Download Chapter 3 Forces Section A Multiple Choice 1 A cylindrical block of

Chapter 3
Forces
Section A Multiple Choice
A cylindrical block of wood has a cross-sectional area A and weight
W. It is totally immersed in water with its axis vertical. The block
experiences pressures pt and pb at its top and bottom surfaces
respectively.
Which of the following expressions is equal to the upthrust on the
block?
1
(
02s)
A (pb - pt)A + W
B (pb - pt)
C (pb - pt)A
D (pb - pt)A - W
2 The vector diagram shows three coplanar forces acting on an object at
P.
(02s)
The magnitude of the resultant of these three forces is 1 N.
What is the direction of this resultant?
A ↓
B ↘
C ↙
D ↗
3 A submarine descends vertically at constant velocity. The three forces
acting on the submarine are viscous drag, upthrust and weight.
(02s)
Which relationship between their magnitudes is correct?
A weight < drag
B weight = drag
C weight < upthrust
D weight > upthrust
4 A ruler of length 0.30mis pivoted at its centre. Equal and opposite
forces of magnitude 2.0N are applied to the ends of the ruler, creating
a couple as shown.
What is the magnitude of the torque of the couple on the ruler when
it is in the position shown?
(02s)
A 0.23Nm
B 0.39Nm
C 0.46Nm
D 0.60Nm
5 The diagram shows two vectors X and Y.
(02s)
In which vector triangle does the vector Z show the magnitude and
direction of vector X – Y?
6
uniform metre rule of mass 100 g is supported by a knife-edge at the
40 cm mark and a string at the 100 cm mark. The string passes round
a frictionless pulley and carries a mass of 20 g as shown in the
diagram.
(02w)
At which mark on the rule must a 50 g mass be suspended so that the
rule balances?
A 4 cm
B 36 cm
C 44 cm
D 96 cm
7 The diagrams represent systems of coplanar forces acting at a point.
The lengths of the force vectors represent the magnitudes of the forces.
(02w)
Which system of forces is in equilibrium?
8 What is meant by the weight of an object?
(02w)
A the gravitational field acting on the object
B the gravitational force acting on the object
C the mass of the object multiplied by gravity
D the object’s mass multiplied by its acceleration
9 Which of the following pairs of forces, acting on a circular object,
constitutes a couple?
(02w)
10
A pendulum bob is held stationary by a horizontal force H. The three
forces acting on the bob are shown in the diagram.
(02w)
The tension in the string of the pendulum is T. The weight of the
pendulum bob is W.
Which statement is correct?
A H = T cos30
B T= H sin30
C W = T cos30
D W = T sin30
11
Two forces, each of 10 N, act at a point P as shown in the diagram.
The angle between the directions of the forces is 120°.
(03s)
What is the magnitude of the resultant force?
A 5N
B 10N
C 17N
D 20N
12 The diagram shows four forces applied to a circular object.
(03s)
Which of the following describes the resultant force and resultant
torque on the object?
resultant force
resultant torque
A
zero
zero
B
zero
non-zero
C
non-zero
zero
D
non-zero
non-zero
13 A balloon is acted upon by three forces, weight, upthrust and sideways
force due to the wind, as shown in the diagram.
(03s)
What is the vertical component of the resultant force on the balloon?
A 500 N
B 1000 N
C 10 000 N
D 10 500N
14
A force of 5N may be represented by two perpendicular components OY
and OX as shown in the diagram, which is not drawn to scale.
(03w)
OY is of magnitude 3N.
What is the magnitude of OX?
A 2N
B 3N
C 4N
D 5N
15 A hinged door is held closed in the horizontal position by a cable.
Three forces act on the door: the weight W of the door, the tension
T in the cable, and the force H at the hinge.
(03w)
Which list gives the three forces in increasing order of magnitude?
A H,T,W
B T,H,W
C W,H,T
D W,T,H
16 A spanner is used to tighten a nut as shown.
(03w)
A force F is applied at right-angles to the spanner at a distance of
0.25 m from the centre of the nut. When the nut is fully tightened,
the applied force is 200 N.
What is the resistive torque, in an anticlockwise direction,
preventing further tightening?
A 8Nm
B 25Nm
C 50Nm
D 800Nm
17 Two parallel forces, each of magnitude F, act on a body as shown.
(03w)
What is the magnitude of the torque on the body produced by these
forces?
18
A Fd
B Fs
C 2Fd
D 2Fs
The diagram shows a sign of weight 20 N suspended from a pole, attached
to a wall. The pole is kept in equilibrium by a wire attached at point
X of the pole.
(04s)
The force exerted by the pole at point X is F, and the tension in the
wire is 40 N.
Which diagram represents the three forces acting at point X?
19
A uniform beam of weight 50 N is 3.0 m long and is supported on a pivot
situated 1.0 m from one end. When a load of weight W is hung from that
end, the beam is in equilibrium, as shown in the diagram.
(04s)
What is the value of W ?
A 25 N
B 50 N
C 75 N
D 100 N
20 Which two vector diagrams represent forces in equilibrium?
(04w)
A P and Q
B Q and R
C R and S
D S and P
21 A long uniform beam is pivoted at one end. A force of 300 N is applied
to hold the beam horizontally.
(04w)
What is the weight of the beam?
A 300 N
B 480 N
C 600 N
D 960 N
22 The vector diagram shows three coplanar forces acting on an object
a
t
P
.
(
0
5
s
)
The magnitude of the resultant of these three forces is 1 N.
What is the direction of this resultant?
A↓
B ↘
C↙
D↗
23 An L-shaped rigid lever arm is pivoted at point P.
(05s)
Three forces act on the lever arm, as shown in the diagram.
What is the magnitude of the resultant moment of these forces about
point P?
A 30 Nm
B 35 Nm
C 50 Nm
D 90 Nm
24 What is the centre of gravity of an object?
(05s)
A the geometrical centre of the object
B the point about which the total torque is zero
C the point at which the weight of the object may be considered to
act
D the point through which gravity acts
25
A stone is projected horizontally in a vacuum and moves along a path
as shown. X is a point on this path. XV and XH are vertical and
horizontal lines respectively through X. XT is the tangent to the path
at X.
(05w)
Along which direction or directions do forces act on the stone at X?
A XV
B XH
C XV and XH
D XT
26 A uniform beam of weight 100 N is pivoted at P as shown. Weights of
10 N and 20 N are attached to its ends.
(05w)
The length of the beam is marked off at 0.1 m intervals.
At which point should a further weight of 20 N be attached to achieve
equilibrium?
27 The diagram shows four forces applied to a circular object.
(05w)
Which of the following describes the resultant force and resultant
torque on the object?
resultant force
resultant torque
A
non-zero
non-zero
B
non-zero
zero
C
zero
non-zero
D
zero
zero
28 The gravitational field strength on the surface of planet P is one
tenth of that on the surface of planet Q.
(05w)
On the surface of P, a body has its mass measured to be 1.0 kg and
its weight measured to be 1.0 N.
What results are obtained for measurements of the mass and weight of
the same body on the surface of planet Q?
mass on Q
weight on Q
A
1.0kg
0.1N
B
1.0kg
10N
C
10kg
10N
D
10kg
100N
29 A force F is applied to a beam at a distance d from a pivot. The force
acts at an angle θ to a line perpendicular to the beam.
(06s)
Which combination will cause the largest turning effect about the
pivot?
30
F
d
A
large
large
B
large
large
C
small
small
D
small
large
A rigid uniform bar of length 2.4 m

large
small
large
small
is pivoted horizontally at its
m
i
d
p
o
i
n
t
.
(
0
6
s
)
Weights are hung from two points of the bar as shown in the diagram.
To maintain horizontal equilibrium, a couple is applied to the bar.
What is the torque and direction of this couple?
A 40 Nm clockwise
B 40 Nm anticlockwise
C 80 Nm clockwise
D 80 Nm anticlockwise
31 The diagrams show three forces acting on a body.
(06s)
In which diagram is the body in equilibrium?
32
X?
A rigid circular disc of radius r has its centre at X. A number of
forces of equal magnitude F act at the edge of the disc. All the forces
are in the plane of the disc.
(06w)
Which arrangement of forces provides a moment of magnitude 2Fr about
33
Three coplanar forces, each of magnitude 10 N, act through the same
point of a body in the directions shown.
(06w)
What is the magnitude of the resultant force?
A 0 N
B 1.3 N
C 7.3 N
D 10 N
34 Which force is caused by a pressure difference?
(06w)
A friction
B upthrust
C viscous force
D weight
35 Two 8.0 N forces act at each end of a beam of length 0.60m. The forces
are parallel and act in opposite directions. The angle between the
forces and the beam is 60°.
(07s)
What is the torque of the couple exerted on the beam?
A 2.4Nm
B 4.2Nm
C 4.8Nm
D 9.6Nm
36 What is meant by the weight of an object?
(07s)
A
B
C
D
37
the
the
the
the
gravitational field acting on the object
gravitational force acting on the object
mass of the object multiplied by gravity
object’s mass multiplied by its acceleration
The diagram shows a plan view of a door which requires a moment of
12Nm to open it.
(07w)
What is the minimum force that must be applied at the door’s midpoint
to ensure it opens?
A 4.8N
B 9.6N
C 15N
D 30N
38 The symbol represents the acceleration of free fall.
(07w)
Which of these statements is correct?
A is gravity.
B is reduced by air resistance.
C is the ratio weight / mass.
D is the weight of an object.
39 Which two vector diagrams represent forces in equilibrium?
(07w)
A P and Q
40
Y.
B Q and R
C R and S
D S and P
The diagram shows a diving-board held in position by two rods X and
(01s)
Which additional forces do these rods exert on the board when a diver
of weight 600N stands on the right-hand end?
at X (downwards) at Y (upwards)
A
400N
1000N
B
600N
1200N
C
900N
600N
D
900N
1500N
41 A small ball of weight W is suspended by a light thread. A strong wind
blows horizontally. exerting a constant force F on the ball. The
thread makes an angle  to the vertical as shown.
(01s)
Which equation correctly relates  , F and W?
42
A cos  = FIW
B sin  = FIW
C tan  = FIW
D tan  = WIF
Two co-planar forces act on the rim of a wheel. The forces are equal
i
n
m
a
g
n
i
t
u
d
e
.
(
0
1
s
)
Which arrangement of forces is a couple?
43 Two forces act on a circular disc as shown.
(01s)
Which diagram shows the line of action of the resultant force?
44 What is the definition of force?
(01w)
A the mass of a body multiplied by its acceleration
B
C
D
45 A
(01w)
the power input to a body divided by its velocity
the rate of change of momentum of a body
the work done on a body divided by its displacement
street lamp is fixed to a wall by a metal rod and a cable.
Which vector triangle represents the forces acting t point P?
46 A wheel of radius 0.70m has a couple applied to it as shown.
(01w)
What is the torque on the wheel?
A 0
B 28Nm
C 56Nm
47
D 112Nm
Two forces X and Y act at a point P as shown. The lengths of the lines
represent the magnitudes of the forces.
(01w)
Which vector diagram shows the resultant R of these two forces?
48
A trailer of weight 30 KN is hitched to a cab at the point X as shown
in the diagram below.
(01w)
What upward force is exerted by the cab on the trailer at the point
X?
49
A 3Kn
B 15kN
C 30kN
D 60kN
A ball of weight W slides along a smooth horizontal surface until it
falls off the edge at time T.
(01w)
Which graph represents how the resultant vertical downwards force F,
acting on the ball, varies with time t as the ball moves from position
X to position Y?
Section B Structured Questions
1
(a) State the conditions necessary for the equilibrium of a body which
is acted up on by a number of forces.
(01w)
1 ............................................................
..............................................................
..................2...........................................
..............................................................
.................................[2]
(b) Three identical springs S1, S2 and S3 are attached to a point A such
that the angle between any two of the spring is 120°, as shown
in Fig.3.1.
Fig.3.1
The springs have extended elastically and the extensions of S1 and
S2 are x. Determine, in terms of x, the extension of S3 such that
the system of springs is in equilibrium. Explain your working.
extension of S3
= .....................[3]
(c) The lid of a box is hinged along one edge E, as shown in Fig.3.2.
The lid is held open by means of a horizontal cord attached to the
edge F of the lid. The centre of gravity of the lid is at point
C.
On Fig.3.2 draw
(i) an arrow,
(ii) an arrow,
acting on
(iii) an arrow,
the lid.
labelled W, to represent the weight of the lid,
labelled T, to represent the tension in the cord
the lid,
labelled R, to represet the force of the hinge on
[3]
2 (a) Explain what is meant by the centre of gravity of an object.
(02s)
..............................................................
..............................................................
..................
..............................................................
......[2]
(b) A non-uniform plank of wood XY is 2.50 m long and weighs 950 N.
Force-meters (spring balances) A and B are attached to the plank
at a distance of 0.40 m from each end, as illustrated in Fig. 3.1.
When the plank is horizontal, force-meter A records 570 N.
(i) Calculate the reading on force-meter B.
reading
= ................ N
(ii) On Fig. 3.1, mark a likely position for the centre of gravity of
the plank.
(iii) Determine the distance of the centre of gravity from the end X
of the plank.
distance
= ............. m[6]
3 (a) Define the moment of a force.
(03w)
..............................................................
..............................................................
...............[2]
(b) State the two conditions necessry for a body to be in equilibrium.
1. ...........................................................
..............................................................
..................
2. ...........................................................
..............................................................
...............[2]
(c) Two parallel atrings S1 and S2 are attached to a disc of diameter
12cm, as shown in Fig.3.1.
The disc is free to rotate about an axis normal to its plane. The
axis passes
through the centre C of the disc.
A lever of length 30cm is attached to the disc. When a force F is
applied at right angles to the lever at its end, equal forces are
produced in S1 and S2. The disc remains in equilibrium.
(i) On Fig.3.1, show the firection of the force in each string that
acts on the disc.
[1]
(ii) For a force F of magnitude 150N, determine
1. the moment of force F about the centre of the disc.
moment
= .....................Nm
2. the torque of the couple produced by the forces in the
strings,
torque
= ...................Nm
3. the force in S1.
force= ...................N[4]
4 (a) Explain what is meant by the centre of gravity of a body.
(05w)
..............................................................
..............................................................
..................
..............................................................
..... [2]
(b) An irregularly-shaped piece of cardboard is hung freely from one
point near its edge, as shown in Fig. 2.1.
Explain why the cardboard will come to rest with its centre of
gravity vertically below the pivot. You may draw on Fig. 2.1 if
you wish.
..............................................................
..............................................................
..................
..............................................................
......[2]
5
A rod AB is hinged to a wall at A. The rod is held horizontally by means
of a cord BD, attached to the rod at end B and to the wall at D, as
shown in Fig. 2.1.
(06s)
The rod has weight W and the centre of gravity of the rod is at C. The
rod is held in equilibrium by a force T in the cord and a force F produced
at the hinge.
(a) Explain what is meant by
(i) the centre of gravity of a body,
...........................................................
...........................................................
...........................................................
....................... [2]
(ii) the equilibrium of a body.
...........................................................
...........................................................
..................
...........................................................
..... [2]
(b) The line of action of the weight W of the rod passes through the
cord at point P.
Explain why, for the rod to be in equilibrium, the force F produced
at the hinge must also pass through point P.
..............................................................
..............................................................
..................
..............................................................
..............................................................
.............. [2]
(c) The forces F and T make angles α and β respectively with the rod
2
and AC =
AB, as shown in Fig. 2.1.
3
Write down equations, in terms of F, W, T, α and β, to represent
(i) the resolution of forces horizontally,
...........................................................
......[1]
(ii) the resolution of forces vertically,
...........................................................
......[1]
(iii) the taking of moments about A.
...........................................................
......[1]