- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

**5. **Introduction Mechanics – the state of rest of motion of bodies subjected to the action of forces
Static – equilibrium of a body that is either at rest or moves with constant velocity
Dynamics – deals with accelerated motion of a body
1) Kinematics – treats with geometric aspects of the motion
2) Kinetics – analysis of the forces causing the motion

**6. **Rectilinear Kinematics: Continuous Motion Rectilinear Kinematics – specifying at any instant, the particle’s position, velocity, and acceleration
Position
1) Single coordinate axis, s
2) Origin, O
3) Position vector r – specific location of particle P at any instant

**7. ** 4) Algebraic Scalar s in metres
Note : - Magnitude of s = Dist from O to P
- The sense (arrowhead dir of r) is defined by algebraic sign on s
=> +ve = right of origin, -ve = left of origin

**8. **Displacement – change in its position, vector quantity

**9. **If particle moves from P to P’
=>
is +ve if particle’s position is right of its initial position
is -ve if particle’s position is left of its initial position

**10. **Velocity
Average velocity,
Instantaneous velocity is defined as

**11. **Representing as an algebraic scalar,
Velocity is +ve = particle moving to the right
Velocity is –ve = Particle moving to the left
Magnitude of velocity is the speed (m/s)

**12. ** Average speed is defined as total distance traveled by a particle, sT, divided by the elapsed time .
The particle travels along
the path of length sT in time
=>

**13. **Acceleration – velocity of particle is known at points P and P’ during time interval ?t, average acceleration is
?v represents difference in the velocity during the time interval ?t, ie

**14. ** Instantaneous acceleration at time t is found by taking smaller and smaller values of ?t and corresponding smaller and smaller values of ?v,

**15. **Particle is slowing down, its speed is decreasing => decelerating => will be negative.
Consequently, a will also be negative, therefore it will act to the left, in the opposite sense to v
If velocity is constant,
acceleration is zero

**16. **Velocity as a Function of Time
Integrate ac = dv/dt, assuming that initially v = v0 when t = 0.

**17. **Position as a Function of Time
Integrate v = ds/dt = v0 + act, assuming that initially s = s0 when t = 0

**18. **Velocity as a Function of Position
Integrate v dv = ac ds, assuming that initially v = v0 at s = s0

**19. **PROCEDURE FOR ANALYSIS
Coordinate System
Establish a position coordinate s along the path and specify its fixed origin and positive direction.
The particle’s position, velocity, and acceleration, can be represented as s, v and a respectively and their sense is then determined from their algebraic signs.

**20. **The positive sense for each scalar can be indicated by an arrow shown alongside each kinematics eqn as it is applied

**21. **2) Kinematic Equation
If a relationship is known between any two of the four variables a, v, s and t, then a third variable can be obtained by using one of the three the kinematic equations
When integration is performed, it is important that position and velocity be known at a given instant in order to evaluate either the constant of integration if an indefinite integral is used, or the limits of integration if a definite integral is used

**22. **Remember that the three kinematics equations can only be applied to situation where the acceleration of the particle is constant.

**27. **A small projectile is forced downward into a
fluid medium with an initial velocity of 60m/s.
Due to the resistance of the fluid the
projectile experiences a deceleration equal to a =
(-0.4v3)m/s2, where v is in m/s2.
Determine the projectile’s
velocity and position 4s
after it is fired.

**28. **Solution:
Coordinate System. Since the motion is
downward, the position coordinate is downwards
positive, with the origin located at O.
Velocity. Here a = f(v), velocity is a function of
time using a = dv/dt, since this equation relates v,
a and t.