FORCE
We know by experience that all bodies in nature interact in some way with one another.
Force is a measure of the interaction of bodies or of the particles of which the bodies consist. The force may produce either deformation (change in the size or shape of bodies) or acceleration (change in magnitude or direction of velocity).
Force is a measure of the interaction of bodies or of the particles of which the bodies consist. The force may produce either deformation (change in the size or shape of bodies) or acceleration (change in magnitude or direction of velocity).
Force is a vector quantity. Every force has a definite direction and the result of its action depends on the direction and the magnitude of the force.
If several forces are applied to a particle, they can be replaced by a resultant force. This resultant is the vector sum of the forces and can be found by any of the methods illustrated earlier.
SOME COMMON FORCES
There are basically five forces which we commonly encounter in mechanics problems, namely Weight, Normal Force, Friction Force, Tension and Spring Force.
WeightThe weight W⃗ of a body is a force that pulls the body directly towards the earth. The force is due to gravitational attraction between two bodies. We will discuss this in detail later. Here, we consider an object of mass m located at a point where the free fall acceleration has magnitude g. Then the magnitude W of the weight is
Its direction being vertically downward (towards the centre of the earth).Normally we assume that weight is measured in an inertial frame. If it is measured in a non-inertial frame, it is called apparent weight.
Contact ForcesWhenever two surfaces are in contact they exert forces on each other. Such forces are known as contact forces. It is convenient to resolve these contact forces into components, one parallel to the contact surface, the other perpendicular to that surface.
Normal ForceThe normal force is the component of the contact force that is perpendicular to the surface. It is a measure of howstrongly the surfaces in contact are pressed together. As an example push your hand straight down on the table. The force you feel resisting your push is the normal force of the table pushing up on your hand.
Frictional ForceThe component of the contact force parallel to the contact surface is called frictional force. The direction of the frictional force is opposite to the relative motion (or attempted motion) of the two surfaces in contact.
TensionThe force exerted at any point in the rope/string/wire/rod is called the tension at that point. We may measure the tension at any point in the rope by cutting a suitable length from it and inserting a spring scale; the tension is the reading of the scale. The tension is same at all points in the rope only if the rope is unaccelerated and assumed to be massless.
Spring ForceAs you may have discovered for yourself, springs resists attempts to change their length. In fact, the more you alter a spring’s length, the harder it resists. The force exerted by a spring may be represented as:
where x is the change in length, and k is the stiffness constant or simply, the spring constant.
Unit of spring constant is N/m.
This equation is also known as Hooke’s law. The minus sign in Hooke’s law shows that the direction of the force exerted by the spring is opposite to the displacement that produces it.
The spring constant depends on geometry of the spring and on the material property. For us, it is important to know that the spring constant is inversely proportional to its length, other things remaining the same. i.e.
Unit of spring constant is N/m.
This equation is also known as Hooke’s law. The minus sign in Hooke’s law shows that the direction of the force exerted by the spring is opposite to the displacement that produces it.
The spring constant depends on geometry of the spring and on the material property. For us, it is important to know that the spring constant is inversely proportional to its length, other things remaining the same. i.e.
Therefore if you cut a spring into two parts whose length are in ratio 1 : 2, their spring constants will be in ratio of 2 : 1. As in case of rope, we will usually deal with a massless spring, the force at each point of which is the same. Such spring and ropes are normally referred to as ideal.
NEWTON'S LAWS
Newton’s First Law
When there is no net force on an object- an object at rest remains at rest, and- an object in motion continues to move with a velocity that is constant in magnitude and direction.
Note1) Newton’s first law really describes a reference frame. The property of the body to remain at rest or to retain its uniform linear motion in the absence of applied force is called inertia.The first law is often called the law of inertia and the reference frames to which it applies are termed as inertial reference frames.Thus an inertial reference frame is one which is either at rest or moves with a constant velocity relative to earth. Truly speaking, the earth itself is not an inertial reference frame (because it rotates as well as moves round the sun in an orbit) but for most practical purposes we can treat it as an inertial reference frame.
2) This law does not differentiate between objects at rest and objects moving with constant velocity. Indeed, an object moving with constant velocity in one inertial reference frame can be at rest in another inertial reference frame.
3) No net force here may mean the absence of all forces or the presence of forces whose resultant is zero.
Newton’s Second Law
We know from the first law, what happens when there is no unbalanced force on an object: its velocity remains constant. Now let us see What happens when there is an unbalance force on an object ? The Newton’s second Law gives answer to this question, that is, net force acting on a body will produce an acceleration.When there is a constant unbalanced force on an object, the object moves with constant acceleration. Furthermore, if the force varies, the acceleration varies in direct proportion with larger force producing larger acceleration. Twice the force produces twice the acceleration in the same mass.
The magnitude of the acceleration produced depends on the quantity of matter being pushed. The quantity of matter is referred to as the inertial mass.Newton’s second law states the relation between the net force and the inertial mass.
Note that the direction of acceleration is in the direction of the net force.In terms of components ∑Fx=max Towards x axis
Newton’s Third Law
Experiments show that forces occur in pairs. If you push against a wall, the wall pushes back at you. If one body A applies a force F⃗ BA on another body B, body Bapplies an equal but oppositely directed force F⃗ AB on A i.e.
Normally, one of these force (it does not matter which) is called the action forceand the other is called the reaction force. Thus the third law is also sometimes stated as “To every action there is always an equal and opposite reaction”. Note that the action and reaction always act on different objects.
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