FORCE AND LAWS OF MOTION

IMPORTANT TERMS

Force: - Pull or push of an object is called force.

Balanced force: - If the resultant of all forces acting on a body is zero, then the forces are called balanced forces.

Unbalanced Force: - If the resultant forces acting on a body is not zero, then the forces are called unbalanced forces.

Friction force: - Friction force is a force which resist the motion and arises between two surfaces in contact.

Inertia: - It is the natural tendency of an object that resists the change in state of motion or rest of the object.

First law of motion: - An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.

Second law of motion: - The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.     

Third law of motion: - To every action, there is an equal and opposite reaction and they act on two different bodies.

 

Momentum: - The product of velocity and mass is called the momentum. Momentum is denoted by p.

Law of Conservation of Momentum: - It states that in an isolated system, the total momentum remains conserved.

FORCE

Pull or push of an object is called force. It is denoted by ‘F’. Its SI unit is Newton.

Effect of Force:

• Force can make a stationary body in motion
• Force can stop a moving body.
• Force can change the direction of a moving object.
• Force can change the speed of a moving body.
• Force can change the shape and size of an object.
• There are two types of forces namely balanced forces and unbalanced forces.

                          

Balance forces

• If the resultant of all forces acting on a body is zero, then the forces are called balanced forces.
• These forces do not cause any change of state of an object.
• These are equal in magnitude and opposite in direction.
• Although balanced forces cannot produce motion in a stationary body or stop a moving body but they can change the shape and size of an object.

 

Unbalance forces

• If the resultant forces acting on a body is not zero, then the forces are called unbalanced forces.
• These forces can move a stationary body as well as stop a moving body.
• These forces can accelerate the body and thus resulting force acting on a body can    either change the magnitude of its velocity or change the direction of its velocity.

 

Friction force

It is a force which resist the motion and arises between two surfaces in contact. Force of friction always opposes motion of objects.

Newton’s Laws of Motion

Newton investigated the ideas of Galileo and formulated the three laws of motion. These laws are known as Newton’s Laws of Motion.

Newton's First Law of Motion 

“An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.”

 

• The first law of motion is also known as the law of inertia because all objects resist a change in their state of motion or rest.
• The tendency of undisturbed objects whether they are at rest or moving with uniform velocity is called inertia.
• A body having more inertia required more force to bring the change in the state of rest or uniform motion of the body.
• Heavier objects have more inertia then lighter objects and thus mass is the measure of the inertia of the body.

 

Examples/Applications of first law of motion

• A person standing in a bus falls backward when bus starts moving suddenly due to inertia of rest. The person and bus both are in rest while bus is not moving, as the bus starts moving the legs of the person start moving along with bus but rest portion of his body has tendency to remain in rest.
• A person standing in a moving bus falls forward if driver stops suddenly due to inertia of motion. The person and bus both are in motion while bus is moving, as the bus stops moving, the legs of the person stop moving along with bus but rest portion of his body has tendency to remain in motion. Therefore, he falls forward due to inertia of motion.
• When a pile of coin on the carom-board is hit by a striker, only the coin at the bottom moves away leaving rest of the pile of coin at same place. It happens because of the inertia of rest of all the coins that are in the pile. As the striker hits the bottom coin, so only the bottom coin comes in the motion, while rest of the pile of coin stay at same place.
• When we beat a carpet, we are forcing the dust to move along with the carpet. Due to the dust having inertia, it resists motion. This is why dust comes out of a carpet when it is beaten with a stick.
• Seat belts are car's safety accessories that prevent passengers to resist passengers' motion of inertia and thereby protect passengers from flying out of the seat during car accidents.
• When a tree is shaken, it moves to and fro, but fruits or leaves remain at rest due to its inertia of rest and therefore fruit and leaves break off the tree.

Momentum

• It is defined as the product of its mass and velocity. Momentum is denoted by ‘p’.
• Therefore, momentum of the object = Mass x Velocity.

Or, p = m x v

Where, p = momentum, m = mass of the object and v = velocity of the object.

• Momentum is a vector quantity and its SI unit is kgms-1.
• The momentum of an object in the rest is equal to zero.

Or, p = m x v

Thus, p = m x 0= 0 (v=0, as the object is not moving).

• A person gets injured in the case of hitting by a moving object, such as stone, pebbles etc. because of momentum of the object.
• Even a small bullet is able to kill a person when it is fired from a gun because of its momentum due to great velocity.

 

Newton's Second Law of Motion

“The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.”

Let an object of mass ‘m’ is moving with ′u′ velocity and after time ′t′ its velocity becomes ′v′. Then,

Momentum (p) of the object at its initial velocity (u) = m x u = mu

Momentum (p) of the object at its final velocity (v) = m x v = mv

Change in momentum = mv – mu = m(v-u)

Rate of change of momentum = m(v-u)/t-----(i)

 

According to the Newton’s second law of motion, force is directly proportional to the rate of change of momentum.

          Therefore, Force ∝ Rate of change of momentum

After substituting the value of rate of change of momentum from equation (i) we get.

                  F ∝ m(v-u)/t

                  F ∝ ma [acceleration (a) is the rate of change in velocity and thus = (v-u)/t]

                  F =Kma ----(ii), Where K is the proportionality constant.

1unit force is defined as the mass of 1kg object produces the acceleration of 1m/s2

            1 unit of force = K x 1kg x 1m/s2

By putting the value of k=1 in equation (ii)

                  F =ma ----(iii)

Force = mass x acceleration.

Thus, the second law of motion gives us a method to measure the force acting on an object as a product of its mass and acceleration.

Examples/Applications of second law of motion

• While catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball. By doing this, the fielder increases the time during which the high velocity of the moving ball decreases to zero and subsequently the rate of change of momentum decreases.

• If the cricket ball is caught without backing a hand, then the ball would come to rest in fraction of second with high rate of change of momentum. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.
• In a high jump athletic event, athletes are made to fall either on a cushioned bed or on a sand bed. This is done to decrease the rate of change of momentum by increasing the time. Since the rate of change of momentum is small, hence the impact of the force will be also decreased.

 

Newton's Third Law of Motion 

 

“To every action, there is an equal and opposite reaction and they act on two different bodies.”

• These two forces are always equal in magnitude but opposite in direction.
• These forces act on different objects and never on the same object.

 

Examples/Applications of third law of motion

• During walking, we push the road in backward direction, and in the reaction the road also pushes our feet with equal magnitude of force but in opposite direction. This enables us to move in forward direction against the push.
• When bullet is fired from a gun, gun exerts a forward force on the bullet. The bullet also exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun and the gunman feeling a backward push from the butt of gun.
• Sailor pushes water with oar in backward direction, resulting in the water pushing the oar in forward direction. Consequently, the boat is pushed in forward direction. Force applied by oar and water are of equal magnitude but in opposite directions.

 

Law of conservation of linear momentum

 

“The sum of momenta of the two objects before collision is equal to the sum of momenta after the collision provided there is no external unbalanced force acting.”

 

It is an extremely important consequence of Newton's third law of motion in combination with the second law of motion.

 

Suppose two objects (A and B) of masses mA and mB are travelling in the same direction along a straight line at different velocities uA and uB, respectively.

 

There are no other external unbalanced forces acting on them. Let uA > uB and thus these two objects collide with each other.

 

During collision which lasts for a time t, let A impart an average force equal to FAB on B and let B exert an average FBA on A.

 

Suppose vA and vB are the velocities of the two balls A and B after the collision, respectively.

 

Therefore, Change in momentum of A=mA(vA-uA) 

                  Change in momentum of B=mB(vB-uB)

 

The rate of change of momentum of object A during the collision = mA(vA-uA)/t 

 

Or, FAB = mA(vA-uA)/t 

 

The rate of change of momentum of object B during the collision = mB (vB-uB)/t 

 

                               Or, FBA = mB(vB-uB)/t 

 

We know that from third law of motion FAB=-FBA

 

    Or, mA (vA-uA)/t = -mB(vB-uB)/t 

 

After cancelling ‘t’ on both sides and rearranging the equation we get
                       mAuA+ mBuB = mAvA + mBvB      

    

Since, mAuA+ mBuB represents the total momentum of objects A and B before collision and mAvA + mBvB represents the total momentum of objects after collision. This means that 

            

 Total momentum before collision=total momentum after collision

 

• mAuA+ mBuB = mAvA + mBvB is known as the law of conservation of momentum.

 

• Above equation states that total momentum of object A and B before collision is equal to the total momentum of object A and B after collision. This means there is no loss of momentum, i.e. momentum is conserved. This situation is considered assuming there is no external force acting upon the object.

 

• One of the applications of conservation of momentum is the launching of rockets. The rocket fuel burns that pushes the exhaust gases downwards, and due to this the rocket gets pushed upwards.

 

Interesting Facts

• Two natural forces that we have experienced are the force of gravity and magnetic forces. These two forces act at a distance and do not require direct contact between the objects to function. 
• Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.
• Inertia comes from the Latin word, iners, meaning idle, sluggish.
• Newton's first law is a restatement of the law of inertia which Galileo had already described.