Class 9 Science Notes | Force and Laws of Motion Notes

Force and Laws of Motion

Understanding the concepts of force and the laws of motion is fundamental to the study of physics. This chapter covers the basic principles governing the motion of objects and the forces that act upon them. Here we delve into the key concepts and laws proposed by Sir Isaac Newton, which form the foundation of classical mechanics.

Force

Definition: Force is a push or pull exerted on an object. It can change the object's state of motion or shape.

Types of Forces:

1. Contact Forces: Forces that act on objects through direct physical contact. Examples include friction, tension, normal force, and applied force.
2. Non-contact Forces: Forces that act on objects without physical contact. Examples include gravitational force, electrostatic force, and magnetic force.

Effects of Force:

1. Force can change the speed of an object (accelerate or decelerate it).
2. Force can change the direction of motion of an object.
3. Force can change the shape and size of an object.

Newton's Laws of Motion

Newton's First Law of Motion (Law of Inertia):

• Statement: An object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by an external force.
• Explanation: This law defines inertia, which is the property of an object to resist changes in its state of motion. The greater the mass of an object, the greater its inertia.

Examples:

• A book lying on a table remains at rest until someone applies a force to move it.
• A rolling ball eventually stops due to the external force of friction acting against its motion.

Newton's Second Law of Motion:

• Statement: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The law is mathematically represented as $F = ma$.
  • $F$ is the net force applied to the object.
  • $m$ is the mass of the object.
  • $a$ is the acceleration produced.

Explanation:

• This law quantifies the relationship between force, mass, and acceleration. It implies that for a given mass, an increase in the applied force results in an increase in acceleration. Conversely, for a given force, an increase in the mass of the object results in a decrease in acceleration.

Examples:

• Pushing a lighter object requires less force to accelerate it compared to a heavier object.
• A car accelerates faster when more force is applied to the gas pedal.

Newton's Third Law of Motion:

• Statement: For every action, there is an equal and opposite reaction.
• Explanation: This law implies that forces always occur in pairs. When one body exerts a force on another, the second body exerts an equal and opposite force on the first.

Examples:

• When you jump off a boat, you push the boat backward (action), and the boat pushes you forward (reaction).
• When a bird flaps its wings downward (action), it is propelled upward (reaction).

Momentum

Definition: Momentum is the product of the mass and velocity of an object. It is a vector quantity, represented as $p = mv$, where:

• $p$ is the momentum,
• $m$ is the mass,
• $v$ is the velocity.

Conservation of Momentum:

• The total momentum of a closed system remains constant if no external forces act on it. This principle is known as the law of conservation of momentum.

Examples:

• In a collision between two cars, the total momentum before and after the collision remains the same if no external forces are involved.

Applications of Newton's Laws

1. Automotive Safety:

• Seat belts and airbags are designed based on Newton's laws. In a sudden stop, an unbelted passenger would continue moving forward (First Law) until an external force (the dashboard) acts on them, causing injury. Seat belts provide the external force to decelerate the passenger safely.

2. Sports:

• Athletes use Newton's laws to improve performance. For instance, sprinters push against the ground (action) to propel themselves forward (reaction).

3. Space Exploration:

• Rockets operate on Newton's Third Law. Expelling gas backward from the rocket's engines produces an equal and opposite reaction, propelling the rocket forward.

Problems and Solutions

Problem 1: A car of mass 1000 kg accelerates from rest to a velocity of 20 m/s in 10 seconds. Calculate the force applied by the engine.

Solution:

• Initial velocity, $u = 0$ m/s
• Final velocity, $v = 20$ m/s
• Time, $t = 10$ s
• Mass, $m = 1000$ kg
• Acceleration, $a = \frac{v - u}{t} = \frac{20 - 0}{10} = 2$ m/s²
• Force, $F = ma = 1000 \times 2 = 2000$ N

Problem 2: A 50 kg cart is pushed with a force of 250 N. Calculate the acceleration of the cart.

Solution:

• Force, $F = 250$ N
• Mass, $m = 50$ kg
• Acceleration, $a = \frac{F}{m} = \frac{250}{50} = 5$ m/s²

Problem 3: Two ice skaters, one with a mass of 50 kg and the other with a mass of 70 kg, push off each other. If the 50 kg skater moves with a velocity of 3 m/s, find the velocity of the 70 kg skater.

Solution:

• Using conservation of momentum:
• Initial momentum = Final momentum
• Before push-off, both skaters are at rest, so initial momentum = 0.
• After push-off, let the velocity of the 70 kg skater be $v$.
• Momentum of 50 kg skater = $50 \times 3 = 150$ kg·m/s
• Momentum of 70 kg skater = $70 \times v$
• $50 \times 3 + 70 \times v = 0$
• $150 + 70v = 0$
• $70v = -150$
• $v = -\frac{150}{70} = -2.14$ m/s (negative sign indicates opposite direction)

Conclusion

Understanding force and the laws of motion is crucial for comprehending how objects interact in the physical world. Newton's laws provide a comprehensive framework to analyze the motion of objects under various forces. These principles have profound implications and applications in various fields such as engineering, astronomy, sports, and everyday life. Mastery of these concepts enables a deeper appreciation of the mechanics governing the universe and lays the groundwork for more advanced studies in physics.