Force and Laws of Motion
Class 09 ScienceA force can be used to change the magnitude of velocity of an object (to make the object move faster or slower) or to change its direction of motion. A force can change the shape and size of objects.
Balanced and Unbalanced Forces
Two strings X and Y are tied to the two opposite faces of the block. If you apply a force by pulling the string X, the block begins to move to the right. Similarly, if you pull the string Y, the block moves to the left. But, if the block is pulled from both the sides with equal forces, the block will not move. Such forces are called balanced forces and do not change the state of rest or of motion of an object.
Now, two opposite forces of different magnitudes pull the block. In this case, the block would begin to move in the direction of the greater force. Thus, the two forces are not balanced and the unbalanced force acts in the direction the block moves. This suggests that an unbalanced force acting on an object brings it in motion.
First Law of Motion
Newton presented three fundamental laws that govern the motion of objects. These three laws are known as Newton’s laws of motion.
The first law of motion is stated as: 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.
All objects resist a change in their state of motion. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. This is why, the first law of motion is also known as the law of inertia.
We tend to remain at rest with respect to the seat until the driver applies a braking force to stop the motorcar. With the application of brakes, the car slows down but our body tends to continue in the same state of motion because of its inertia.
An opposite experience is encountered when we are standing in a bus and the bus begins to move suddenly. Now we tend to fall backwards. This is because the sudden start of the bus brings motion to the bus as well as to our feet in contact with the floor of the bus. But the rest of our body opposes this motion because of its inertia.
When a motorcar makes a sharp turn at a high speed, we tend to get thrown to one side. We tend to continue in our straight-line motion. When an unbalanced force is applied by the engine to change the direction of motion of the motorcar, we slip to one side of the seat due to the inertia of our body.
Inertia and Mass
There is a resistance offered by an object to change its state of motion. If it is at rest it tends to remain at rest; if it is moving it tends to keep moving. This property of an object is called its inertia.
Heavier or more massive objects offer larger inertia. Quantitatively, the inertia of an object is measured by its mass.
Inertia is the natural tendency of an object to resist a change in its state of motion or of rest. The mass of an object is a measure of its inertia.
Second Law of Motion
The impact produced by the objects depends on their mass and velocity. Similarly, if an object is to be accelerated, a greater force is required to give a greater velocity.
The momentum, p of an object is defined as the product of its mass, m and velocity, v.
$$ p = mv $$
Momentum has both direction and magnitude. Its direction is the same as that of velocity, v. The SI unit of momentum is kilogram-metre per second (kg m s-1). Since the application of an unbalanced force brings a change in the velocity of the object, a force also produces a change of momentum.
The force necessary to change the momentum of an object depends on the time rate at which the momentum is changed.
The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.
Mathematical Formulation
Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively.
Change in momentum ∝ p2 – p1
∝ mv – mu
∝ m × (v – u)
$$ \text{Rate of change of momentum} \propto m \times \frac{(v − u )}{t} $$
$$ F \propto m \times \frac{(v − u )}{t} $$
$$ F = km \times \frac{(v − u )}{t} = k \, m \, a $$
The quantity, k is a constant of proportionality. The SI units of mass and acceleration are kg and m s-2 respectively. The unit of force is so chosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m s-2 in an object of 1 kg mass.
F = ma
The unit of force is kg m s-2 or newton, which has the symbol N.
The second law of motion gives a method to measure the force acting on an object as a product of its mass and acceleration.
While catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball. In doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is decreased and therefore the impact of catching the fast moving ball is also reduced.
The first law of motion can be mathematically stated from the mathematical expression for the second law of motion.
F = ma
$$ F = m \frac{(v − u)}{t} $$
Ft = mv – mu
When F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest.
Third Law of Motion
The first two laws of motion tell us how an applied force changes the motion and provide us with a method of determining the force. The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object.
The third law of motion states that to every action there is an equal and opposite reaction. The action and reaction always act on two different objects, simultaneously.
When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite force on the gun. This results in the recoil of the gun. Since the gun has a much greater mass than the bullet, the acceleration of the gun is much less than the acceleration of the bullet.