Force and motion are intricately related. Throwing a ball sets the ball in motion; pushing a block can displace it from its position, pulling a door can move the door from its place, catching a ball can bring it to rest. Forces are always involved in throwing, pushing, pulling, hitting, catching etc. Throughout our day, we use different kinds of forces to start or stop the motion of a moving object. But are forces always involved when we deal with motion? Let us study and learn in detail about the types of forces and the laws that govern the motion of objects.

Balanced and Unbalanced Forces

A force is a push or a pull that results in interactions between an object and its surroundings. Forces acting on an object can be of two types: balanced or unbalanced. 

Balanced forces: The forces that are equal in magnitude but opposite in direction are said to be balanced forces. When balanced forces are acting on an object, the net force acting on it will be zero. Thus, the object will not accelerate. An object moving under the effect of balanced forces either stay at rest or remain moving with uniform velocity. Balanced forces can not bring a change in the state of motion of an object. Thus, a body under the action of balanced forces acts as if no net external forces are acting on it.

Unbalanced forces: The forces that are unequal in magnitude and act in different directions on a surface are called unbalanced forces. When the forces acting on an object are unbalanced, the net force on the object will be non-zero. Thus, these forces will cause an acceleration in the object. An object under the effect of unbalanced forces can start to move (if they are at rest initially), speed up or slow down, or undergo a change in their direction of motion.

When we are pushing a block, the block does not move till the push force is balanced by the force of friction. When the push force becomes greater than the force of friction, the block starts moving, indicating that an unbalanced external force can change an object’s state of motion.

The First Law of Motion

Galileo’s performed several experiments and concluded that no forces are required to move an object at a constant speed. He studied the motion of marble over two inclined planes and observed that external unbalanced forces are required to change the motion of an object. Still, no external forces are required to maintain the uniform motion of an object. Although in a practical scenario, the forces acting on an object can never truly be balanced because of resistive force like frictional force, which acts opposite to the direction of motion.

Based on Galileo’s experiments, Newton gave three laws of motion.

According to Newton’s first law of motion, an object in the state of rest or uniform motion continues to be at rest or in uniform motion along the same straight lines unless an external unbalanced force compels it. In simple words, any object resists a change in its state of motion. The property that allows undisturbed objects to remain in their original state of rest or uniform velocity is inertia. Thus, the first law of motion is also called the law of inertia. Inertia can be of three types:

1. The inertia of rest: To understand this, consider the following example- When a tree is shaken, the fruits fall due to inertia of rest.
2. The inertia of motion: To understand this, consider the following example- When brakes are applied in a fast-moving bus, the passengers experience a force in the forward direction due to inertia of motion.
   
3. The inertia of direction: To understand this, consider the following example- When a fast-moving car suddenly turns right, all the passengers experience a force towards the left due to inertia of direction.

Inertia and Mass

Mass and inertia are interrelated quantities. Greater is the mass of an object; larger would be inertia offered by it, and similarly smaller is the mass of an object; lesser would be the inertia it offers. Thus, the inertia of an object can be quantified by its mass. Thus, we can define inertia as the natural tendency of an object to resist a change in its state of motion or of rest.

The Second Law of Motion

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 in the direction of the force.

The momentum \((p)\) of an object is the measure of the kinetic energy of an object. It is equal to the product of its mass and velocity. Mathematically,

\(p=m.v\)

Momentum is a vector quantity; it has both magnitude and direction. The SI unit of momentum is kilogram-metre per second.

According to the first law, a change in velocity is always brought by an externally applied force. Thus, a change in momentum is associated with an applied force.

Mathematical Expression for the Second Law of Motion

Consider an object of mass \(m\), moving with an initial velocity \(u\) along a straight line. Let it achieve a final velocity \(v\) over the time \(t\), under the action of a constant force \(F\).

The initial momentum of the object, \(p_{1}=m u\)

The final momentum of the object, \(p_{2}=m v\)

The change in momentum: \(\propto p_{2}-p_{1}\)

\(\propto m v-m u\)

\(\propto m(v-u)\)

The rate of change of momentum: \(\propto \frac{m(v-u)}{t}\)

According to the second law of motion,

\(F \propto \frac{m(v-u)}{t}\)

\(F=k \frac{m(v-u)}{t}……….(1)\)

[Since \(a = \frac{{\left( {v – u} \right)}}{t}\)].

Thus, \(F=kma\)

Here, \(k\) is the constant of proportionality.

For, \(k=1, F=m a\)

The SI unit of force is kilogram-metre per second squared or newton (N).

The second law of motion can be visualized in our daily lives. For example, while catching a ball, a fielder gradually pulls his hand backwards to increase the time for catching the ball, thereby the ball takes a longer time to come at rest, and hence its impact is reduced. For a similar reason, athletes performing long jumps are made to fall either on sand or a cushioned bed to increase the time of impact and thereby reduce its effect.

We can conceptualize the first law from the second law. Substitute, \(F=0\) in equation \((1)\), we will get \(v=u\). This means that object will continue to move at a uniform velocity \(u\) throughout the motion. If its initial velocity is zero, it will remain at rest in the absence of an external force.

Third Law of Motion

According to newton’s third law of motion, when a force is exerted by one object on the other, the second object exerts a force on the first object simultaneously. The forces exerted by the two objects on each other are equal in magnitude but opposite in direction. If the force applied by the first object is “action”, then the force exerted by the second object is nothing but the “reaction” to the applied force. Thus, in simple words, the third law can be stated as: to every action, there is an equal and opposite reaction—action and reaction forces act on two different objects simultaneously. The recoil of a gun after firing a bullet, walking on the ground, launching a spaceship are examples of the third law of motion.

Conservation of Momentum

The conservation of linear momentum principle states that in the absence of an external force, the total momentum of a system remains conserved. 

Let us consider the collision between two balls. Let \(m_{1}\) and \(m_{2}\) be the masses of the two balls. If \(u_{1}\) and \(u_{2}\) be the speeds of the two balls before the collision. Let \(v_{1}\) and \(v_{2}\) be the speeds of the two balls after the collision. Then,

The total momentum of the balls before the collision is given as: \(P_{i}=m_{1} u_{1}+m_{2} u_{2}\)

The total momentum of the balls before the collision is given as: \(P_{f}=m_{1} v_{1}+m_{2} v_{2}\)

Let \(F_{12}\) be the force exerted by the first ball on the second ball and \(F_{21}\) be the force exerted by the second ball on the first ball during the collision.

Then, by Newton’s third law of motion,

\(F_{12}=F_{21}\)

From Newton’s second law of motion,

\(F_{12}=\frac{m_{2} v_{2}-m_{2} u_{2}}{t}\)

\(F_{21}=\frac{m_{1} v_{1}-m_{1} u_{1}}{t}\)

Where \(t\) is the time of the collision.

Thus, \(m_{1} v_{1}+m_{2} v_{2}=m_{1} u_{1}+m_{2} u_{2}\)

Therefore, in an ideal collision (i.e. in the absence of an external force), the initial total momentum is equal to the final total momentum, i.e., momentum is conserved.

Summary

According to Newton’s first law of motion, an object in the state of rest or uniform motion continues to be at rest or in uniform motion along the same straight lines unless an external unbalanced force compels it. In simple words, any object resists a change in its state of motion.

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 in the direction of the force. 

According to newton’s third law of motion, when a force is exerted by one object on the other, the second object exerts a force on the first object simultaneously. The forces exerted by the two objects on each other are equal in magnitude but opposite in direction.

The conservation of linear momentum principle states that in the absence of an external force, the total momentum of a system remains conserved. 

FAQs on Force and laws of motion

Q.1. What is the other name for newton’s first law of motion?
Ans: The first law of motion is also called the law of inertia.

Q.2. Write the relation between force and acceleration as given by the second law of motion.
Ans: According to the second law of motion. Force \((F)\) acting on an object of mass \((m)\), moving with constant acceleration \((a)\) is \(F=ma\).

Q.3. What is momentum?
Ans: Momentum is the product of the mass and velocity of an object.

Q.4. How is inertia related to the mass of an object?
Ans: Greater is the mass of an object; larger will be inertia offered by it and vice versa. Thus, the inertia of an object is directly proportional to its mass.

Q.5. An object is moving with a uniform velocity \(u\). Suppose the mass of the object is \(m\). Calculate the force required to keep it moving at the same velocity.
Ans: According to the first law of motion, no force is required to keep an object moving at a uniform velocity. Thus, the force acting on the object is zero.

Study Fundamental Forces of Nature

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