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### Force and Laws of Motion Notes

A force is a push or pull upon an object resulting from the object’s interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.

Balanced and Unbalanced Forces

Balanced forces do not cause a change in motion. They are equal in size and opposite in direction.

For example
If any one man compete against another one who is just about as strong as second is , there will probably be a time when both men are pushing as hard as they can, but both men’s arms stay in the same place. This is an example of balanced forces. The force exerted by each person is equal, but they are pushing in opposite directions, in this case together.
Because the force that each man is exerting is equal, the two forces cancel each other out and the resulting force is zero. Therefore, there is no change in motion.

Unbalanced forces always cause a change in motion. They are not equal and opposite.

When two unbalanced forces are exerted in opposite directions, their combined force is equal to the difference between the two forces and is exerted in the direction of the larger force.

#### First Law of Motion

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

There are many more applications of Newton’s first law of motion. Several applications are listed below.

• Blood rushes from head to r feet while quickly stopping when riding on a descending elevator.
• The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.
• A brick is painlessly broken over the hand of a physics teacher by slamming it with a hammer.
• To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted.
• Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.
• While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other objects which abruptly halts the motion of the skateboard.

Inertia and Mass

Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a straight line at constant velocity. The principle of inertia is one of the fundamental principles of classical physics that are used to describe the motion of objects and how they are affected by applied forces.
The law of inertia states that it is the tendency of an object to resist a change in motion. According to Newton, an object will stay at rest or stay in motion (i.e. “maintain its velocity” in modern terms) unless acted on by a net external force, whether it results from gravity, friction, contact, or some other source. The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of Nicolaus Copernicus in the 16th century, who argued that the earth (and everything on it) was in fact never “at rest”, but was actually in constant motion around the sun.Galileo, in his further development of the Copernican model, recognized these problems with the then-accepted nature of motion and, at least partially as a result, included a restatement of Aristotle’s description of motion in a void as a basic physical principle:

“A body moving on a level surface will continue in the same direction at a constant speed unless disturbed.”

#### Second Law of Motion

The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

MATHEMATICAL FORMULATION OF SECOND LAW OF MOTION

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.
The change in momentum       a p2 – p1

a mv – mu
a m × (v – u)

The rate of change of momentum $\alpha {{m*(\upsilon - u)} \over t}$

or the applied force  $F\alpha {{m*(\upsilon - u)} \over t}$
$F\alpha {{km*(\upsilon - u)} \over t} = kma$

Here $a = {{(\upsilon - u)} \over t}$

is the acceleration, which is the rate of change of velocity.
The quantity, k is a constant of proportionality. The SI units of mass and acceleration are kg and ms-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. That is,

1 unit of force = k × (1 kg) × (1 m s-2).

#### Third Law of Motion

For a force there is always an equal and opposite reaction or the forces of two bodies on each other are always equal and are directed in opposite directions.

For example Let us consider two spring balances connected together. The fixed end of balance B is attached with a rigid support, like a wall. When a force is applied through the free end of spring balance A, it is observed that both the spring balances show the same readings on their scales. It means that the force exerted by spring balance A on balance B is equal but opposite in direction to the force exerted by the balance B on balance A. The force which balance A exerts on balance B is called the action and the force of balance B on balance A is called the reaction. This gives us an alternative statement of the third law of motion i.e., to every action there is an equal and opposite reaction.

Conservation of Momentum

Suppose two objects (two balls A and B, say) of masses mA and mB are travelling in the same direction along a straight line at different velocities uA and uB, respectively  And there are no other external unbalanced forces acting on them. Let uA > uB and the two balls collide with each other as shown in . During collision which lasts for a time t, the ball A exerts a force FAB on ball B and the ball B exerts a force FBA on ball A. Suppose vA and vB are the velocities of the two balls A and B after the collision, respectively

Point Notes

• 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 natural tendency of objects to resist a change in their state of rest or of uniform motion is called inertia.
• The mass of an object is a measure of its inertia. Its SI unit is kilogram (kg).
• Force of friction always opposes motion of objects.
• 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.
• The SI unit of force is kg m s–2. This is also known as newton and represented by the symbol N. A force of one newton produces an acceleration of 1 m s–2 on an object of mass 1 kg.
• The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. Its SI unit is kg m s–1 .
• Third law of motion: To every action, there is an equal and opposite reaction and they act on two different bodies.
• In an isolated system (where there is no external force), the total momentum remains conserved.