Engr 240 Agenda Name Game Web Access start

Engr 240: Agenda • • • Name Game Web. Access (start recording) Syllabus Dynamics: Introduction To be done at home: • First Day Survey • Diagnostic Test

Engr 240 – Week 1 Kinematics of Particles

Review of Physics 1 Mechanics – study of forces and their effects Statics – bodies at rest (or with constant velocity) Dynamics – bodies in motion Kinematics – study of geometry of motion Kinetics – relationship between motion and their causes (forces, torques) Bodies: Particles, Rigid Bodies, Deformable Bodies, Fluids

A. Kinematics of Particles • Study of “geometry” of motion • “How” particle moves • Kinematic variables: – position, velocity, acceleration, time

B. Kinetics of Particles • “Why” particle moves because of forces • Relates forces with kinematic variables 1. Newton’s Second Law:

2. Impulse-Momentum Principle • Relates F with v and t • Change in Momentum = Impulse

3. Work-Energy Principle – relates F with v and x – Work done = Change in K. E.

Comparison of Kinetic Principles • Each one relates F with specific kinematic variable/s • 1 & 2 are vector equations; 3 is scalar • 1 is instantaneous (true at any instant of time); 2 & 3 are applied between initial and final states

C. Kinematics of Rigid Bodies • Rotation: angular position, velocity and acceleration D. Kinetics of Rigid Bodies • Relates Forces and Torques with kinematics variables • Moment of Inertia, angular momentum, rotational kinetic energy

RECTILINEAR MOTION • Motion along a straight line Consider a particle moving along the x-axis: - position - displacement during time interval Average velocity: Instantaneous velocity:

Average acceleration: Instantaneous acceleration:

Common Classes 1. The acceleration given as a function of time.

2. The acceleration given as a function of position. Solve for time:

3. The acceleration given as a function of velocity.

Example 11. 3. Brake mechanism used to reduce gun recoil consists of piston attached to barrel moving in fixed cylinder filled with oil. As barrel recoils with initial velocity v 0, piston moves and oil is forced through orifices in piston, causing piston and cylinder to decelerate at rate proportional to their velocity. Determine v(t), x(t), and v(x).

Special Cases: • Uniform Motion: • Uniformly Accelerated Motion: Also, Example: Free fall a = -9. 81 m/s 2 , or a = -32. 2 ft/s 2

Relative Motion Consider particles A and B, both moving along the x-axis. relative position of B with respect to A relative velocity of B with respect to A relative acceleration of B with respect to A

Example 11. 4 Ball thrown vertically from 12 m level in elevator shaft with initial velocity of 18 m/s. At same instant, open-platform elevator passes 5 m level moving upward at 2 m/s. Determine (a) when and where ball hits elevator and (b) velocity of ball at contact.