Chapter 2 continuation...

Tuesday, January 29

Spring 2008

Galileo’s Kinematic Equations

With constant acceleration, a, and initial velocity, vi, at any time, t:

In freefall, the acceleration (a) due to gravity, g, is constant:

v = vi + at

g = 9.8 m/s2 ≈ 32 ft/s2

d = vit + (½)at2

Velocity:

Distance:

Equations of “pure” motion – without reference to mass of object or forces acting on it

Galileo and Projectile Motion

g

vi,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

F2 = –F1 F1 + F2 = 0

F2F1

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 =Fm

Units of Force

F = ma

Unit of force = unit of mass × unit of acceleration

= kg · (m/s)/s

= kg · m/s2 (metric system)

1 newton = 1 N = 1 kg·m/s2

1 N is the amount of force required to accelerate a 1-kg mass at a rate of 1 m/s2.

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 = — =Fm

W – Rm

Centripetal Acceleration

As the speed decreases, ac decreases.

As the speed increases, ac increases.

v1v2

v2

-v1a

a

effect of velocity: lesser speed = smaller v value

v1v2

a

v2

-v1a

v

v

a

a

Centripetal Acceleration

As the radius increases, ac decreases.

As the radius increases, ac decreases.

effect of radius: larger radius = less rapid change in direction of v

r

r a

a

v1v2

a

v2

-v1

v1

v2

-v1

v2

a

Centripetal Forces

The net force that produces a centripetal acceleration is referred to as the centripetal force.

Fc = mac = m—v2

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.