A-Level Physics Lecture 3: Forces
©Ryan Zhong
Lecture 3: Forces
Lecturer: Ryan Zhong
2024.06.22
1 Newton’s Laws of Motion
Now we have learnt the basic motion laws of an object, with 3 essential Physical quantities: x, v, a.
What are the Physical causes to these quantities?
In 1687, Issac Newton published the Philosophiæ Naturalis Principia Mathematica, where he described
the relations between motions and forces via three laws, which is called Newton’s Laws of Motions:
i. A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is
acted upon by a force.
ii. At any instant of time, the net force on a body is equal to the body’s acceleration multiplied by its
mass or, equivalently, the rate at which the body’s momentum is changing with time.
iii. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
1.1
Newton’s 1st Law
The 1st law is called the “Principle of Inertia”. Inertia, 惯性, is the tendency of objects in motion
to stay in motion and objects at rest to stay at rest. For example, an observer on the ground sees the train
moving smoothly in a straight line at a constant speed, then a passenger sitting on the train will be an
inertial observer: the train passenger feels no motion. The principle expressed by Newton’s 1st law is that
there is no way to say which inertial observer is “really” moving and which is “really” standing still. This
law is totally separated from the 2nd law, with the purpose of strengthening the idea of inertial system.
Figure 1
This law is derived and analysed from Galileo Galilei’s ideal experiment in the 16th century:
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A-Level Physics Lecture 3: Forces
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Figure 2
where the surfaces are all smooth. From Figure 2A to 2C, the ball is released from a certain height h,
and can travel at a further distance when the gradient of the slope is smaller. As the gradient becomes 0,
the ball tends to travel infinitely far. This tendency is what later called inertia.
1.2
Newton’s 2nd Law
The 2nd law is also called the “Acceleration Law”, which can be expressed via the formula:
F = ma
[N, kg m s−2 ]
(1)
where m is defined as “inertia mass” (comparing to the wider definition in the relativity theory), only
suitable for an object with a relatively slow velocity. The Equation (1) can also be written as:
F=m
1.3
dv
d2 x
=m 2
dt
dt
(2)
Newton’s 3rd Law
The 3rd law describes the pattern of force and counterforce when two bodies interact with each other.
These two forces follow the rules below:
1. They act on different objects.
2. They are equal in magnitude.
3. They are opposite in direction.
4. They are forces of the same type.
or a simple mathematic equation:
F12 = −F21
(3)
Figure 3
In this lecture, we will firstly discuss the 2nd law to demonstrate the relations between forces and
motions. The 1st and 3rd law will be further discussed in subsequent lectures.
Ex[1] Calculate the force needed to give a car of mass 800 kg an acceleration of 2.0 m s−2 .
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A-Level Physics Lecture 3: Forces
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Ex[2] A motorcyclist of mass 60 kg rides a bike of mass 40 kg. As she sets off from the lights, the
forward force on the bike is 200 N. Assuming the resultant force on the bike remains constant, calculate the
bike’s velocity after 5.0 s.
2 Types of Forces
Forces push or pull and squeeze or stretch. In physics, a force is an influence that can cause an object
to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced
by other forces. There are several ways of classifying forces: in classic Newtonian mechanics, forces are
devided into distant and contact forces depending on whether there is a contact surface; in modern Physics,
forces are devided into four fundamental interactions: Gravitation, Weak Interaction, Strong Interaction,
Electromagnetic Interaction.
2.1
Forces at a Distance
2.1.1 Gravitational Force
The Gravitational Force (or Gravity, Weight), denoted by FG , is a fundamental interaction which causes
mutual attraction between all things that have mass. This force between two objects depends on the mass
of the objects and their separation1 (Figure 3). They are very small unless one or both of the masses is
extremely large. In the surface of Earth, FG can be given by:
FG = mg
(4)
where g is the gravitational acceleration, 重力加速度, or gravitational field strength, 重力场强2 , with a
value of 9.81 N kg−1 (m s−2 ). The direction always points to the mass centre of the Earth. Notice!!
Actually, g is not a fixed quantity worldwide. The higher the latitude is, the greater the g is. (Why?)
Also, the quantity changes if the measurement is NOT on the Earth surface. For example, the gravitational
acceleration on Moon surface is gm = 1.6 m s−2 , which is approximately one fourths of the Earth’s.
When describing the gravitational force acted on an object, we can use an arrow starting
from the centre of mass and pointing towards the ground (Earth) like Figure 4.
Figure 4
GM1 M2
.
r2
2 Here, the expression “field strength” is a special concept to describe the strength at a particular space of a field, while a
“field” is a physical quantity to describe the distribution and mechanism of force, mass and energy, etc. What we can know
now is that forces are conveyed via fields.
1 Actually, the expression of F
G is: FG =
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Mass and Weight
The concepts of Mass and Weight are often messed in daily lives. However, in Physics
studies, these two Physical quantities have different meanings.
The mass of an object is only determined by its material composition, i.e., the atoms. In
an ieal experiment, mass is unchanged when moving the object from one place to another. The
symbol of mass is m, with a SI unit [kg].
The weight of an object depends on the gravitational force that acts on the object, mg, with a SI unit
[N]. The mass of an apple is ∼ 300 g, and the weight of it is ∼ 3 N on Earth, whereas it changes to ∼ 0.48
N on Moon.
Ex[3] Estimate the mass and weight of each of the following at the surface of the Earth:
1. a kilogram of potatoes
2. a PC
3. a student
4. a truck
Ex[4] In 1590, Galileo Galilei made a famous experiment on the Tower of Pisa. He released two iron
balls of 1 lb and 10 lbs at rest. Then he found that two balls almost hit the ground at the same time. Why?
Ex[5] When releasing an iron ball and a feather at the same time at rest, will the two objects hit the
ground at the same time? Why or why not?
2.1.2 Electrostatic Force and Electromagnetic Force
Electrostatic and electromagnetic forces are also examples of forces
that act over a distance.
Insulating rods can be given positive or negative charges by rubbing
with woollen dusters or cotton rags. The electrostatic forces produced can
be investigated by suspending one rod from a thread and holding another
rod close to it (Figure 5). Unlike gravitational forces, both pulling and
pushing effects are observed. Similar charges repel and opposite charges
attract. A similar effect is observed when magnets are used. We will specifically focusing on this topic in the AL Physics.
2.2
Contact Forces
In highschool Physics, a contact force is any force that occurs as a result
of two objects making contact with each other. When placing a block on
a rough incline which remains at rest (Figure 6a), the block will contact
with the surface immediately. In this situation, the block receives a normal
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Figure 5
A-Level Physics Lecture 3: Forces
©Ryan Zhong
contact force N vertical to the surface upwards, the static friction force f preventing from sliding down the
incline, and the gravitational force G = mg pointed towards the ground.
(a)
(b)
Figure 6
In Figure 6b, the ball A receives the normal contact force N from the incline, the gravitational force
mg pointed towards the ground, and the tention from the rope T , elastic force from the string F . We will
introduce these forces on textbook, P47.
2.2.1 Normal Contact Force
The normal contact force FN , or N is defined as the net force compressing two
parallel surfaces together, and its direction is perpendicular to the surfaces. In this
situation on the right, the normal contact force is N = F . When standing on the
floor of the elevator, the normal force supports our body. Notice!! When in an
accelerated motion, the normal force is usually NOT equal to the weight of a body.
We will discuss this matter in the next lecture.
2.2.2 Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers,
Figure 7
and material elements sliding against each other. There are two main kinds of
friction: one is static friction (or, stiction), one is kinetic friction.
Static friction is the force that needs to be overcome to
enable relative motion of stationary objects in contact. Any
solid objects pressing against each other (but not sliding) will
require some threshold of force parallel to the surface of contact
in order to overcome static adhesion. The static friction force
must be overcome by an applied force before an object can
move. The maximum of static friction is given as:
Fmax = µs N
(5)
Figure 8
where µs is the coefficient of static friction, N is the normal contact force. When there is no sliding occurring,
the friction force can have any value from zero up to Fmax .
An example of static friction is the force that prevents a car wheel from slipping as it rolls on the
ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary
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relative to the ground, so it is static rather than kinetic friction. Upon slipping, the wheel friction changes
to kinetic friction.
Figure 9
Kinetic friction, or sliding friction, occurs when two objects are moving relative to each other and rub
together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as µk , and is
usually less than the coefficient of static friction µs for the same materials.
The friction force between two surfaces after sliding begins is the product of the coefficient of kinetic
friction and the normal force:
(6)
f = Fk = µk N
In microscale, any kinds of friction, or contact forces are caused by the mutual repulsion between atoms.
The electrons are against each other due to electromagnetic forces, so that in a macroscale, the result of
this repulsion is force.
2.2.3 Tension
Tension is the pulling or stretching force transmitted axially along an object
such as a string, rope, chain, rod, truss member, or other object, so as to stretch
or pull apart the object. In the string issue, a simple tension force acts to return a
spring to its natural length. If ∆x is the displacement from the natural length, the
force exerted by an ideal spring equals to
(7)
F = k∆x
Figure 10
where k is the spring constant particular to the spring. This equation was firstly described by Robert Hooke.
2.2.4 Upthrust
Any object placed in a fluid such as water or air experiences an upwards force. This is what makes it
possible for something to float in liquid. Upthrust arises when the repelling volume of liquid arises. We will
discuss this matter in Materials.
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3 Exercises and Homework
Q[1] A ball is dropped inside a railway carriage. Use Newton’s first law to explain whether the ball will
hit the floor in front of, level with or behind the point of release if
(a) the train is stationary
(b) the train is moving forward at constant speed
(c) the train is moving backward at constant speed
(d) the train is accelerating in a forward direction.
Q[2]Draw a diagram to show the forces which act on a car as it travels along a level road at its top speed.
Q[3] Imagine throwing a shuttlecock straight up in the air. Air resistance is more important for
shuttlecocks than for a tennis ball. Air resistance always acts in the opposite direction to the velocity of an
object. Draw diagrams to show the two forces, weight and air resistance, acting on the shuttlecock:
(a) as it moves upwards
(b) as it falls back downwards.
Q[4] Describe one ‘Newton’s third law pair’ of forces involved in the following situations. In each case,
state the object that each force acts on, the type of force and the direction of the force.
(a) You step on someone’s toe.
(b) A car hits a brick wall and comes to rest.
(c) A car slows down by applying the brakes.
(d) You throw a ball upwards into the air.
Q[5] A car of mass 1500 kg tows a trailer of mass 2500 kg. The horizontal driving force of the road
on the wheels of the car is 7000 N and both the car and the trailer experience resistive forces of 1000 N.
Calculate:
(a) The acceleration of the vehicles.
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(b) The tension in the coupling when the driving force is reduced so that the acceleration falls to 1.00
m s−2 .
Q[6] When a golfer hits a ball his club is in contact with the ball for about 0.0005 s and the ball leaves
the club with a speed of 70 m s−1 . The mass of the ball is 46 g.
(a) Determine the mean accelerating force.
(b) What mass, resting on the ball, would exert the same force as in (a)?
Q[7] The mass of a spacecraft is 70 kg. As the spacecraft takes off from the Moon, the upwards force
on the spacecraft caused by the engines is 500 N. The gravitational field strength on the Moon is 1.6 m s−2 .
Determine:
(a) the weight of the spacecraft on the Moon
(b) the resultant force on the spacecraft
(c) the acceleration of the spacecraft.
Q[8] A car starts to move along a straight, level road. For the first 10 s, the driver maintains a constant
acceleration of 1.5 m s−2 . The mass of the car is 1100 kg.
(a) Calculate the driving force provided by the wheels, when:
i. the force opposing motion is negligible,
ii. the total force opposing the motion of the car is 600 N.
(b) Calculate the distance travelled by the car in the first 10 s.
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