N
32 N
C.
24 N
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 3
 1.2
Different Types of Forces (Elastic Force)
1. Combination of Springs
In Series

The same force F is applied on each spring. The extension in spring 1 and spring 2 is given by
F = k1e1
F = k2e2
kk
k 1 2
 The force constant of the combination is
k1  k 2
Proof
In Parallel

The two springs have the same extension e. The restoring force
in spring 1 and spring 2 is
F1 = k1e
F2 = k2e
 The force constant of the combination is
k = k1 + k2
Proof
Question 10 (89/I/4)
spring A
2N
spring B
3N
Two objects of weights 2 N and 3 N are suspended from a fixed point by two identical light springs A and B as
shown in the diagram. The force constants of the springs are both 1 N/cm. What are the extensions of springs A
and B?
A.
B.
C.
D.
E.
Extension of spring A
5 cm
5 cm
3 cm
3 cm
2 cm
Extension of spring B
3 cm
2 cm
2 cm
5 cm
3 cm
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 4
Question 11 (96/II/5; 96AS/II/5)
A
B
The figure shows two blocks A and B, each of mass m, connected by two light springs to a fixed support. Each
spring has a force constant k. What is the total extension of the system when it is at static equilibrium?
A.
D.
mg/(2k)
2mg/k
B.
E.
mg/k
3mg/k
C.
3mg/(2k)
Question 12 (98/II/1; 98AS/II/1)
Two identical light springs are connected with two masses of 1.0 kg and 0.5 kg as shown. Which of the
following statement is/are correct?
(1) The tension in the upper spring is double that in the lower spring.
(2) The force acting on the ceiling by the whole system is 15 N.
(3) The tension in the upper spring will remain unchanged if the two masses are exchanged in position.
A.
D.
(1) only
(2) and (3) only
B.
E.
(3) only
(1), (2) and (3)
C.
(1) and (2) only
Question 13 (99/II/1; 99AS/II/1)
Two object A and B of equal mass m are connected by two identical light springs and are placed on a horizontal
smooth surface. A horizontal force F is applied to B so that the system is in equilibrium. If the applied force F is
suddenly removed, what are the magnitudes of the acceleration of each object at the instant when force F is
removed?
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 5
Acceleration of A
A.
zero
B.
zero
F
2m
F
m
F
m
C.
D.
E.
 1.2
Acceleration of B
F
m
zero
F
m
zero
F
m
Different Types of Forces (Friction)
Example 1
A 2.0 kg block of wood is placed on a rough
horizontal surface. The coefficient of static friction
between the block and the surface is 1.2. What is the
friction on the block when a horizontal force equal to
its weight is applied on it? How large is the force
required to start the block moving?
Example 2
A 3 kg block of wood is pulled with a 30 N force on
a horizontal rough table. The acceleration is 2 ms-2.
Determine the coefficient of kinetic friction between
the block and the table.
1. Effect of Changing Surface Area on Friction
 Changing the “surface area” of the body has little effect on the “actual area” of contact, for the same normal
reaction. Thus, the limiting static friction is independent on the surface area of the body unless it is very
small.
2. Reducing Friction



By lubricant oil - Friction can be reduced by putting a liquid (e.g. lubricant oil) between the interfaces.
Molecules in a liquid are able to slip over each other. Graphite is commonly used to
coat surface to reduce friction because the planes of atoms can easily slip over one
another.
By bearing - Bearing are small steel spheres inserted between a fixed support and a rotating shaft. The
bearings roll as the shaft turns. This prevents sliding between contact surfaces.
By Magnetic Force - Levitation by magnetic force eliminates direct surface contact altogether.
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 6
3. Role of friction
1.
Static friction is very useful, although sometimes we are not aware of it. Without friction, objects like
plates and cups would slide off a table. The frictional push on the tyres of a car by the road enables the car
to accelerate, turn around a bend and decelerate.
2.
As there is no relative motion between the surfaces, _____________ friction never contributes to energy
loss.
3.
Since __________________ friction occurs when there is relative motion between two surfaces, it is
responsible for nearly all the mechanical energy loss.
4. Friction in a car
1.
When a car accelerates, _______________ friction exists between the tyres and the road and is responsible
for the propelling force. Meanwhile, ________________ friction exists between the shaft and the chassis
(body of the car).
2.
When a car undergoes normal braking without skidding, ________________ friction exists between the
brake pads and rotating wheels, while _________________ friction is found between the tyres and the
road.
3.
However, on wet or icy road, the _____________ friction is greatly reduced and the wheels would be
easily locked, casing skidding. Skidding would also occur if the brake pads are pressed too hard.
4.
Once skidding occurs, the motion of the car will be out of control. It simply slides straight away. Since the
turning of a car relies on the ____________ friction between the tyres and the road, steering is impossible.
5.
It is interesting to note that the ________________ friction does not contribute to energy loss when a car is
in motion. It functions as an external force to accelerate or decelerates the car only.
5. Anti-lock Braking System (ABS)

In normal driving, a moving car is stopped by the static friction between the tyres and the road. In usual,
pressing the pedal harder produces a greater deceleration. But if the pedal is pressed too hard, the wheels
are locked up and sliding occurs. The driver can no longer control the car’s direction. Panic follows, and
the natural reaction is to stamp even harder on the brake, which makes things worse.

Anti-lock brakes are designed so that the brakes are released and applied in quick succession
automatically. It consists of an electronic sensor system which can detect how rapid the wheels are
decelerated. Signals from the sensor system control the hydraulic pressure on the brakes so as to achieve
the best and safest deceleration.
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 7
Question 14 (80/I/1)
A body is subject to an applied driving force F and a constant resistive force. Which of the graphs below
represents the variation of the acceleration a of the body with the applied driving force F?
A.
B.
D.
E.
C
Question 15 (82/I/4)
A builder using a pulley system to lift a bucket of cement of weight 150 N exerts a steady force F and pulls
30 m of rope through the system in order to raise the bucket 10 m. The friction in the system is small but NOT
negligible. The value of the force F is most probably
A.
D.
less than 50 N.
between 150 N and 450 N.
B.
E.
exactly equal to 50 N.
more than 450 N.
C.
between 50 N and 150 N.
Question 16 (84/I/1)
P
A horizontal force P is applied to a wooden block at rest on a rough horizontal table. P is increased uniformly
from zero. Which of the following graphs best describes the variation of the frictional force F acting on the
block with P?
A.
B.
C
0
0
P
D.
P
0
P
E.
F
0
F
F
F
F
P
0
P
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 8
Question 17 (91/I/2)
An object of mass m slides with constant acceleration a down a plane making an angle  with the horizontal.
The frictional force acting on the object is
A.
D.
mg - ma
(mg - ma) sin 
B.
E.
mg - ma sin 
(mg + ma) sin 
C.
mg sin  - ma
Question 18 (95/II/1)
When given a slight push, a toy car moves freely with constant velocity down a plane inclined at 20º to the
horizontal. If the mass of the car is 0.5 kg, find the force parallel to the inclined plane for pulling the car up the
plane with constant velocity.
A.
D.
1.7 N
6.7 N
B.
E.
3.4 N
9.4 N
C.
4.7 N
Question 19 (97/II/1; 97AS/II/1)
A
B
F
Two wooden blocks A and B are connected by a string which passes over a smooth, fixed pulley as shown. The
maximum friction between any two surfaces is 2 N. If a horizontal force F is applied to block B, find its
minimum value for moving B.
A.
D.
2N
8N
 1.4
B.
E.
4N
10 N
C.
6N
Moment of a Force
Example 3
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 9
Example 4
A uniform ladder 8 m long and of mass 75 kg stands on the pavement resting at an angle of 30 against a
smooth vertical wall. A boy of mass 50 kg climbs the ladder to a point 3 m above the ground. Calculate the
magnitudes and directions of the forces exerted by the ladder
a) on the wall
b) on the ground.
Question 20 (94/II/3)
Q
P
R
X
A uniform metre rule of mass 0.15 kg is hinged to a wall at P and the other end R is connected by a wire
attached to the wall at Q, vertically above P. A block X of mass 0.1 kg is hung from the rule 30 cm from R. The
metre rule is horizontal. Find the moment about P produced by the tension in the wire.
A.
D.
1.45 Nm
0.70 Nm
B.
E.
1.05 Nm
0.25 Nm
C.
0.75 Nm
Question 21 (95/II/8; 95AS/II/6)
C
wire
wall
B
beam
A
W
The figure shows a uniform rigid beam AB, pivoted at A, held in horizontal position by a wire attached to a wall
at point C, vertically above A. The beam carries a load W. If W is shifted gradually from A towards B, which of
the following quantities will increase?
(1) The tension in the wire.
(2) The horizontal compression force in the beam.
(3) The vertical component of the reaction at A.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 10
Example 5
A man holds a tray at one edge with the thumb and fingers of one hand, so that the forces acting on it are as
shown in the following figure.
(a) (i)
ii)
If the weight W of the tray is 5 N, find the force X while the tray is empty.
Calculate the value of the force Y.
(b) The man now puts a can of drink of weight 5 N on the tray. Calculate the new values of X and Y
if he puts the drink
(i) in the middle of the tray.
(ii) at the extreme right-hand end.
(c) Where should he put the drink so as not to change the value of X?
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 11
Example 6
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 12
Exercise on Moments
1.
2.
3.
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Chapter 1: Statics
Page 13
4.
5.
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Chapter 1: Statics
Page 14
6.
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Chapter 1: Statics
Page 15
7.
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 16
Answer for Exercise on Moments
1.
3.
2.
a)
(i)
B
4.
(a) (i)
Upwards
(iii) Yes. The applied force is 5 times less than the force holding the
cap at B.
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 17
6.
(c) (i)
A smaller force can be used.
5.
(iv) Same as the total weight of the boy and the piece of wood.
The total upward force equals to the total downward force.
(b) Yes. The reaction at the pivot provides the rest of the force required.
No. End B should be pulled downward by a string.
(ii) No. It is because the piece of wood will turn over.
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 18
Example 6
7.
a)
No. It is because those with a larger mass should be placed near the
housewife, or else a much larger effort has to be required.
(C) (i)
Left:
downwards
Right:
upwards
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Examples & Past Paper for AL Physics
Chapter 1: Statics
Page 19