In the previous chapter we studied how objects move. But why do objects move at all? Why does a ball stop after rolling on the ground? Why does a car need fuel to keep moving? The answers to these questions are found in the study of force and the laws of motion given by Sir Isaac Newton.
A force is a push or a pull acting on an object. Force can change the state of motion of a body, change its speed, change its direction, or change its shape. The modern understanding of force and motion began when Galileo and Newton questioned the ancient idea that a force is needed to keep a body moving.
In this chapter we study balanced and unbalanced forces, Newton's three laws of motion, momentum, the law of conservation of momentum and its applications.
When two or more forces act on an object, they can be balanced or unbalanced. If the forces acting on an object cancel each other, the net force is zero, and the forces are called balanced forces. Balanced forces cannot change the state of motion of an object; they can only change its shape. For example, when we push a heavy box and it does not move, the forces are balanced.
If the net force acting on an object is not zero, the forces are called unbalanced forces. An unbalanced force acting on an object can: 1. Change its speed (make it move faster or slower). 2. Change its direction of motion. 3. Change its shape.
For example, when we kick a ball, the unbalanced force makes the ball move, and a rolling ball slows down and stops because of the unbalanced force of friction.
Galileo studied the motion of a ball rolling down an inclined plane and concluded that a body continues in its state of motion unless an external force acts on it. He argued that the ball rolling on a rough surface stops because of friction, and that on a frictionless surface it would keep moving forever at a constant speed. This idea of Galileo was later refined by Newton into the first law of motion.
Galileo also proposed the concept of inertia, which is the natural tendency of objects to resist a change in their state of motion.
Newton's first law of motion states: "An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force."
This law has two parts: 1. If no force acts on a body at rest, it will continue to be at rest. 2. If no force acts on a moving body, it will continue to move in a straight line with uniform speed.
The first law of motion is also called the law of inertia. Inertia is the natural tendency of an object to resist a change in its state of rest or of uniform motion. Inertia is directly related to mass - the greater the mass of an object, the greater is its inertia, and the more difficult it is to change its state of motion.
Examples of inertia in daily life: - When a bus suddenly starts moving, the passengers fall backwards because their body tends to remain at rest (inertia of rest). - When a bus suddenly stops, the passengers fall forward because their body tends to keep moving (inertia of motion). - When a hanging carpet is beaten with a stick, the dust particles fall off because they tend to remain at rest while the carpet moves.
The momentum of an object is the product of its mass and velocity. Momentum is a vector quantity, and it has both magnitude and direction, with the direction being the same as that of the velocity.
Momentum (p) = mass (m) x velocity (v)
The SI unit of momentum is kilogram metre per second (kg m/s). A heavy truck moving slowly can have the same momentum as a small car moving fast. Momentum describes the quantity of motion contained in a moving body.
Newton's second law of motion states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force, and takes place in the direction of the force.
If a body of mass m has initial velocity u and final velocity v in time t, then:
Initial momentum = mu, Final momentum = mv
Rate of change of momentum = (mv - mu) / t = m(v - u)/t = m x a
Hence, Force = mass x acceleration, that is, F = ma
This equation shows that a larger force produces a larger acceleration, and the acceleration of a body is directly proportional to the net force and inversely proportional to the mass.
The SI unit of force is the newton (N). One newton is the force needed to give a mass of 1 kg an acceleration of 1 m/s^2. The CGS unit of force is the dyne, and 1 N = 10^5 dyne.
Applications of the second law: Cricketers lower their hands while catching a fast ball to increase the time of impact, which reduces the force on their hands (F = change in momentum / time). When we fall on a cushioned surface, the impact time increases and the force is reduced. Vehicles are provided with safety airbags for the same reason.
Newton's third law of motion states: "To every action there is an equal and opposite reaction."
This means that when one object exerts a force (action) on another object, the second object exerts an equal and opposite force (reaction) on the first object. The action and reaction forces always act on two different objects and act simultaneously.
Examples: - When we walk, we push the ground backwards (action); the ground pushes us forward (reaction), which enables walking. - A rocket launches by ejecting gases downwards (action); the gases push the rocket upwards (reaction). - A boatman pushes water backwards with his oars; the water pushes the boat forward. - A gun recoils backwards when a bullet is fired forward because the bullet and gun exert equal and opposite forces on each other.
The law of conservation of momentum states that the total momentum of an isolated system of objects remains constant if no external force acts on it. In a collision, the total momentum of the objects before collision equals the total momentum after collision.
For two objects A and B of masses m1 and m2 with velocities u1 and u2 before collision and v1 and v2 after collision:
Total momentum before collision = Total momentum after collision
m1u1 + m2u2 = m1v1 + m2v2
For example, when a gun of mass M fires a bullet of mass m with velocity v, the recoil velocity of the gun V is given by M x V = m x v, so the gun recoils backwards.
The recoil of a gun, the movement of a rocket and the propulsion of a jet aircraft are all applications of the law of conservation of momentum.
| Law of Motion | Statement | Formula |
|---|---|---|
| First law | Body stays at rest or uniform motion unless a force acts | Law of inertia |
| Second law | Rate of change of momentum is proportional to force | F = ma |
| Third law | Every action has an equal and opposite reaction | Action = - Reaction |
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | newton (N) |
| Momentum | p | kg m/s |
| Acceleration | a | m/s^2 |
| Mass | m | kg |
In this chapter we learned that a force is a push or a pull which can change the state of motion of a body, and that balanced and unbalanced forces have different effects. Galileo's idea that a moving body continues to move until a force acts was formalised by Newton in his first law of motion, which introduced the concept of inertia. We defined momentum as the product of mass and velocity, and derived Newton's second law, F = ma, from the rate of change of momentum. Newton's third law showed that action and reaction are equal and opposite, and the law of conservation of momentum explained collisions and the recoil of guns. These laws describe the motion of everything around us - from a cricket ball to a rocket - and form the very foundation of classical mechanics.