# Balanced Force – Newton’s First & Third Law of Motion

Show/Hide Sub-topics (Forces & Turning Effect Of Forces | O Level Physics)
Show/Hide Sub-topics (Forces And Dynamics | A Level Physics)

## Newton’s 3 Laws Of motion

Newton’s 3 laws of motion are:

1. 1st law: Newton’s first law of motion states that a body will continue in its state of rest or uniform motion in a straight line unless an external resultant force acts on it.
2. 2nd law: Newton’s second law states that the rate of change of momentum of a body is proportional to the resultant force acting on it and the change takes place in the direction of the force.
3. 3rd law: Newton’s third law states that: If body A exerts a force on body B, then body B exerts a force of equal magnitude but in the opposite direction on body A.

We will explore first and third law of motion in this post and the 2nd law of motion in greater details in the subsequent posts.

## Newton’s First Law Of Motion

When two or more external forces acting on a body produce no net resultant force, i.e., vector sum of forces is zero, we say that the forces are balanced. The lack of resultant force produces no net acceleration and hence, the body will remain at rest or moves at its original constant velocity in a straight line.

• This is Newton’s First Law of Motion
• An external force is one whose source lies outside of the body being considered. e.g. weight of a body and friction
• The resultant force is the vector sum of all external forces exerted on a body.

Newton’s First Law of Motion is also known as the law of inertia. Inertia is a property of mass resisting any change from its original state of rest or motion. The greater the mass of a body, the greater will be its inertia and the greater will be its resistance to changes to its state of rest or motion.

Every material object has inertia and the amount of matter present in the object.

• Mass is the quantity of matter in an object and is independent of the body’s surroundings and method used to measure it (scalar quantity)
• Inertial mass mi specifies how much inertia an object has. It is a measure of the response of an object to an external force.
• Gravitational mass, mg is determined by measuring the force on an object in a gravitational field (i.e. its weight)

Newton’s First Law of Motion implies that

• The state of rest requires no resultant force to maintain.
• A body at rest implies that the net resultant force exerted on the body is zero.
• The state of uniform velocity also requires no resultant force to maintain.
• However, it is not necessarily that there is no forces acting on the body.
• For instance, a box resting on a table has zero net resultant force. But there are two forces acting on the box! One of the force is the gravitational force due to the weight of the box, while the other is the normal force.

### Normal Force

Consider the picture above,

• The normal force and weight (gravitational force acting on the box) arrows are of the same length (same magnitude) but in opposite directions.
• Normal force (or reaction force) is an external force exerted perpendicularly by the surface in reaction to any body placed against it. The normal force arrow starts from the base of the box (contact between the box and the table top).
• The weight arrow starts from the centre of mass of the box (labelled as C.M.), as indicated by the black dot.

For objects on Earth which are resting on a surface, the normal force balances the force of gravity and provides equilibrium.

The magnitude of the normal force is not necessarily equal to the magnitude of gravitational force. To see and understand this:

Consider the picture above again, imagine if you place your hand on the box and pushes downwards. What happens?

• When you pushes downwards on the box with a force $\vec{F}$, the box doesn’t move.
• When the box doesn’t move, by Newton’s Second Law Of Motion, we know that the resultant force is ZERO.
• If the resultant force is zero, this means that $\vec{F}$ + $\vec{F}_{g}$ is equals to $\vec{n}$, where $\vec{F}_{g}$ is the gravitational force acting on the box and $\vec{n}$ is the normal force.
• Hence, the normal force $\vec{n}$ is greater than the force of gravity and is given by:

$$\vec{n} = \vec{F}_{g} + \vec{F}$$

### Weight

Main Article: Weight

The force exerted by the Earth on an object is called the weight of the object.

\begin{aligned} \text{Weight} &= \vec{F}_{\text{weight}} \\ &= m \vec{a} \\ &= m \vec{g} \end{aligned}

Since weight depends on geographical (or astronomical) location, it is not an inherent property of a body.

## Newton’s Third Law Of Motion

Newton’s third law states that: If body A exerts a force on body B, then body B exerts a force of equal magnitude but in the opposite direction on body A.

Forces always occur in pairs – Action force and reaction force.

### Action & Reaction Forces

Some properties of the action and reaction forces are as follows:

• Forces always occur in pairs. Each pair is made up of an action force and a reaction force.
• The action and reaction forces are equal in magnitude.
• The action and reaction forces act opposite to one another.
• The action and reaction forces act on different bodies.

Note:

1. It does not matter which force is called action and which is called reaction
2. The two forces must be of the same type i.e. if one is an electrical force, then the other must be electrical
3. The two forces act on different bodies thus they do not produce zero resultant force (do not cancel each other) on any one object.

## [A Level] Problem-Solving Strategy Involving Newton’s Three Laws of Motion

Solving physics problems, especially those involving Newton’s Three Laws of Motion, requires a systematic approach. By following a structured strategy, you can simplify complex problems into manageable components, leading to clearer understanding and solutions. Here’s how you can approach such problems:

1. Draw a Neat, Simple Diagram of the System: Begin by creating a visual representation of the problem. This diagram should be as clear and simple as possible, helping in understanding the situation and identifying forces. When drawing your diagram, assume objects are point masses if this simplification is applicable. This assumption can simplify the analysis by focusing on the dynamics of the system without considering the distribution of mass.
2. Isolate Each Body Being Analysed and Draw a Free-Body Diagram Showing All External Forces: Isolate each object of interest and draw a free-body diagram (FBD) to show all external forces acting upon it. Include forces such as gravity, normal forces, and tensions. Neglect the mass of ropes and consider the effects of friction only if specified. This step is vital for understanding how external forces interact with each object, keeping in mind that internal forces, such as the tension in a rope assumed to be massless, do not appear in the FBD.
3. Establish Convenient Axes for Each Body and Find the Component Forces Along These Axes: Choose axes orientation that simplifies the problem, typically aligning one axis with the direction of motion. Decompose forces into components along these axes, neglecting frictional forces unless the problem specifies to consider them. This decomposition facilitates the application of Newton’s laws by breaking down complex force interactions into manageable calculations.
4. Apply Newton’s First or Second Law in Component Form: Apply Newton’s First Law for systems in equilibrium or Newton’s Second Law for systems under acceleration. Focus on external forces that act on each body, as internal forces have been eliminated from consideration by the assumption of point masses and neglect of rope mass. Newton’s Second Law, (F = ma), is particularly useful for relating the net external force acting on an object to its acceleration.
5. Solve the Component Equations. Ensure That You Have as Many Independent Equations as You Have Unknowns: Algebraically manipulate the equations to solve for unknowns such as forces, accelerations, or velocities. It’s important to ensure you have a sufficient number of equations for all unknowns. If not, reassess your diagrams or the principles you’ve applied, keeping in mind the simplifications and assumptions made earlier.
6. Check Your Results: After solving, evaluate if the results are physically plausible. Consider if the directions and magnitudes of forces and accelerations align with the problem’s setup and the assumptions made, such as neglecting friction or rope mass where applicable. This critical step ensures the solution’s validity and helps reinforce the understanding of physical principles.

By systematically following these steps, you can tackle problems involving Newton’s Three Laws of Motion with greater confidence and clarity. This methodical approach not only facilitates problem-solving but also deepens your understanding of the physical principles at play.

## [A Level] Newton’s First Law In Terms Of Vectors

Newton’s First Law states that a body acted on by no net forces moves with constant velocity (which may be zero) and zero acceleration.

This means that if $\sum \vec{F} = 0$, then $\vec{v} = \, \text{constant}$ and $\vec{a} = 0$. Note that $\sum \vec{F} = 0$ if $\sum \vec{F}_{x} = \sum \vec{F}_{y} = \sum \vec{F}_{z} = 0$

## [A Level] Newton’s Third Law

Newton’s Third Law states that if a body A exerts a force on body B (an “action”), then body B exerts a force on body A (a “reaction”), these two forces have the same magnitude but are opposite in direction and they act on different bodies.

$$\vec{F}_{12} =-\vec{F}_{21}$$

The force $\vec{F}_{\text{A on B}}$ exerted by object A on object B is equal in magnitude to and opposite in direction to the force $\vec{F}_{\text{B on A}}$ exerted by object B on object A.

## Worked Examples

### Example 1

Ignoring air resistance and upthrust, describe the action-reaction pair for a ball in free-fall.

The ball experiences the gravitational pull of the Earth and the Earth experiences an upward pull due to the ball. The forces act on different bodies and are both gravitational forces.

### Example 2

A ball falls vertically and bounces on the ground.

The following statements are about the forces acting on the ball while it is in contact with the ground. Which statement is correct?

1. The force that the ball exerts on the ground is always equal to the weight of the ball.
2. The force that the ball exerts on the ground is always equal in magnitude and opposite in direction to the force that the ground exerts on the ball.
3. The force that the ball exerts on the ground is always less than the weight of the ball.
4. The weight of the ball is always equal in magnitude and opposite in direction to the force that the ground exerts on the ball.

By Newton’s 3rd law, the two interacting forces will act on different bodies but not on the same body.

### Example 3

A man is standing on a beam which is resting on the ground. Which of the following pair forms an action-reaction pair of forces?

1. Contact force on man due to beam and the gravitational force on beam due to Earth.
2. Weight of man and the gravitational force on Earth due to man.
3. Contact force on man due to beam and weight of man.
4. Gravitational force on man due to Earth and gravitational force on beam due to Earth.

Action reaction pair needs to fulfil the following:

• has the same magnitude,
• acts along the same line but in opposite direction,
• acts on a different object,
• of the same type.

Thus only option 2 meets the above criteria. Option 4 is not correct because they act in the same direction.