## EME-102, UPTU, FORCE, FORCE SYSTEM, MECHANICS

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S Y S T E M

To understand force one has to understand Energy. Energy is the tranferable physical quantity of an object which has the capacity to do work. Energy can be transfered from one place to another place, or from one object to another object.

Force is the physical quantity which when acts on a body, may do some work on the body by displacing from a certain point in the space to another point in the space. When a body gets displaced due to the application of force, some work has been done on the object. So work done on a body is basically nothing but putting some more energy on the body.

Any kind of displacement of an object is called a change in position and it is a universal truth that to go through any kind of change in position, an object needs some time interval, the process of changing position involves time, hence we can say an amount of x change in position it needs t amount of time. Hence, we can get a rate of change of position with respect to time.

If in (t) time the body travels a distance (x) than,

in unit time the body travels a distance (x/t) and it is known as average velocity.

When the time interval is very small, then the ratio of (x/t) is represented by differential operator and then it is called instantenous veldocity.

An heavier object needs more energy to attain the same velocity of that of a lighter object. It has been observed that body at a higher motion needs more energy to change velocity incrementally. Suppose we have two identical object A and B, while the velocity of A is (u), the velocity of B is larger at (v), now if we try to increase the velocity of both the body by a amount ðv, then the body with the higher motion would need more energy per unit change in velocity. Therefore a body in motion can store energy and larger a body, larger is the capacity to store energy at the same velocity.

One more important concept that emerges out from these statements is the concept of momentum. We have seen that the capability to store energy by a body depends upon the mass (m) and velocity (v). If we try to increase the energy carried by a moving body, its capability to carry energy must be increased. Hence, either we have to increase its mass or velocity or both. Thus, we can define a physical quantity which will tell us information about the capability to carry energy by a particle. Suppose the quantity is denoted by P, so P will be directly proportional to the product of m and v. Thus, we define P as,

P=mv and it is called as Momentum.

Suppose a moving body of mass (m) and velocity (v) increases its velocity by (dv), the increase in energy by (dE), Such that dE = mv.dv or we can write,

d/dv(E) = mv = P

It means the rate of change of Energy with respect to velocity is directly proportional to its momentum. So, higher the velocity of an object, it needs more energy to increase the velocity by an unit.

Change of Position

Suppose, in a coordinate system we have a particle at a certain point A in any instant of time. We can determine the position by its horizontal and vertical coordinates or its position vector r. Let after a certain very small amount time (dt) the particle changes its position by (dr), so that its new position will be (r + dr). Here the change in position is (dr) and it is called displacement.

If an object is moving and after some time it reaches the original place from where it started moving, then the displacement will be zero as displacement is change of position and in the above case initial and final position are same. Hence, there is no net change of position.

Now, we should consider the time involved during the change of position.

Suppose we have two identical particle undergone a same amount of change of position. But, while the first particle takes (dt) time to move from one position to another position, the second particle take a longer time (dt'). What does it mean? Here, we shall definitely call the first object is fast while the second object is slow.

A fast moving particle means the rate of change of position is large. This is a physical quantity, that we can perceive