Chapter 2 continuation... Tuesday, January 29 Spring 2008

Galileo’s Kinematic Equations With constant acceleration, a, and initial velocity, v i, at any time, t : In freefall, the acceleration ( a ) due to gravity, g, is constant: v = v i + at g = 9.8 m/s 2 ≈ 32 ft/s 2 d = v i t + (½) at 2 Velocity: Distance: Equations of “pure” motion – without reference to mass of object or forces acting on it

Galileo and Projectile Motion g v i,x

Sir Isaac Newton & Classical Mechanics Newton and the Universal Laws of Motion Isaac Newton (1642 – 1727) Which path will the ball follow? "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done."

The First Law An object will continue moving in a straight line at a constant speed, and a stationary object will remain at rest, unless acted upon by an unbalanced force Uniform motion vs. acceleration Inertia F 2 = –F 1 F 1 + F 2 = 0 F2F2 F1F1

The Second Law The acceleration produced on an object by a net force is proportional to the magnitude of the force and inversely proportional to the mass of the object Equation: F = ma a = F m

Units of Force F = ma Unit of force = unit of mass × unit of acceleration = kg · (m/s)/s = kg · m/s 2 (metric system) 1 newton = 1 N = 1 kg·m/s 2 1 N is the amount of force required to accelerate a 1-kg mass at a rate of 1 m/s 2.

The Third Law Interacting objects exert equal but opposite forces upon each other The reactions may not be equal and opposite The two forces are called an “action-reaction pair.”

What force produces the forward motion of a car?

Identifying Forces & Resultant Motion Forces that are perpendicular to one another are usually treated separately. Motion in the vertical direction: no acceleration, F = ma so total force = 0, W = –N Motion in horizontal direction: F = ma, so F = P – f > 0 to get chair moving.

Free Fall and Air Resistance Air resistive force, R, acts in opposite direction of gravitational force, W. R depends on the velocity. Eventually, the magnitude of R equals that of W, and the object reaches “terminal velocity.” a = — = F m W – R m

Centripetal Acceleration As the speed decreases, a c decreases. As the speed increases, a c increases. v1v1 v2v2 v2v2 -v1-v1 a a effect of velocity: lesser speed = smaller v value v1v1 v2v2 a v2v2 -v1-v1 a v v a a

Centripetal Acceleration As the radius increases, a c decreases. effect of radius: larger radius = less rapid change in direction of v r ra a v1v1 v2v2 a v2v2 -v1-v1 v1v1 v2v2 -v1-v1 v2v2 a

Centripetal Forces The net force that produces a centripetal acceleration is referred to as the centripetal force. F c = ma c = m — v2v2 r

Centripetal Forces The tension force from a pull on a string, produces the necessary centripetal force to keep a ball on the end of the string in circular motion.