Kinetics of a Particle in Plane Motion

Kinetics of a Particle in Plane Motion - Kinetics of a...

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Kinetics of a particle in plane motion 3.1 Introduction In the previous chapters we have studied the kinematics of a point moving in a plane; velocity and acceleration have been defined in various co-ordinate systems and for a variety conditions. It is now necessary to consider the forces associated with the motion. The concept of force is useful because it enables the branches of mechanical science to be brought together. For example, a knowledge of the force required to accelerate a vehicle makes it possible to decide on the size of the engine and transmission system suitable as regards both kinematics and strength; hence force acts as a ‘currency’ between thermodynamics or electro- technology or materials science. 3.2 Newton’s laws of motion Newton’s laws define the concept of force in terms of the motion produced by the force if it acted alone - which is why we have yet to discuss statics. We will first state the three laws in the form that is most common in current literature. First law Every body continues in a state of rest or of uniform rectilinear motion unless acted upon by a force. Second law The rate of change of momentum of a body is proportional to the force acting on the body and is in the direction of the force. Third law To each action (or force) there is an equal and opposite reaction. The term ‘momentum’ is prominent in the formulation of the laws of mechanics and a formal definition is given below, together with a definition of mass. The reader concerned with the philosophical implications of the definitions of mass, length and time should consult a text on pure physics. Momentum Momentum is defined simply as the product of mass and velocity. Mass Mass is a measure of the quantity of matter in a body and it is regarded as constant. If two bodies are made from the same uniform material and have the same volume then their masses are equal. The first law says that if a body changes its velocity then a force must have been applied. No mention is made of the frame of reference - whether a change in velocity occurs depends on the observer! This point will be considered in detail in section 3.6. The second law establishes a relationship between the magnitude of the force and the rate of change of momentum: d dt force CC- (momentum) d dv or Fx- (mv) = m- = ma when all points on the body have the same acceleration. Equivalance of mass If two objects made from different materials collide, then by Newton’s third law they receive equal but opposite forces at any given time and it follows that the momentum gained by one body must be equal to that lost by the other. If we conduct a simple collision experiment and measure the velocities of the bodies before and
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Note that in this treatment the symbol representing the unit is considered as a simple algebraic quantity. This approach simplifies the conversion from one system of units to another.
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This note was uploaded on 04/01/2008 for the course ESM 2304 taught by Professor Lgkraige during the Fall '08 term at Virginia Tech.

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Kinetics of a Particle in Plane Motion - Kinetics of a...

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