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Unit 3: The 2nd

and 3rd LawsNo Vectors!

Brent RoyukPhys-109

Concordia University

Newton and the Big Picture• Philosophiae Naturalis Principia Mathematica

(The Mathematical Principles of Natural Philosophy), (see below for year of publication)

Newton and the Big Picture• When asked about which scientist he'd like to

meet, Neil deGrasse Tyson said, "Isaac Newton. No question about it. The smartest person ever to walk the face of this earth. The man was connected to the universe in spooky ways. He discovered the laws of motion, the laws of gravity, the laws of optics. Then he turned 26.”

Newton and the Big Picture• “Nature and Nature's laws lay hid in night:

God said, Let Newton be! and all was light.” -Alexander Pope

• Newton was not only the greatest genius that ever existed, but also the most fortunate, inasmuch as there is but one universe, and it can therefore happen to but one man in the world’s history to be the interpreter of its laws. –Pierre-Simon Laplace

Newton and the Big Picture• I do not know what I may appear to the world; but to myself I seem to have

been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. -Isaac Newton

• If I have seen further it is by standing upon the shoulders of Giants. -Isaac Newton

• He who thinks half-heartedly will not believe in God; but he who really thinks has to believe in God. –Isaac Newton

• Lest we forget, the birth of modern physics and cosmology was achieved by Galileo, Kepler and Newton breaking free not from the close confining prison of faith (all three were believing Christians, of one sort or another) but from the enormous burden of the millennial authority of Aristotelian science. The scientific revolution of the sixteenth and seventeenth centuries was not a revival of Hellenistic science but its final defeat.― David Bentley Hart, Atheist Delusions: The Christian Revolution and Its Fashionable Enemies

Forces• Kinematics vs. Dynamics• So Far: Velocity, acceleration, falling, inertia

– Now we add force and mass to cause motion.

• Definition– Remember how we defined force?– Now we will learn how forces cause motion.

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The Second LawA two-part law:1. What if you push harder?

– a α FNET

2. What if the object is more massive?– a α 1/m

• The Law: FNET = ma• The Force Unit

Weight• What is a one-word synonym for

weight?• W = mg• A newton-weight• Mass vs. weight: how are they

different?• In Orbit

– Can a weightless hammer crack a nut?– A giant boulder.

• Galileo and the Tower of Pisa again– Two kinds of mass?– mg = ma?

• Examples– What is the weight of a 5-kg

object?– What is the mass of a 750-N man?

ConcepTestA hockey puck slides on ice at a constant velocity. What is the net force acting on the puck?

a. More than its weight.b. Equal to its weight.c. Less than its weight but more than zero.d. It depends on the speed of the puck.e. Zero

Free Fall• So a hammer and a feather fall at the

same rate in vacuum.– But why is that? Isn’t the hammer still heavier?– Check Yourself, p. 62: “Would it be correct to

say that equal forces of gravity act on both the coin and the feather when in a vacuum?”

The Drag Force• An object moving through a fluid experiences a drag force.

– cannon ball sinking in water, car on highway, baseball, parachutist, dust, coffee filters

• Fdrag α v2

• At terminal speed, Fdrag = mg• Equation:

• ρ is the density of the fluid (1.2 kg/m3 for air), A is cross-sectional area, C is a shape coefficient, generally ranging from 0.5-1

Weight vs. Mass

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Some Approximate Terminal Speeds• Object Speed (m/s)• cannonball 250• 16-lb shot 145 • high caliber bullet 100• sky diver 60-100 • baseball 42 • tennis ball 31 • basketball 20 • mouse 13• ping-pong ball 9 • penny 9• raindrop 7 • parachutist 5• snowflake 1• sheet of paper (flat) 0.5• fluffy feather 0.4

You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. -J.B.S. Haldane, British geneticist, 1892-1964

Some Approximate Terminal Speeds• Object Speed (m/s)• cannonball 250• 16-lb shot 145 • high caliber bullet 100• sky diver 60-100 • baseball 42 • tennis ball 31 • basketball 20 • mouse 13• ping-pong ball 9 • penny 9• raindrop 7 • parachutist 5• snowflake 1• sheet of paper (flat) 0.5• fluffy feather 0.4

Cat Terminal SpeedsTerminal Velocity

In a study from the Journal of the American Veterinary Medical Association, two veterinarians examined 132 cases of cats that had fallen out of high-rise windows. On average they fell 5.5 stories, but 90 percent survived, although many suffered severe injuries. The number of broken bones and injuries increased with the number of stories the cat had fallen – up to seven stories. Above seven stories, however, the number of injuries declined. In other words, the farther the cat fell, the better were his chances of escaping injury.

The reason for this may be that after falling five stories or so, cats reach a terminal velocity. The velocity or speed of a falling body does not increase forever because the rate of speed is interrupted by air resistance. A skydiver reaches a terminal velocity of around 130 to 140 mph after about 30 seconds of free-falling. Cats reach terminal velocity much sooner at a speed of 60 mph.

It’s instinctive for both humans and animals to tense up their muscles when free-falling, which makes them more susceptible to injury. When cats land before reaching top speed, they are rigid and flexed and prepared for the landing. This results in most of the force impacting the parts of the body that hit initially. However, after reaching terminal velocity, cats relax their muscles and spread themselves out like flying squirrels. This allows the impact of the fall to be spread across a larger surface area.

http://petplace.netscape.com/netscape/nsArtShow.asp?artID=4076

Newton’s Third Law• For every _____ there is an equal and opposite

_____.• The “bathroom scale” law.• Force Pairs• The Mule and Cart Fallacy

Newton’s Third Law Newton’s Third Law