How Forces Affect Motion Class 9 Science Notes

The Concept of Force

A force is a push or a pull that can cause a change in the motion, position, or shape of an object. When we interact with objects, we often exert forces. For example, kicking a ball, striking a cricket ball with a bat, or squeezing a lemon with our fingers are all examples of applying force.

Forces are physical quantities that have both magnitude (how strong the push or pull is) and direction. This is similar to quantities like position, displacement, velocity, and acceleration, which also require a direction to be fully described.

The SI unit of force is the newton, symbolized by N. The magnitude of a force tells us its strength. If either the magnitude or direction (or both) of a force acting on an object changes, the effect of that force also changes.

Measuring the magnitude of a force

We can measure the magnitude of a force using a spring balance. A spring balance works by using the extension of a spring to indicate the magnitude of the force applied. When a force is applied to the free end of the spring balance, it stretches or compresses the spring inside. The amount of stretch or compression is proportional to the force applied.

Weight of an object: A spring balance is commonly used to measure the weight of an object. Weight is itself a force – the gravitational force with which the Earth pulls an object towards it.

In practical terms:

The smallest forces we can typically feel directly are around millinewtons ( $10^{- 3} N$ ), like a gentle touch.
Scientists, however, can measure forces much smaller, down to yoctonewtons ( $10^{- 24} N$ ) in specialized experiments.

Remember
Force is a vector quantity, meaning it has both magnitude and direction. Always consider both when analyzing how a force affects an object.

Exam-smart
Case studies might describe a scenario (e.g., a tug-of-war) and ask you to determine the direction and relative strength of forces. You would need to identify the pushes and pulls and their directions to understand the net effect.

Balanced and Unbalanced Forces

When multiple forces act on an object, their combined effect determines whether the object's motion changes. This is particularly important in real-life scenarios where objects are rarely acted upon by just a single force.

Consider pushing a box on the floor. The force you apply is met by the force of friction acting in the opposite direction. Similarly, a ball floating on water experiences the gravitational force pulling it down and the buoyant force from the water pushing it up. The net outcome depends on how these forces interact.

Types of Forces and Their Effects

Forces acting on an object can be categorized based on whether they result in a net change in motion.

Balanced Forces: When two or more forces acting on an object are equal in magnitude and opposite in direction, they cancel each other out. This results in a net force of zero. An object subjected to balanced forces will either remain at rest or continue to move with a constant velocity.
Example: In a tug-of-war, if both teams pull with equal strength, the rope doesn't move because the forces are balanced.
Unbalanced Forces: When forces acting on an object are not equal in magnitude or not opposite in direction, they do not cancel each other out. This results in a non-zero net force. An object subjected to unbalanced forces will experience a change in its state of motion; it will accelerate in the direction of the larger force.
Example: If one team in a tug-of-war pulls harder, the rope moves towards that team because the forces are unbalanced.

Calculating Net Force

The net force is the vector sum of all forces acting on an object.

Forces in the Same Direction: When forces act in the same direction, the magnitude of the net force is the sum of the magnitudes of the individual forces. The direction of the net force is the same as the direction of the individual forces.
If force $F_{1}$ and force $F_{2}$ act in the same direction, then Net Force = $F_{1} + F_{2}$ .
Forces in Opposite Directions: When forces act in opposite directions, the magnitude of the net force is the difference between the magnitudes of the individual forces. The direction of the net force is the same as the direction of the larger force.
If force $F_{1}$ acts to the right and force $F_{2}$ acts to the left, and $F_{1} > F_{2}$ , then Net Force = $F_{1} - F_{2}$ (acting to the right).

Example 6.1: Two forces of 10 N and 6 N act on a block.

(a) If both forces act to the right: Net Force = 10 N + 6 N = 16 N (to the right)
(b) If 10 N acts to the right and 6 N acts to the left: Net Force = 10 N - 6 N = 4 N (to the right, since 10 N is larger)
(c) If 10 N acts to the left and 6 N acts to the right: Net Force = 10 N - 6 N = 4 N (to the left, since 10 N is larger)

Feature	Balanced Forces	Unbalanced Forces
Magnitude	Net force is zero ( $F_{n e t} = 0$ N)	Net force is non-zero ( $F_{n e t} \neq 0$ N)
Direction	Forces cancel each other out.	Forces do not cancel each other out.
Effect on Motion	Object remains at rest or moves with constant velocity.	Object accelerates (changes speed or direction).

Remember
Balanced forces do not cause a change in an object's motion. It's the unbalanced forces that cause acceleration.

Exam-smart
You might be given a scenario with multiple forces acting on an object (e.g., a diagram showing arrows representing forces). You will need to identify if the forces are balanced or unbalanced by calculating the net force. If the net force is zero, the object's motion will not change. If it's non-zero, you'll need to determine the direction and magnitude of the acceleration based on the net force.

The Force of Friction: Often Net force Overlooked but Always Present

You have learnt about the force of friction in an earlier grade. This force arises between surfaces in contact and opposes their relative motion or tendency of motion. It is crucial to understand that multiple forces can act on an object, but its motion is determined by the net force.

When you apply a force to push an object (like a box on the floor), and it doesn't move, it's because of the force of friction acting in the opposite direction. The object only moves when your applied force is greater than the force of friction, resulting in a net force that causes motion.

Several forces can act on an object. Besides the applied force and friction, we also have:

Gravitational force (weight): Acts downwards.
Normal force: Exerted by the surface, acting upwards and perpendicular to the surface. These two forces are usually balanced.
Air resistance: A type of friction from the air, often negligible in many scenarios.

When a moving object, like a bicycle after you stop pedalling or a ball after you stop pushing it, comes to rest, it's due to the continuous action of friction opposing its motion. To keep an object moving at a constant velocity, we must apply a force to counteract this frictional force.

Factors Affecting Friction

The force of friction depends on the nature of the surfaces in contact. Smoother surfaces generally have less friction than rougher surfaces.

Activity 6.1: Investigating Distance Travelled on Different Surfaces

This activity uses a stack of coins and a rubber band to observe how far an object travels on different surfaces.

Setup: Stack four coins and tape them together. Stretch a rubber band and use it to pull the coin stack. Mark points on the surface to ensure consistent stretching.
Observation: When the rubber band releases the coins, observe their motion. The coins move due to the force from the rubber band and friction.
Analysis:

Initially, the rubber band force is greater than friction, causing acceleration.
Once released, only friction acts, opposing motion and causing the coins to slow down and stop.
The distance travelled and the rate of slowing down depend on the force of friction.

Observations and Conclusions from Activity 6.1:

The stack of coins travels a larger distance and its velocity decreases more slowly on smoother surfaces (like polished marble) compared to rougher surfaces (like a wooden table).
This indicates that the force of friction is different for different surfaces. Smoother surfaces exert less friction.

Activity 6.2: Measuring Force of Friction

This activity uses a spring balance to measure the force needed to overcome friction.

Setup: Attach a wooden block to a spring balance. Pull the block horizontally on different surfaces.
Observation: Note the reading on the spring balance just as the block starts moving. This reading approximates the force of friction.
Analysis:

When the block just starts moving, the force applied by the spring balance is equal to the force of static friction.
If the velocity is constant (not changing), the net force is zero.

Observations and Conclusions from Activity 6.2:

The spring balance readings are different for different surfaces.
The reading is smallest for surfaces where the coin stack travelled the largest distance (indicating lower friction).
The reading is largest for surfaces where the coin stack travelled the smallest distance (indicating higher friction).
A smaller reading on the spring balance means a smaller force of friction.

Thought Experiment: Zero Friction

If the force of friction between an object and a horizontal floor were zero, and you gave the object a push, it would continue moving forever at a constant velocity. Its velocity would not decrease, and it would never come to rest.

Remember
Friction is a contact force that always opposes motion or the tendency of motion between surfaces. The unit of force is the newton (N), named after Sir Isaac Newton.

Exam-smart
A question might describe a scenario where an object moves on different surfaces (e.g., ice, sand, a rough road) after an initial push. You would need to apply your understanding of friction to predict which surface allows the object to travel furthest or stop soonest, and relate the observations to the magnitude of the frictional force. For example, on ice, friction is low, so an object moves longer; on sand, friction is high, and it stops quickly.

Newton’s First Law of Motion

Newton's First Law of Motion states that an object at rest remains at rest, and an object in motion continues to move with a constant velocity, unless acted upon by a net external force.

This law essentially describes inertia, the tendency of an object to resist changes in its state of motion.

Object at rest: If an object is stationary, it will stay stationary indefinitely if no force pushes or pulls it.
Object in motion: If an object is moving, it will continue to move in a straight line at the same speed if no force interferes.

Key Concepts:

Net Force: The net force is the vector sum of all forces acting on an object. If the net force is zero, the forces are balanced.
If forces are balanced, an object at rest stays at rest, and an object in motion continues with constant velocity.
If the net force is non-zero, the forces are unbalanced, and the object's velocity will change.
Constant Velocity: This means two things:
Constant Speed: The object's rate of movement does not change.
Constant Direction: The object moves in a straight line.
Zero Acceleration: When velocity is constant, acceleration is zero because there is no change in velocity.

How Newton's First Law Explains Motion

The law explains why objects behave the way they do when forces are either absent or balanced.

Why objects stay still: A book on a table remains still because the force of gravity pulling it down is balanced by the upward force from the table. The net force is zero, so it doesn't move.
Why moving objects keep moving (ideally): Imagine a puck on an air hockey table. The air cushion significantly reduces friction. If you give the puck a push, it glides smoothly for a long time because friction is very low, and there's no significant opposing force. If there were absolutely no friction and no air resistance, the puck would theoretically move forever at the same speed and direction.
Why forces are needed to change motion: To start a stationary object moving (like pushing a stalled car), to stop a moving object (like applying brakes), or to change its direction (like steering a car), an unbalanced force must be applied.

Examples and Applications

A Stationary Ball: A football lying on the ground remains motionless because the forces acting on it (gravity downwards, normal force from the ground upwards) are balanced. A net force is needed to kick it.
A Moving Car: When a car is moving at a constant speed on a straight, level road, the forward thrust from the engine (or momentum) balances the forces of air resistance and friction acting backward. If the driver applies the brakes, an unbalanced backward force is applied, causing the car to decelerate.
Seatbelts in Cars: When a car suddenly stops, the passengers tend to continue moving forward. This is because their bodies have inertia and tend to maintain their state of motion. The seatbelt provides an unbalanced backward force to stop the passenger along with the car.

Graphs for Zero Net Force

When the net force acting on an object is zero, its acceleration is zero. This leads to two possible scenarios:

Object at Rest:
Position-time graph: A horizontal line, showing position does not change over time.
Velocity-time graph: A horizontal line on the time axis, showing velocity is zero.
Object Moving with Constant Velocity:
Position-time graph: A straight line with a constant slope, indicating constant speed.
Velocity-time graph: A horizontal line parallel to the time axis, at a non-zero velocity value, indicating constant speed and direction.

Remember
Newton's first law defines inertia. Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest. The more mass an object has, the greater its inertia.

Exam-smart
Case studies often involve scenarios with balanced or unbalanced forces. For example, you might be given a description of a box on a surface where applied forces (like pushing or pulling) and resistive forces (like friction) are mentioned. You'll need to determine if the net force is zero and, therefore, if the object will remain at rest or move with constant velocity, or if it will accelerate. You might also be asked to interpret position-time or velocity-time graphs representing motion with zero net force.

Newton’s Second Law of Motion

Newton’s Second Law of Motion establishes a fundamental relationship between the net force acting on an object and its resulting acceleration. It states that when a net force acts on an object, the object will accelerate in the direction of that force.

The magnitude of this acceleration is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object.

Mathematical Formulation

This relationship is mathematically expressed by the equation:

F = m a

Where:

$F$ represents the net force acting on the object (in Newtons, N).
$m$ represents the mass of the object (in kilograms, kg).
$a$ represents the acceleration of the object (in meters per second squared, m/s²).

This equation can also be written as:

a = \frac{F}{m}

This form clearly shows that acceleration ( $a$ ) is directly proportional to net force ( $F$ ) and inversely proportional to mass ( $m$ ).

Units of Force

The SI unit of force is the Newton (N). It is defined as the force required to accelerate a mass of 1 kilogram by 1 meter per second squared:

1 N = 1 kg \cdot {m/s}^{2}

Force, Mass, and Acceleration: A Deeper Look

Direct Proportionality to Force: If you apply a larger net force to an object of the same mass, it will experience a greater acceleration. Imagine pushing a swing: a gentle push causes a small motion, while a strong push results in a larger, faster swing.
Inverse Proportionality to Mass: For the same net force applied, an object with a smaller mass will accelerate more than an object with a larger mass. This is why it's easier to push a bicycle than a car with the same effort.

Momentum and Newton's Second Law

A more complete formulation of Newton's second law involves momentum.

Momentum (p) is defined as the product of an object's mass ( $m$ ) and its velocity ( $v$ ):

p = m v

The direction of momentum is the same as the direction of velocity.

Newton's Second Law (in terms of momentum): The rate of change of momentum of an object is directly proportional to the net force acting on it, and this change occurs in the direction of the net force. Mathematically:

F = \frac{Δ p}{Δ t}

Where $Δ p$ is the change in momentum and $Δ t$ is the time over which the change occurs. This form is particularly useful when the mass of the object is not constant.

Real-Life Applications

Newton's Second Law helps explain many everyday phenomena:

Catching a Cricket Ball: Fielders pull their hands back when catching a fast-moving ball. This increases the time ( $Δ t$ ) over which the ball's momentum changes, thus reducing the force ( $F = Δ p / Δ t$ ) they need to apply to stop it, minimizing injury.
Airbags in Cars: Airbags increase the time of impact during a collision, spreading the force over a longer period. This reduces the acceleration and thus the impact force on the passenger, lowering the risk of severe injuries.
Cracking a Coconut: A coconut dropped from a height hits the ground with high velocity, meaning it has significant momentum. When it hits the hard ground, its momentum changes very rapidly (small $Δ t$ ). This results in a very large force that breaks the shell.

Examples

Example 6.4: Weightlifter A weightlifter holds a barbell.

Mass of each weight: 10 kg
Mass of the bar: 10 kg
Total mass ( $m$ ): $10 kg + 10 kg + 10 kg = 30 kg$
Acceleration due to gravity ( $g$ ): $9.8 {m/s}^{2}$
Force applied to hold the barbell steady is equal to the gravitational force (weight) acting downwards.
Weight ( $F_{g}$ ) $= m g = 30 kg \times 9.8 {m/s}^{2} = 294 N$
The weightlifter applies an upward force of 294 N to keep the barbell steady.

Example 6.5: Pushing a Block A block of mass 25 kg is on a horizontal floor. Maximum friction is 50 N. Rahul pushes with a constant force for 2 seconds.

Case (i): Force applied = 50 N
Applied force = Frictional force.
Net force $= 50 N - 50 N = 0 N$ .
Since the net force is zero, the block remains stationary.
Case (ii): Force applied = 55 N
Net force $= 55 N - 50 N = 5 N$ (forward).
Mass ( $m$ ): 25 kg
Acceleration ( $a$ ) $= F / m = 5 N / 25 kg = 0.2 {m/s}^{2}$ .
Initial velocity ( $u$ ): 0 m/s
Time ( $t$ ): 2 s
Displacement ( $s$ ) $= u t + \frac{1}{2} a t^{2} = (0 \times 2) + \frac{1}{2} (0.2 {m/s}^{2}) (2 s)^{2} = 0.4 m$ .
The block will be displaced by 0.4 m in the forward direction.

Example 6.6: Sports Car Velocity-Time Graph Car mass = 1500 kg.

Interval 0 s to 5 s:
From the graph, acceleration ( $a$ ) $= \frac{10 m/s - 0 m/s}{5 s} = 2 {m/s}^{2}$ .
Force ( $F$ ) $= m a = 1500 kg \times 2 {m/s}^{2} = 3000 N$ (towards the east).
Interval 5 s to 10 s:
Velocity is constant (10 m/s).
Acceleration ( $a$ ) = 0 m/s².
Net force ( $F$ ) $= m a = 1500 kg \times 0 {m/s}^{2} = 0 N$ .
Interval 10 s to 15 s:
From the graph, acceleration ( $a$ ) $= \frac{0 m/s - 10 m/s}{5 s} = - 2 {m/s}^{2}$ .
Force ( $F$ ) $= m a = 1500 kg \times (- 2 {m/s}^{2}) = - 3000 N$ (acting towards the west, opposite to motion).

Remember
The net force is crucial. If multiple forces act on an object, you must first calculate their vector sum to find the net force before applying $F = m a$ .

Exam-smart
You will be given information about forces acting on an object or a situation describing motion (like a velocity-time graph, or a scenario involving friction). You will need to apply $F = m a$ or its momentum form to calculate acceleration, force, mass, or displacement, considering the direction of forces. You might also be asked to explain real-life phenomena using this law.

Newton’s Third Law of Motion

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that forces always occur in pairs. When one object exerts a force on a second object, the second object simultaneously exerts a force back on the first object. These two forces are equal in magnitude and opposite in direction.

It is crucial to understand that these action-reaction forces act on two different objects. Therefore, they do not cancel each other out. If they acted on the same object, they would balance.

How Forces Occur in Pairs

Interaction is Key: A force cannot exist in isolation. It always involves an interaction between at least two objects.
Simultaneous Action: The action force and the reaction force happen at the exact same time.
Equal Magnitude, Opposite Direction: The strength of the force exerted by object A on object B is precisely the same as the strength of the force exerted by object B on object A. The direction of the force from B on A is exactly opposite to the direction of the force from A on B.

Example: When you push a wall, you exert a force on the wall. Simultaneously, the wall exerts an equal and opposite force on your hand.

Real-life Examples of Newton's Third Law

Scenario	Action Force	Reaction Force	Object 1	Object 2
Walking or Running	Foot pushes backward on the ground.	Ground pushes forward on the foot.	Foot	Ground
Rocket Launch	Rocket engine expels hot gases downwards.	Expelled gases push the rocket upwards.	Rocket	Gases
Rowing a Canoe	Paddle pushes water backward.	Water pushes the paddle (and canoe) forward.	Paddle	Water
Firing a Gun	Gun pushes the bullet forward.	Bullet pushes the gun backward (recoil).	Gun	Bullet
Jumping	Legs push down on the Earth.	Earth pushes up on the legs.	Legs	Earth
Object at Rest on a Table	Object exerts downward force (due to gravity) on table.	Table exerts upward normal force on the object.	Object	Table
Earth and a Falling Object (e.g., fruit)	Earth pulls the fruit down.	Fruit pulls the Earth up.	Earth	Fruit
Magnets	Magnet 1 exerts force on Magnet 2.	Magnet 2 exerts equal and opposite force on Magnet 1.	Magnet 1	Magnet 2
Charged Objects (Electrostatic Force)	Charged object 1 exerts force on Charged object 2.	Charged object 2 exerts equal and opposite force on 1.	Charged obj 1	Charged obj 2

Why Forces Don't Cancel Out

The key to understanding why action-reaction pairs don't cancel is that they act on different objects.

Balanced Forces: Balanced forces are two or more forces acting on the same object that are equal in magnitude and opposite in direction, resulting in no change in the object's motion. (This concept relates to Newton's First and Second Laws).
Action-Reaction Forces: These are forces between two objects. They are equal and opposite but act on their respective objects, causing acceleration on both (unless one object's mass is extremely large).

Example: When you push a heavy table, your force on the table causes the table to move. The table's reaction force on you might cause you and your chair to move backward. These are two separate effects on two separate objects.

The Role of Mass and Acceleration

While the forces are always equal in magnitude, the effect of these forces (acceleration) depends on the mass of the objects involved, as described by Newton's Second Law ( $F = m a$ , or $a = F / m$ ).

Example: When a bullet is fired, the gun exerts a force on the bullet, and the bullet exerts an equal force on the gun. However, the bullet has a very small mass, so it experiences a large acceleration. The gun has a much larger mass, so it experiences a much smaller acceleration (recoil).
Earth and Fruit: The Earth pulls a falling fruit with a certain force, and the fruit pulls the Earth with an equal force. Because the Earth's mass is enormous, its acceleration due to the fruit's pull is negligible and unnoticeable. The fruit's acceleration due to the Earth's pull is significant.

Remember
Newton's third law applies to all types of forces, including contact forces (like pushing, friction) and non-contact forces (like gravity, magnetism, electrostatic forces).

Exam-smart
Case study questions will present scenarios like a rocket launch, a person walking, or a boat moving. You'll need to identify the action-reaction pairs, specify which object each force acts upon, and explain why motion occurs despite equal and opposite forces, often linking it to mass differences and the resulting accelerations. For instance, a question might ask why a gun recoils less than the bullet's forward speed, requiring you to mention $F_{g u n} = F_{b u l l e t}$ but $m_{g u n} a_{g u n} = m_{b u l l e t} a_{b u l l e t}$ , leading to $a_{g u n} / a_{b u l l e t} = m_{b u l l e t} / m_{g u n}$ .

Forces Acting on a System of Objects

When Newton's laws of motion are applied to a single object, they help us predict its position and velocity under the influence of forces. However, these laws can also be extended to analyze the motion of a system of objects, which are two or more objects connected or interacting with each other.

Treating a System as a Single Object

Instead of analyzing each object within a connected system individually, we can often simplify the analysis by treating the entire system as a single entity. This approach is particularly useful when dealing with internal forces (forces acting between objects within the system) that do not affect the overall motion of the system. By focusing only on the external forces (forces acting on the system from outside), we can more easily determine the system's acceleration.

For example, consider two boxes, Box 1 and Box 2, connected by a string on a frictionless horizontal surface. If an external force $F$ pulls Box 1 to the right, the string exerts a tension $T$ on both boxes. The tension $T$ is an internal force because it acts between Box 1 and Box 2. The force $F$ is an external force.

According to Newton's second law, the acceleration ( $a$ ) of the system is given by:

a = \frac{Net external force}{Total mass of the system}

In our example, the net external force is $F$ , and the total mass of the system is the sum of the masses of Box 1 ( $m_{1}$ ) and Box 2 ( $m_{2}$ ), i.e., $(m_{1} + m_{2})$ . Therefore, the acceleration of the system is:

a = \frac{F}{m_{1} + m_{2}}

This means the entire system of two boxes accelerates as if it were a single object with a total mass of $(m_{1} + m_{2})$ , experiencing only the external force $F$ .

External forces such as gravity acting downwards and the normal force from the surface acting upwards also act on the system. However, these forces are balanced and do not contribute to the horizontal acceleration of the system.

Remember
Treating connected objects as a single system by considering only external forces simplifies the analysis of their motion.

Exam-smart
A case study might describe a scenario with multiple connected objects (like carts on a track, or a boat with rowers). You'll be asked to find the acceleration of the system. The key is to identify the net external force and the total mass of the system. Internal forces like tension or forces between colliding objects are ignored for the system's overall acceleration.

How Forces Affect Motion — Notes

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