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Physics Tutorial: What Causes Motion? The Meaning of Force

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In this Physics tutorial, you will learn:

What is/are the factor/s affecting the motion?
What effects can a force cause on the object it acts?
What kind of quantity is force?
What is the unit of force?
How can we classify the forces?
How can we express a force in components?
How to find the resultant force?

Dynamics Learning Material
Tutorial ID	Title	Tutorial	Video Tutorial	Revision Notes	Revision Questions
4.1	What Causes Motion? The Meaning of Force

Introduction

If you see a moving object such as a bird flying in the sky, a car moving on the road or a girl walking, do you think they are moving by themselves or maybe something is making them move?

Can you make something that is at rest, such as a stone, a cart etc., move without touching it? Why?

What about the planets revolving around themselves and the Sun? Do you think they move by themselves? Why?

What causes motion?

In the previous chapter "Kinematics", we discussed extensively about various types of motion and the kinematic quantities involved in them. However, nowhere in the entire chapter the factors causing those kinds of motion were mentioned; only the way how objects move and physical quantities such as position, displacement, distance, velocity, speed and acceleration were discussed in it.

This is a serious drawback; it is like a doctor who deals with the disease of a patient without knowing what has caused it. Therefore, it is very important knowing what causes a motion (or a change in motion rhythm) to understand it in full.

In Physics, the factors that cause an object move or change its motion are known as forces. By definition, "a force is any interaction that, when unopposed, will change the motion of an object." In simpler words, a force can be described as a push or a pull.

Basically, a force can cause one of the following effects on objects:

Changing the velocity of an object. This includes starting a motion, stopping a motion, speeding up or slowing down a moving object.
Changing the moving direction of an object. This includes deviating, rotating, swinging.
Changing the shape of an object. This includes squeezing, bending, stretching, compressing, twisting, breaking an object in pieces or welding a broken object.

Remark! A force cannot change the mass of an object. Mass is a physical quantity related to the amount of matter contained in an object, so a force can neither create nor destroy the matter.

Force is a vector quantity. This means it involves the direction. As stated in the Physics tutorial "Vectors and Scalars", the information regarding a vector quantity in physics must contain four elements: direction, magnitude, unit and application point, in order to be considered as complete. If one of them is not given, this creates serious problems in studying any process in which the force in question is involved.

The unit of force is Newton (in short N). Newton is a derived SI quantity because when splitting it into fundamental SI units, we obtain

1[N] = 1[kg × m/s²]

Generally (when not specified the type of force involved), a force is denoted in formulae by the letter F. Also, a vector sign is placed above it to show that it is a vector. Therefore, we can write

F⃗ = ...N

Example 1

An object is hanged on a rope as shown in the figure below.

What effects do the forces in the figure cause on the objects in which they act?

Physics Tutorials: This image provides visual information for the physics tutorial What Causes Motion? The Meaning of Force

F⃗₁ on the object
F⃗₁ on the rope
F⃗₂ on the rope
F⃗₃ on the object
F⃗₃ and F⃗₄ simultaneously on the object

Solution 1

F⃗₁ is not a linear force; it causes the object revolve around itself. Therefore, it causes a rotating effect on the object.

The rotating object causes the rope twist. Therefore, F⃗₁ causes a twisting effect in the rope.

The force F⃗₂ pulls the object downwards. Therefore, it causes a stretching effect on the rope.

If only the force F⃗₃ acts on the object, it makes it displace due right. As a result, the object starts swinging around the vertical position for a while.

If F⃗₃ and F⃗₄ act simultaneously on the object, they compress it due to the simultaneous pushing effect caused on the object by these two opposite forces.

How are forces classified?

Forces are divided in two main categories regarding the way on how they act in objects. They are:

Contact forces. These kinds of forces cause their effect on an object only when they touch it. For example, moving an object by pulling a rope is an example of contact forces as if you don't pull the rope, the object doesn't move from its place.
Field (distant) forces. These kinds of forces are produced by objects, which are able to extend their effect in the space around them (known as "fields") and as a result, all the other objects which enter inside the range of these fields, are affected by their pushing or pulling effect. Therefore, the force is produced indirectly through the field, not through the object itself. For example, Earth attracts objects near its surface through the gravitational field it produces in the space around. As a result, objects that are flying near the Earth surface fall on the ground when the moving force stops.

What is Resultant Force?

When two or more vectors act on the same object, an overall effect is produced. This effect (as discussed in the Physics tutorial "Addition and Subtraction of Vectors"), is known as resultant or net vector. In the specific case, we say when two or more forces act on the same object, the overall effect produced is called "resultant" or "net" force. Symbolically, we write F⃗_R or F⃗_net to express this overall effect that is nothing more but the sum of all forces acting on the same object. Look at the figure:

Numerically speaking, the effect on the object's motion caused by the resultant force is the same (in magnitude) as the effect of all single forces taken separately. For example, if in the above figure F⃗₁ = 40N, F⃗₂ = 20N and F⃗₃ = 30N, the resultant force F⃗_R will be

F⃗_R = F⃗₁ + F⃗₂ + F⃗₃
= 40N + 20N + 30N
= 90N

If possible, the length of the resultant force vector when compared to the lengths of each single force vector, must reflect their respective magnitudes. Thus, in the specific case, the vector F⃗₁ is the longest and the vector F⃗₃ is the shortest as this description corresponds to their numerical values. Also, the force vector F⃗_R is longer than each single force vector as it represents their sum.

On the other hand, if two forces act in the opposite direction, the first thing to do is to choose a positive direction. As a result, one force (the one that lies in the positive direction) is taken as positive and the other as negative. For example, in the figure below,

we take F⃗₁ as positive and F⃗₂ as negative. Therefore, we obtain for the resultant force:

F⃗_R = F⃗₁ + F⃗₂
= 70N + (-30)N
= 70N - 30N
= 40N

This means the resultant of two forces acting in the opposite direction (which in this case is 40N due right) represents their numerical difference (this derives from the fact that subtraction is the opposite operation of addition).

Expressing Forces in Components

When two or more forces acting at the same object are neither in the same direction nor in the opposite, it is better to express them in components. Then, after calculating the resultant force in each direction, the Pythagorean Theorem is used to calculate the magnitude of the resultant force. Let's illustrate this point by a numerical example.

Example 2

Calculate the resultant force F⃗R acting at the object in the figure.

Solution 2

From the figure, we can see that 1 unit = 4 N.

First, let's express all forces in components. We have two directions involved here: the horizontal (or x-direction) and the vertical (y-direction). Also, we take left as negative and right as positive in the horizontal direction and up as positive and down as negative in the vertical direction. Therefore, we can write:

F_1x = ( + 4) units × N/unit = + 16 N
F_1y = ( + 6) units × 4 N/unit = + 24 N
F_2x = ( + 2) units × 4 N/unit = + 8 N
F_2y = (-4) units × 4 N/unit = -16 N
F_3x = (-6) units × 4 N/unit = -24 N
F_3y = (-2) units × 4 N/unit = -8 N

Thus, we have for the resultant forces of the each direction

F_Rx = F_1x + F_2x + F_3x
= ( + 16)N + ( + 8)N + (-24)N
= 0
F_Ry = F_1y + F_2y + F_3y
= ( + 24)N + (-16)N + (-8)N
= 0

In this case, there is no need to calculate the total resultant force because it is obvious it is zero (the object remains at rest). However, in the general case, we would write

F_R(tot) = √F²_Rx + F²_Ry
= √0² + 0²
= 0

Remark! When the object is voluminous as the one in the specific example, we take the force vectors as acting at the centre of the object.

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