Page 174 - Standard Handbook Of Petroleum & Natural Gas Engineering

Dynamics 159

point on a line through B perpendicular to v,. These two lines intersect at C, the
instantaneous center.
AC = L cos e = z x 0.866 = 1.73 ft

w,, = -
AC 1.73ft
where wAB = 2.31 rad/s = the angular velocity of the link and of any line on the link

Iv,I = 2.31ft/s

Kinetics
In kinetics, Newton's second law, the principles of kinematics, conservation of
momentum, and the laws of conservation of energy and mass are used to develop
relationships between the forces acting on a body or system of bodies and the result-
ing motion.

Applications of Newton's Second Law. Problems involving no unbalanced couples
can often be solved with the second law and the principles of kinematics. As in statics,
it is appropriate to start with a free-body diagram showing all forces, decompose the
forces into their components along a convenient set of orthogonal coordinate axes,
and then solve a set of algebraic equations in each coordinate direction. If the
accelerations are known, the solution will be for an unknown force or forces, and if
the forces are known the solution will be for an unknown acceleration or accelerations.
Example 2-8

In Figure 2-15a, a 10-lb block slides down a ramp inclined at an angle of 30". If the
coefficient of kinetic friction between the block and the ramp is 0.1, what will be the
acceleration of the block?
As shown in the free-body diagram of Figure 2-15b, all the motion of the block is
parallel to the surface of the ramp; thus there is a static force balance in they direction.

Fy = N - W cos 30" = 0
N = W cos 30"

+ F,= pN = pW cos 30"
Also, by Newton's second law, the force in the x direction produces an acceleration ax:

W
Fx = W~in30O-F~ =ma, =-a,
g