Chapter 2 continuation...Tuesday, January 29Spring 2008
With constant acceleration, a, and initial velocity, vi, at any time, t:
In freefall, the acceleration (a) due to gravity, g, is constant:Galileos Kinematic Equationsv = vi + atg = 9.8 m/s2 32 ft/s2d = vit + ()at2Velocity:
Distance:Equations of pure motion without reference to mass of object or forces acting on it
Galileo and Projectile Motion
Sir Isaac Newton & Classical MechanicsNewton and the Universal Laws of MotionIsaac 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 LawAn 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
The Second LawThe 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 = maa =Fm
Units of ForceF = maUnit of force = unit of mass unit of acceleration = kg (m/s)/s = kg m/s2 (metric system)
1 newton = 1 N = 1 kgm/s2
1 N is the amount of force required to accelerate a 1-kg mass at a rate of 1 m/s2.
The Third LawInteracting objects exert equal but opposite forces upon each otherThe reactions may not be equal and oppositeThe two forces are called an action-reaction pair.
What force produces the forward motion of a car?
Identifying Forces & Resultant MotionForces 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 ResistanceAir 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 = =FmW Rm
Centripetal AccelerationAs the speed decreases, ac decreases. As the speed increases, ac increases.v1v2v2-v1aaeffect of velocity: lesser speed = smaller Dv valuev1v2av2-v1avvaa
Centripetal AccelerationAs the radius increases, ac decreases. As the radius increases, ac decreases.effect of radius: larger radius = less rapid change in direction of vrraav1v2av2-v1v1v2-v1v2a
Centripetal ForcesThe net force that produces a centripetal acceleration is referred to as the centripetal force.
Fc = mac = mv2r
Centripetal ForcesThe 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.