Kinetics of Particle

Lecture 8: Tuesday, 9/15/15

Today’s ObjectiveKinetics of rectilinear motion

What is Kinetics?

• Kinetics is the study of the relations between unbalanced forces and the resulting changes in motion.

Solution Methods for kinetics problems:

• (A) direct application of Newton's second law (called the force-

mass-acceleration method),

• (B) use of work and energy principles, and

• (C) solution by impulse and momentum methods

What is Mechanics?

A. Application of Newton’s Second Law

Newton’s second law equation:

F = ma

Units

Equation of Motion

Types of problems:• Unconstrained motion• Constrained motion• Rectilinear motion• Curvilinear motion

Rectilinear Motion

• Motion along a straight line

Free Body and Inertia Body DiagramsProblem 3/1 : The 50-kg crate is projected along the floor with an initial speed of 7 m/s at x = 0. The coefficient of kinetic friction is 0.40. Calculate the time required for the crate to come to rest and the corresponding distance x travelled.

Problem 3/35Given: The nonlinear spring has a tensile force-deflection relationship given by: , where x is in meters and is in newtons. Determine the acceleration of the 6-kg block if it is released from rest at x = 100 mm

Kinetics of Particle – Curvilinear Motion

Lecture 9: Thursday, 9/17/15

Today’s ObjectiveKinetics of Curvilinear motion

Kinetics of a Particle

Curvilinear Motion:1. Normal and Tangential (n-t) coordinates

Curvilinear Motion

Curvilinear Motion:

2. Polar (r, ) coordinates

Problem 3/50The 4-oz slider has a speed v = 3 ft/s as it passes point A of the smooth guide, which lies in a horizontal plane. Determine the magnitude R of the force which the guide exerts on the slider.a. Just before it passes point A of the guideb. As it passes point B.

Problem 3/53The hollow tube is pivoted about a horizontal axis through point O and is made to rotate in the vertical plane with a constant ccw angular velocity of 3 rad/s. If a 0.2 lb particle is sliding in the tube toward O with a velocity of 4 ft/s relative to the tube when the = 300 is passed, calculate the normal force exerted by the wall of the tube on the particle at this instant.