Force And Laws Of Motion - CBSE Class 9 Science

What is Force?

In our daily lives, we constantly interact with objects by pushing, pulling, lifting, or throwing them. These actions – push or pull – are what we call a Force. A force is an external effort that can change or tends to change the state of rest or uniform motion of an object, or change its shape. For example, kicking a football applies a force that changes its state from rest to motion, and pressing a spring applies a force that changes its shape. Force is a vector quantity, meaning it has both magnitude and direction. Its SI unit is the Newton (N).

Forces can be broadly classified into two types based on their effect:

1. Balanced Forces: When two or more forces acting on an object are equal in magnitude and opposite in direction, their net effect is zero. The object remains in its state of rest or continues to move with uniform velocity. For instance, in a tug-of-war, if both teams pull with equal force, the rope doesn't move.

1. Unbalanced Forces: When the forces acting on an object are unequal in magnitude or are not in opposite directions, there is a net resultant force. This unbalanced force causes a change in the object's state of motion, meaning it will either start moving, speed up, slow down, stop, or change direction. For example, if one team pulls harder in a tug-of-war, the rope moves in their direction due to an unbalanced force.

Newton's First Law of Motion and Inertia

Inertia

Inertia is the inherent property of an object by virtue of which it resists any change in its state of rest or uniform motion along a straight line. It is a measure of an object's mass; a more massive object has greater inertia.

Newton's First Law of Motion

An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force. This law is also known as the Law of Inertia.

Understanding Inertia and the First Law

Newton's First Law essentially states that objects are 'lazy' and prefer to continue doing what they are already doing. If an object is at rest, it wants to stay at rest. If it's moving, it wants to keep moving at the same speed and in the same direction. This natural tendency to resist changes in its state of motion is called inertia. The more mass an object has, the greater its inertia, and the harder it is to change its motion.

Think about it: it's easier to push an empty shopping cart than a full one because the full cart has more mass, hence more inertia. When a moving bus suddenly applies brakes, passengers tend to fall forward due to their inertia of motion. Their bodies want to continue moving forward even as the bus slows down. Conversely, when a stationary bus suddenly starts, passengers tend to fall backward due to their inertia of rest; their bodies want to remain at rest while the bus moves forward. This law highlights that force is required not to maintain motion, but to change motion.

Newton's Second Law of Motion: Quantifying Force

1. Understanding Momentum — Before defining the second law, we need to understand momentum. Momentum (p) is a measure of the 'quantity of motion' contained in an object. It is defined as the product of an object's mass (m) and its velocity (v). Formula: p = m × v Momentum is a vector quantity, and its SI unit is kilogram-meter per second (kg m/s). A heavier object moving at the same speed has more momentum than a lighter one, and a faster object of the same mass has more momentum than a slower one.
2. Statement of Newton's Second Law — Newton's Second Law states that the rate of change of an object's momentum is directly proportional to the applied unbalanced force and takes place in the direction of the force. This means a larger force will produce a greater change in momentum over a given time, or the same change in momentum in a shorter time.
3. Mathematical Formulation (F = ma) — Let's derive the common formula for force: 1. Change in Momentum: If an object of mass 'm' changes its velocity from initial velocity 'u' to final velocity 'v' in time 't', its initial momentum is p1 = mu, and final momentum is p2 = mv. Change in momentum (Δp) = p2 - p1 = mv - mu = m(v - u). 2. Rate of Change of Momentum: Δp / t = m(v - u) / t. 3. Relating to Force: From the definition of acceleration (a = (v-u)/t), we can write: Rate of change of momentum = m × a. 4. Second Law Application: According to Newton's Second Law, Force (F) ∝ (Rate of change of momentum). So, F ∝ m × a. To remove the proportionality sign, we introduce a constant 'k'. F = k × m × a. In SI units, the constant k is taken as 1. Thus, the most famous formula for force is: F = m × a Where F is the applied force, m is the mass of the object, and a is its acceleration. The unit of force, Newton (N), is defined such that 1 N is the force required to produce an acceleration of 1 m/s² in an object of mass 1 kg (1 N = 1 kg m/s²).

Worked Example: Applying Newton's Second Law

• Problem: A force of 5 N acts on an object of mass 2 kg. Calculate the acceleration produced in the object. Solution: Step 1: Identify the given values. Force (F) = 5 N Mass (m) = 2 kg Step 2: Recall Newton's Second Law formula. F = m × a Step 3: Rearrange the formula to find acceleration (a). a = F / m Step 4: Substitute the values and calculate. a = 5 N / 2 kg a = 2.5 m/s² Final Answer: The acceleration produced in the object is 2.5 m/s².

Newton's Third Law of Motion: Action and Reaction

Newton's Third Law of Motion explains how forces always occur in pairs. It states: To every action, there is always an equal and opposite reaction.

This law emphasizes that forces always exist in pairs and act simultaneously. When one object exerts a force (action) on a second object, the second object simultaneously exerts an equal force (reaction) in the opposite direction on the first object. It's crucial to understand that these action and reaction forces always act on different objects and therefore cannot cancel each other out. If they acted on the same object, they would indeed cancel, and no motion would occur.

Examples:

• Walking: When you walk, your foot pushes the ground backward (action force). The ground, in turn, pushes your foot forward with an equal and opposite force (reaction force), propelling you forward.
• Swimming: A swimmer pushes the water backward (action force), and the water pushes the swimmer forward (reaction force).
• Rocket Propulsion: A rocket expels hot gases downwards at high speed (action force). The gases, in return, exert an equal and opposite upward force on the rocket (reaction force), pushing it into space.
• Recoil of a Gun: When a bullet is fired from a gun, the gun exerts a forward force on the bullet (action force). The bullet, in turn, exerts an equal and opposite backward force on the gun (reaction force), causing it to recoil.

Law of Conservation of Momentum

The Law of Conservation of Momentum is a powerful principle derived from Newton's Laws. It states that in an isolated system (where no external unbalanced force acts on the system), the total momentum of the system remains constant. This means that the total momentum before an interaction (like a collision or explosion) is equal to the total momentum after the interaction.

Consider two objects, A and B, with masses m1 and m2, and initial velocities u1 and u2 respectively, moving in a straight line. If they collide and their velocities after collision become v1 and v2, the law of conservation of momentum can be expressed as:

Total momentum before collision = Total momentum after collision

m1u1 + m2u2 = m1v1 + m2v2

This principle is widely applicable, from understanding collisions in billiards to explaining how rocket engines work. For instance, in a collision between two billiard balls, the total momentum of the two balls before the collision is exactly the same as their total momentum after the collision, assuming no external forces like friction are significant. When a gun fires a bullet, the forward momentum gained by the bullet is equal in magnitude to the backward momentum (recoil) gained by the gun, but in the opposite direction, ensuring the total momentum of the gun-bullet system remains conserved.

YoLearn's Exam Tip: Common Pitfalls to Avoid

To ace your exams on Force and Laws of Motion, pay close attention to these common mistakes:

1. Confusing Action-Reaction with Balanced Forces: Remember, action and reaction forces always act on two different bodies, so they cannot cancel each other out. Balanced forces, on the other hand, act on the same body and do cancel each other.
2. Incorrect Units: Always use SI units (meters, kilograms, seconds, Newtons) consistently in your calculations. A common error is mixing grams with kilograms or cm/s with m/s.
3. Vector Directions in Momentum Problems: Momentum is a vector quantity. When applying the conservation of momentum (m1u1 + m2u2 = m1v1 + m2v2), assign positive and negative signs to velocities based on their direction. For instance, if one direction is positive, the opposite direction is negative.
4. Misinterpreting Inertia: Inertia is a property, not a force. It's the resistance to change in motion, directly proportional to mass. Don't confuse it with momentum, which is mass in motion.
5. Derivations: Practice the derivation of F = ma from the second law of motion and the derivation of the conservation of momentum carefully. They are frequently asked in exams.

Practice Questions with Solutions

• Q: A car of mass 1200 kg is moving with a velocity of 54 km/h. When brakes are applied, it stops in 5 seconds. Calculate the force exerted by the brakes. A: Step 1: Convert initial velocity to m/s. Initial velocity (u) = 54 km/h = 54 (1000/3600) m/s = 15 m/s. Final velocity (v) = 0 m/s (since it stops). Mass (m) = 1200 kg. Time (t) = 5 s. Step 2: Calculate the acceleration (a). a = (v - u) / t = (0 - 15) / 5 = -3 m/s² (negative sign indicates deceleration). Step 3: Calculate the force using Newton's Second Law (F=ma). F = 1200 kg (-3 m/s²) = -3600 N. Final answer: The force exerted by the brakes is 3600 N (the negative sign indicates it's an opposing force).
• Q: An object of mass 10 kg is accelerated uniformly from rest to a velocity of 20 m/s in 4 seconds. Calculate the magnitude of the force applied. A: Step 1: Identify given values. Mass (m) = 10 kg Initial velocity (u) = 0 m/s (from rest) Final velocity (v) = 20 m/s Time (t) = 4 s Step 2: Calculate acceleration (a). a = (v - u) / t = (20 - 0) / 4 = 5 m/s². Step 3: Calculate force (F = ma). F = 10 kg * 5 m/s² = 50 N. Final answer: The magnitude of the force applied is 50 N.
• Q: A bullet of mass 20 g is horizontally fired with a velocity of 150 m/s from a pistol of mass 2 kg. What is the recoil velocity of the pistol? A: Step 1: Convert masses to kg and identify given values. Mass of bullet (m1) = 20 g = 0.02 kg Velocity of bullet (v1) = 150 m/s Mass of pistol (m2) = 2 kg Initial velocity of bullet and pistol (u1, u2) = 0 m/s (both at rest initially) Recoil velocity of pistol (v2) = ? Step 2: Apply the Law of Conservation of Momentum. m1u1 + m2u2 = m1v1 + m2v2 (0.02 kg 0 m/s) + (2 kg 0 m/s) = (0.02 kg 150 m/s) + (2 kg v2) 0 = 3 kg m/s + 2 kg v2 Step 3: Solve for v2. 2 kg v2 = -3 kg m/s v2 = -3 / 2 m/s = -1.5 m/s. Final answer: The recoil velocity of the pistol is 1.5 m/s in the opposite direction of the bullet.
• Q: Explain why it is difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity. A: Step 1: Identify the principle involved. This situation demonstrates Newton's Third Law of Motion and the Law of Conservation of Momentum. Step 2: Apply Newton's Third Law. When the fireman holds the hose, the hose ejects water forward at high velocity (action force). According to Newton's Third Law, the water exerts an equal and opposite reaction force on the hose, pushing it backward. Step 3: Relate to momentum. The rapid expulsion of a large mass of water at high velocity results in a significant forward momentum for the water. To conserve total momentum, an equal and opposite momentum is imparted to the hose (and the fireman holding it) in the backward direction. Final answer: It is difficult for a fireman to hold a hose because the water ejected at high velocity creates a significant forward momentum, and by Newton's Third Law, an equal and opposite backward reaction force and momentum are exerted on the hose, causing it to push strongly against the fireman's hands.

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