STATICS
Dr. Duong Viet Anh
Department of Energy
4. Newton's laws and the differential
equation of motion
.
Chapter Outline
4.1 Notion
4.2 Newton's law and Differential equation of particle
4.3 Survey methods of kinetics
4.1. Notion
➢ There are many problems in engineering its solutions require
application of the principles of dynamics
➢ The subject of dynamics will be presented in two parts: kinematics,
which treats only the geometric aspects of the motion, and kinetics,
which is the analysis of the forces causing the motion.
➢ Kinetics is a branch of dynamics that deals with the relationship
between the change in motion of a body and the forces that cause
this change.
4.1. Notion
➢ The basis for kinetics is Newton's second law: F = ma
➢ W = mg (g = 9.81 m/s2 = 32.2 ft/s2) ; mass m is measured in kg or slug
4.2. Newton's law and equation of motion
Equation of motion and Inertial Reference Frame
ΣF = ma => ΣF - ma = 0
4.2. Newton's law and equation of motion
Equation of motion for a System of particles
ΣF = ma => ΣFi + Σfi = Σmiai
ΣFi = Σmiai
ΣF = maG
4.3. Survey methods of kinetics
1. Descartes coordinate method
The equation of motion:
ΣF = ma
=> ΣFxi+ ΣFyj +ΣFzk = m(ax i+ ayj +azk)
ΣFx = max
ΣFy = may
ΣFz = maz
4.3. Survey methods of kinetics
1. Descartes coordinate method
➢The equations of motion are used to solve problems which require a
relationship between the forces acting on a particle and the accelerated
motion they cause.
➢ 1st Step: Drawing Free-Body Diagram
➢ 2nd Step: Equations of Motion
➢ 3rd Step: Kinematics
4.3. Survey methods of kinetics
1. Descartes coordinate method
4.3. Survey methods of kinetics
1. Descartes coordinate method
4.3. Survey methods of kinetics
1. Descartes coordinate method
4.3. Survey methods of kinetics
1. Descartes coordinate method
➢ 3rd Step: Kinematics
Example 3
→ The 2-lb collar C fits loosely on the smooth shaft. If the spring is
unstretched when s = 0 and the collar is given a velocity of 15 ft/s,
determine the velocity of the collar when s = 1 ft
Example 4
→ The tractor is used to lift the 150-kg load B with the 24-m-long rope,
boom, and pulley system. If the tractor travels to the right at a constant
speed of 4 m/s, determine the tension in the rope when sA = 5 m. When
sA = 0, sB = 0.
Example 5
→ The 600-kg dragster is traveling with a velocity of 125 m/s when the
engine is shut off and the braking parachute is deployed. If air resistance
imposed on the dragster due to the parachute is FD = (6000 + 0.9 v2) N,
where is v in m/s, determine the time required for the dragster to come to
rest