Announcements HW4 on Ch 5 due tonight Remember

Announcements • HW#4 on Ch. 5 due tonight • Remember the 1 st midterm, Weds. , Feb. 25, – Covers chapters 1 -5 – No makeup tests Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 1

Forces in Non-uniform Circular Motion The object has both tangential and radial accelerations. Fr F What does this statement mean? The object is moving under both tangential and radial forces. Ft These forces cause not only the velocity but also the speed of the ball to change. The object undergoes a curved motion under the absence of constraints, such as a string. How does the acceleration Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 look? Dr. Andrew Brandt 2

Motion with Resistive Forces A medium can exert resistive forces on an object moving through it due to viscosity or other types frictional properties of the medium. Some examples? Air resistance, viscous force of liquid, etc These forces are exerted on moving objects in the opposite direction of the motion. These forces are proportional to such factors as speed. They almost always increase with increasing speed. Two different cases of proportionality: 1. Forces linearly proportional to speed: Slowly moving or very small objects 2. Forces proportional to square of speed: Large objects w/ reasonable speed Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 3

Resistive Force Proportional to Speed Since the resistive force is proportional to speed, we can write R=bv R v m Let’s consider that a ball of mass m is falling through a liquid. This equation also tells you that mg The above equation also tells us that as time goes on the What does this mean? speed increases and the acceleration decreases, eventually reaching 0. An object moving in a viscous medium will obtain speed to a certain speed (terminal speed) and then maintain the same speed without any more acceleration. What is the terminal speed in above case? The time needed to reach 63. 2% of the terminal speed is defined as the time constant, t=m/b. How do the speed and acceleration depend on time? Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 4

Review: Lectures 1 -3 Significant figures, displacement, velocity, acceleration, 1 -D motion, free fall, constant acceleration equations: Velocity as a function of time Displacement as a function of velocity and time Displacement as a function of time, velocity, and acceleration Velocity as a function of displacement and acceleration Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 5

Lectures 4 -6 Coordinate systems, vectors (defn. , operations, components unit vectors), 2 -D motion, projectile motion, reference frames Range+Max height Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 6

Lectures 6 -9 Force, Newton’s Laws, weight, free body diagrams, inclined planes, pulleys, friction, circular motion. Monday, Feb. 23, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 7