Newton's Laws of motion

2) NEWTON ’S LAWS OF MOTION:

1) First Law of Motion:

If the sum of all forces acting on a particle is zero then and only then the particle remains unaccelerated (i.e. remains at rest or moves with constant velocity).

• We can simply put it as if and only if .
• Newton ’s first law is valid only in inertial frames of reference.

Dumb Question:

1) What is an inertial frames of references?

Ans: A non accelerating frame of reference is called an inertial frame of reference. A frame moving with uniform velocity is an inertial frame of reference.

2) Second Law of Motion:

The acceleration of a particle is measured from an inertial frame and is given by the sum of all forces acting on particle divided by its mass.

Here and are measured at same instant.

3) Third Law of Motion:

To every action, There is an equal and opposite reaction. That is if a body A exerts a force on another body B, Then B exerts a force - on A.

Dumb Question:

1) If you apply some force for moving forward on earth, but earth exerts the same opposite force on you, then how do you move?

Ans: An important point about third law is that action and reaction forces act on different bodies. So here the point is that the man exerts some force but not on himself, but on earth and in reaction earth applies same force over him. The mass of earth is very high as compared to man and so the acceleration of earth becomes negligible.

3) FREE BODY DIAGRAM:

A free body diagram consists of a diagrammatic representation of a single body or a sub system of bodies isolated from the surroundings showing all the forces acting on it.

Illustration:

Draw the FBD in following cases:

Fig (1)

Solution:

Dumb Question:

1) Why is the normal acting like this?

Ans: The direction of the normal force is always perpendicular to the surface of contact (common surface).

2) Why is the tension direction like this?

Fig (2)

Ans:

The direction of tension is always away form the point of contact.

Ex: B is pulling A. If we need to draw FBD for both then?

4) ALGORITHM FOR SOLVING PROBLEMS:

Step 1:

Define the system:

On this system you have to apply Newton ’s laws. A system may consist of any no of particles/component but each component must have same acceleration.

Step 2:

Identify the forces:

List out all the forces acting on the system.

Step 3:

Draw FBD of the system.

Step 4:

Choose Ads and write equation. Proper signs must be put with forces or acceleration.

Illustration:

(Example 5.14 page 182 DC Pandey)

In the arrangement shown in figure (3) the strings are light and inextensible. The surface over which blocks are placed is smooth. Find

a) Acceleration of each block

b) The tension in each string

Fig (3)

Solution:
a) Let a be the acceleration of each block and T₁ and T₂ be the tensions in the two strings as shown in figure (4). Taking the two blocks and the two strings as the system.

Fig (4)

Using

Or 21 = (4 + 2 + 1) a

a = 3m/s².

b) Free body diagram (showing forces in x direction) of 4kg block and 1Kg block are shown in figure.

Fig (5)

Using

For 1Kg block, F-T₁ = (1) (a).

Or 21 – T₁= (1) (3) = 3

\ T₁ = 21-3 = 18N

For 4Kg block,

T₂ = (4) (a)

T₂ = (4) (3) = 12N

Dumb Question:

1) When taken as one system, the tensions do not come into picture why?

Ans: When all blocks are taken as one system, the tension do not come into picture because they now became internal forces and internal forces do not affect motion.