Considered as foundation blocks of mechanical engineering, here are 5 important principles and laws.
According to Newton’s first law of motion, any object in a resting position will stay at rest. And when in motion will remain in motion in the same direction and at the same speed until and unless any force acts upon it.
In Newton’s second law of motion, any force acting on an object body is equal to the mass of that object body multiplied by its acceleration.
Formula for this second law is,
F = m x a
As per the definition of this law, “there are 2 forces representing direction and magnitude which act at a fixed point by adjacent sides of a parallelogram (2 sides). Its result is detected by direction and magnitude of the given parallelogram’s diagonal section passing through that fixed point.”
According to this law, “To every action, there is always an equal and opposite reaction.”
Suppose there are 2 blocks which are placed on each other. The lower one is horizontally placed, and the other is placed vertically over the lower body.
Let the lower body be A, and the upper one is B.
Force exerted on horizontal surfaced by body A = – F1
Force exerted on horizontal surfaced by body B = – F2
Force exertion on body B by body A = F2
At a certain point of a rigid body if a force is acting, and then if that force is shifted to any other point on line of action of force; that external effect remaining unchanged on the body is principle of transmissibility of forces.
Attraction between 2 bodies with their connecting lines with a certain force is directly proportional to the resultant or product of their combined masses. This resultant is also inversely proportional to the square root of distance of both their centers.
According to this law,
F ∝m1 x m2
Here, m1 is the mass of 1st body and m2 is mass of 2nd body.
F is the force of attraction between m1 and m2.
F ∝ m1 x m2
Here, r is distance from center m1 to m2.
F ∝(m1 x m2)/r2
F ∝(G m1 m 2)/r2
In this case, G is universal gravitational constant of proportionality
N = G kg x kg / m2
G = Nm2 / kg2(eq. 1)
1 N = 1 kg x 1m / s2
N = kg x m / s2(eq. 2)
N depicts Force, kg is for m1 and m2, and m is for ‘r’.
Putting the value of N in given equation,
G = Nm2 / kg2
G = (kg x m / s2) x m2 / kg2 = m2 / kg s2
Using equation 1 and 2, we get the dimensional unit of G.
G = m3/kg s2 or N m2/kg2
G = 6.67 X l0 -11 m3kgfs2orN m2/kg2
As per this formula, G = F, and the force in it is extremely small.
The force with whose help a body is attracted towards earth’s center is known as weight. It is with law of gravitation, weight of a body can be explained.
M is body mass
Mass of earth = ME = 5.9761 x 1024 kg
Distance from center of body to earth’s = r =6.371 x 106 m
We already know,
G = 6.67 X l0 -11N m2/kg2
W = G Mg x M / r2
= 6.67 x 10 -11 x 5.9761 x 10 24 M Nm2
= 6.371 x 1012 x m2 Nm2 / kg x kg x kg
= (9.81m) N
Here, acceleration is 9.81 m / s2
GME /r2 = 9.81 m / s2
W = M x gor g x M