Foundation of Engineering

1. FOUNDATIONS OF
ENGINEERING

2. CHAPTER # 10
Newton’s Law

3. ANALYSIS OF MOTION
Some Definition
Position: It is a place or location within a reference frame e.g. A(2,-2)
Displacement: It is a change in position ∆r = r2-r1 ; may called the shortest distance form the initial point; vector
quantity
Distance: Non-negative number indicating the length of a straight or curved path
Average Velocity: Change in position / change in time
Instantaneous Velocity: Limit of average velocity as time approaches to zero
Speed: It is the magnitude of instantaneous velocity
Average acceleration: It is the change in velocity with time
Instantaneous acceleration: It is the limit of average acceleration as time approaches to zero
One-Dimensional Motion
POSITION -> differentiation -> VELOCITY -> differentiation -> ACCELERATION
ACCELERATION -> Integration -> VELOCITY -> integration -> POSITION
See Table 10.1

4. Multidimensional Motion: Fred & Jane throwing the ball
r = x i + y j + z k
| r | = sqrt (x^2 + y^2 + z^2)
V = Vx i + Vy j + Vz k
Vx = dx/dt; Vy= dy/dt; Vz= dz/dt
| V | = sqrt (Vx^2 + Vy^2 + Vz^2)
a = ax i + ay j + az k
ax = dVx/dt; ay= dVy/dt; az= dVz/dt
| a | = sqrt (ax^2 + ay^2 + az^2)
Example 10.2

5. RELATIVE MOTION
Observer
Train moving
to right
Person on train moving
on left
V2=14.5m/s
V1=0.5m/s

6. FORCES
Force: It Is the influence on a body that will cause it to accelerate in the absence of any other
counteracting force e.g. If you were pushed in tug of wars
Fundamental Forces
Gravitational Force: It is an attractive force between two objects that have mass
Electrostatic Force: It is the attractive force when the two objects are charged differently & is a repulsive force
when two objects are charged alike
Magnetic Force: Same in the case of Electrostatic but in this case we have bar magnets
“Other” Forces
Frictional Force: It results when two solid surfaces contact each other
Drag Force: It is another type of fractional force exerted on a body as it moves through a fluid
Spring Force: It results when a spring is compresses or stretched (Hooks Law)

7. EQUATIONS OF MOTION
vf = vi + at
S = vi t + ½ a t^2
2 a s = vf^2 – vi^2
Where vf is final velocity, vi is initial velocity, a is acceleration, t is time, s is the distance,

8. NEWTONS FIRST LAW
“An object is in rest will remain at rest or an object in motion will remain in motion if no external force acts
upon it”
It is basically Law of Inertia
v = constant
dv / dt = 0 (no force)
p = m v = constant
dp / dt = d (mv) /dt = 0 (no force)

9. NEWTONS SECOND LAW
The vector sum of the forces F on an object is equal to the mass m of that object multiplied by
the acceleration vector a of the object: F = ma.
a = F / m
F = dp/dt = d(mv)/dt
F = m dv/dt = ma

10. NEWTONS THIRD LAW
Statement of Newtons third law "For every action, there is an equal & opposite reaction”
Force always exists by the interaction of two (or more) bodies
The force on one body is equal & opposite to the force on the other body
It is impossible to have a single isolated force
The designation of an “action force” and a “reaction force” is arbitrary, because there is a mutual interaction
between the two bodies

11. EXAMPLE APPLICATIONS OF NEWTONS LAW
Example 10.8
Example 10.9
Example 10.10
Example 10.11
Example 10.12
Example 10.10
Example 10.10

12. PLANETARY MOTION
See on book
F = G M m / r^2
Earth & Sun
First calculating the position two days from now we can then able to calculate the Gravitational Force
and velocity

13. CARE & FEEDING OF FORMUALAS
Formulae should be properly used & we should know the variables limitations like in this case T or t. one
should know the limit of time interval & user must understand what the variables stand for