CHAPTER 4
FORCES
The following content has not been through the Cambridge Assessment International Education endorsement process.
1
•
A main force is responsible to
enable the wau bulan to fly.
Where does this force come
from?
•
What other forces are acting
on the kite when it is flying in
the air?
•
A big wau bulan will not fly
when the wind is not strong
enough. Why?
2
4.1 Forces
In this section, you will learn the
following:
•
Know the effects of forces.
•
Sketch, plot and interpret load–extension
graphs and describe the associated
experimental procedures.
•
Define spring constant.
•
Recall and use the equation k =
•
Define and use the term limit of
proportionality, and identify this point on
a load–extension graph.
F
x
3
What are some effects of forces?
Effects of some forces (Figure 4.1 of SB (Student’s Book))
4
What is a load–extension graph?
When a load is attached to the spring, the spring extends.
The extension of the spring depends on the
amount of force applied (Figure 4.2 of SB)
Load–extension graph:
• Shows the relationship between the force and the
extension of an elastic solid
• Helps determine magnitude of an unknown force on an
elastic solid)
A sketch of load–extension graph for
an elastic solid (Figure 4.3 of SB)
5
Objective
To investigate the relationship between force and
the extension of a spring
(Table 4.1 of SB)
Experimental set-up to investigate the
extension of a spring (Figure 4.4 of SB)
6
(Table 4.2 of SB)
A student measures the length of a spring. He then attaches different loads to the spring. He
measures the length of the spring for each load. Table 4.3 shows his results.
(a) Plot the load–extension graph.
(b) Deduce the relationship between force and extension based on the graph.
(c) The student attaches a load of unknown weight to the spring and measures the
length of the spring. The length is found to be 21.0 cm. What is the weight of this load?
Solution
(Table 4.3 of SB)
Graph of Load F/N
against Extension
x/cm (Figure 4.5
of SB)
7
What is spring constant and limit of proportionality?
•
Spring constant, k: Force per unit extension
•
k=
F
x
where k = spring constant
F = force
x = extension
•
Unit for spring constant: Newton per metre
(N/m) or newton per centimetre (N/cm)
Load–extension graph showing the limit
of proportionality (Figure 4.6 of SB)
What happens when the
value of F is too large?
8
1. A student measured the length of a spring which was found to be 25.0 cm. She then attached an 8 N weight to the
spring. She measured the new length, which was found to be 29.0 cm.
(a) Calculate the extension of the spring.
(b) The student decided to plot a load–extension graph for the spring. She repeated the step
above to obtain the extension of the spring for the following weights: 2 N, 4 N, 6 N and
10 N. Sketch a graph to show what her load–extension graph would look like.
9
4.2 Forces and Motion
In this section, you will learn the following:
•
Determine the resultant force.
•
State the effects of a resultant force.
•
Know that an object either remains at rest or
continues in a straight line at constant speed unless
acted on by a resultant force.
•
Describe solid friction.
•
Know that friction acts on an object moving through a
liquid or a gas.
•
Recall and use the equation F = ma and know
that the force and the acceleration are in the
same direction.
•
Describe, qualitatively, motion in a circular path
due to a force perpendicular to the motion.
10
How can we determine the resultant force on an object?
Calculating the resultant force acting on a ball (Figure 4.7 of SB)
11
How does a resultant force affect motion?
•
May change the velocity of an object by changing its direction of motion or its speed.
•
Balanced forces → Resultant force is zero
•
Unbalanced forces → Resultant force is not zero.
•
•
Causes an object to move → object will accelerate in the direction of the resultant force.
F = ma
where F = resultant force acting on an object (in N)
m = mass of object (in kg)
a = acceleration of the object (in m/s2)
12
Figure 4.9 shows the forces acting on an object at rest.
The mass of the object is 20 kg.
(a) Calculate the resultant force on the object.
(b) What effect does this resultant force have on the object?
(c) What is the velocity of the object after 2 s?
(Figure 4.9 of SB)
13
What are the effects of friction?
•
Impedes motion
•
Produces heating
•
Resistive force - acts in the opposite direction to motion
Friction acts in the opposite direction to motion (Figure 4.10 of SB)
Motion through a liquid or a gas will experience drag (Figure 4.11 of SB)
14
How does a force cause an object to move in a circular path?
Force, mass, speed and radius of circular path for an object in circular motion (Table 4.5 of SB)
Motion in a circular path is due to a
force perpendicular to the motion
(Figure 4.12 of SB)
15
1. Read each of the following descriptions carefully. State if it is true or false. Correct any description which is false.
(a) The resultant force on a moving object is zero. The object stops moving.
(b) The resultant force on an object is zero. The object remains at rest.
(c) An object is moving to the right. A resultant force towards the right acts on it. The object slows down.
(d) An object is moving downwards. An upward force with magnitude equals to the weight of the object acts on the
object. The resultant force is zero and the object falls at constant speed.
(e) Friction acts in the direction opposite to the motion of an object.
(f) Friction can cause heating.
(g) There is no friction in liquids or gases.
16
4.3 Turning Effect of Forces
In this section, you will learn the following:
•
Describe the moment of a force and give everyday
examples.
•
Define the moment of a force as moment = force ×
perpendicular distance from the pivot; recall and use this
equation.
•
Apply the principle of moments to situations with one force
on each side of the pivot.
•
•
Apply the principle of moments to other situations,
including those with more than one force on each side
of the pivot.
State that, when there is no resultant force and no resultant
moment, an object is in equilibrium.
•
Describe an experiment to demonstrate that there is
no resultant moment on an object in equilibrium.
17
What is the moment of a force?
•
Moment of a force: moment = force ×
perpendicular distance from the pivot.
•
Commonly used unit:
Newton metre (N m).
•
Moment of a force = F × d
where F = force (in N)
d = perpendicular distance
from the pivot (in m)
•
Vector quantity
•
Direction: Clockwise or anti-clockwise
Turning effect depends on where the force is applied
(Figure 4.16 of SB)
Simplified diagram of a door
being pulled (Figure 4.18 of SB)
Simplified diagram of a door
being pushed (Figure 4.19 of SB)
18
The minimum moment to open a door is 20.5 N m. The door must be opened with a force of 50 N at the handle.
Calculate the minimum distance of the handle from the hinge.
Solution:
Given: Moment = 20.5 N m , minimum force F = 50 N
Moment = Fd
∴d=
moment 20.5 N m
=
= 0.41m
F
50 N
The handle should be at least 0.41 m away from the hinge.
19
What is the principle of moments?
Principle of moments: Total clockwise moment = Total anticlockwise moment
(No resultant turning effect about a pivot)
Comparing the effects when the resultant moment changes
Force FR is
reversed
Forces
Resultant
moment
Effect
Two forces on a
steering wheel acting in
opposite directions
(Figure 4.20 of SB)
Two forces on a
steering wheel acting
in same directions
(Figure 4.21 of SB)
Resultant moment = 48 N cm + 48 N cm
= 96 N cm
Resultant moment = 48 N cm + ( − 48) N cm
= 0 N cm
The wheel turns in the anti-clockwise direction.
The wheel does not turn.
20
Figure 4.22(a) shows a man holding a stiff fishing rod with
two hands. A 3 kg fish hangs at one end.
Figure 4.22(b) shows a simplified diagram of the positions
of the hands and fish. The lifting hand is the pivot while the
supporting hand exerts a downward force F.
The rod is horizontal, stationary and very light, such that
the effect of its weight is negligible.
Calculate the force F.
(Figure 4.22 of SB)
21
What happens when an object is in equilibrium?
No resultant force and no resultant moment → Object is in equilibrium
Objective
To demonstrate that there is no resultant
moment on an object in equilibrium
(Table 4.6 of SB)
(Figure 4.26 of SB)
22
3. A uniform metre rule is balanced at its midpoint as shown in Figure 4.27.
(a) Calculate distance d1.
(b) Calculate the moment of 10.0 N weight.
(c) The ruler is in equilibrium. Find the position R.
(Figure 4.27 of SB)
23
4.4 Centre of Gravity
In this section, you will learn
the following:
•
State what is meant by centre of
gravity.
•
Describe an experiment to
determine the position of the centre
of gravity of an irregularly-shaped
plane lamina.
•
Describe qualitatively the effect of
the position of the centre of gravity
on the stability of simple objects.
24
What is centre of gravity (C.G.)?
•
Centre of gravity of an object: Point through which the weight of the object acts
•
Regular shape and uniform density object: C.G. at its geometrical centre
•
Irregularly shaped plane lamina: Locate the C.G. using a plumb line
Balancing a metre rule on the tip of a finger
(Figure 4.29 of SB)
Forces acting on the metre rule (Figure 4.30 of SB)
25
Objective
To locate the centre of gravity of an irregularly-shaped plane lamina using a plumb line
Experimental set-up to calibrate a simple pendulum (Figure 4.33 of SB)
26
How does the centre of gravity affect the stability of an object?
To increase stability of an object → C.G. kept as low as possible
→ Base area kept as wide as possible
Types of equilibrium
(Table 4.7 of SB)
27
Figure 4.36 shows the rest position and the displaced position of a balancing toy. Its centre
of gravity is indicated by the letter G.
Explain briefly why the toy eventually returns to its rest position after being released from its displaced position.
(Figure 4.36 of SB)
(Figure 4.37 of SB)
28
1. (a) What is the centre of gravity of an object?
(b) Is the centre of gravity of an object the same whether it is near the surface of the Earth
or the Moon? Explain.
2. (a) How does the position of the centre of gravity affect the stability of an object?
(b) A minibus is travelling on the road carrying heavy loads on its roof rack. There are no
passengers inside the minibus. When turning a corner, the driver drives very slowly.
Explain why.
29
What
have you
learnt?
30
What
have you
learnt?
31
Acknowledgements
•
•
•
Slide 1: wau bulan – ID 178832274 © Tiam Seong Yew | Dreamstime.com
Slide 2: wau bulan – ID 178832274 © Tiam Seong Yew | Dreamstime.com
Slide 4: man making roti canai © Hafiz Ismail | 123rf.com, hand pulling sling shot – ID 32009751 © Bunnyphoto |
Dreamstime.com, badminton player © avevizavi | 123rf.com, street – ID 95512144 © Phuongphoto | Dreamstime.com
32