engineering mechanics dynamics chapter 1

5/25/2018 engineering mechanics dynamics chapter 1

1/9


2/9


3/9


4/9


5/9


6/9

Lecture Note, GS/Sp2014

Example

As a body is projected to a high altitude above the earths surface, the variation of the

acceleration of gravity with respect to altitude y must be taken into account. Neglecting air

resistance, this acceleration is determined from the formula

( )22

o

yR

Rga

+

=

where go is the constant acceleration at sea level, R is the radius of the earth, and thepositive direction is taken upwards. If go = 9.81 ms

-2 and R = 6356 km determine the

minimum initial velocity (escape velocity) at which a projectile should be shot vertically

from the earths surface so that it does not fall back to the earth. (Ref. EngineeringMechanics, Dynamics, by R.C. Hibbeler, Prentice Hall, 2010).


7/9


Rectangular Kinematics

When the motion of a particle is erratic it becomes extremely difficult to describe the path of motion

mathematically, and consequently it is difficult to obtain general algebraic expressions for the position,

velocity and acceleration mathematically. In these cases, it is more practical to present the results

graphically (following experimentally determined values). If a plot between any two of the variables t, s,v, a, is given graphically, then the corresponding plot between any other two variables can readily be

determined. This is illustrated below (plots from R.C. Hibbeler).

Case-I

Case-II


8/9


Case-III Case-IV

If the equations of the above plots are known (for example by curve-fitting) then the generation of any

plot is straightforward.


9/9


Example

The v-s graph was determined experimentally to describe the straight-line motion of a

rocket sled. Determine the acceleration of the sled when s = 100 m and s = 200 m. (Ref.

Engineering Mechanics, Dynamics, by R.C. Hibbeler, Prentice Hall, 2010).

engineering mechanics dynamics chapter 1

Documents

Transcript of engineering mechanics dynamics chapter 1