“Seeking… “Weight proportional to height.” What’s that supposed to mean? Here’s a fairly common trait sought after in the personals: Is that a desirable trait? Interlude:

Proportionalities A BCD w x A zA z  ? 1.A/ w 2.A/ x 3.B/ x 4.C/ x 5.D/ x 6.D/ w y z A and z are bases of their respective (isosceles) triangles, i.e, they are “corresponding sides.” D is an “altitude” and so corresponds to x.

R A aA a  ? 1.R/ r 2 2. R 2 / r 2 3. R 2 / r 4. R/ r 5. r /R r The ratio of surface areas A a The ratio of the sides of the square areas S /s = R /r since S is to R as s is to r. However the areas A = S 2 and a = s 2. S s

height, h weight, W Consider this block weighing “W” height, 2h This stack of 2 blocks weighs how much? 2W2W Are these blocks in proportion?

To scale proportionally height, h weight, W And this double-sized block weighs 1. 2  W 3. 6  W5. 10  W 2. 4  W 4. 8  W6. 12  W

More generally, h w L 2h2h 2w2w 2L2L original volume =hwL new volume =(2h)(2w)(2L) = ( 8 )hwL = ( 8 )( ) original volume Is weight meant to be proportional to height?

Weight  (Height) 3 Each 1% increase in height should correspond to a (1.01) 3 = % increase in weight 5% increase in height (5’4”  5’7”) 15.2% gain in weight 10% increase in height (5’10”  6’5”) 30% gain in weight

Easy to push Hard to push To produce the same amount of acceleration, need to push the car much harder! How much? Twice as much mass requires twice the force! 100  as much mass requires 100  the force! F  mF  m

If a lot of others join in, each contributing an additional force, the net force will be greater, and the acceleration greater. F = ma F  aF  a F  mF  m together with can be combined consistently to give Newton’s 2 nd Law

The Toyota FT-HS is a 400-horsepower hybrid sports car its 3.5-liter V6 engine provide an acceleration of 0-to-60-miles-an-hour in 4 seconds Unveiled at yesterday’s International Auto Show in Detroit: acceleration, a = v tv t +60 miles/hour 4 seconds = 15 miles/hour sec

+60 miles/hour 4 seconds = 15 miles/hour sec Notice 60 miles/hour is the same as 60  = miles hour 5280 feet 1 mile feet hour  = feet hour 1 hour 3600 seconds feet sec miles/hour 4 seconds = 22 feet/sec sec So alternately or 22 ft/sec 2

Softball oz. Tennis ball 2 ounces (57 grams) 14 lb. medicine ball 32 times heavier than a softball! 112 times heavier than a tennis ball! If all 3 balls were released simultaneously, from the same height, they would reach ground 1. tennis ball first, medicine ball last. 2. medicine ball first, tennis ball last. 3. together at about the same time.

A large boat whose maximum speed in still water is v 1, tows a smaller boat whose maximum speed is the smaller v 2. across the lake. If both outboard motors run together at full bore, the speed that they travel together with will be 1. the smaller value v the larger value v somewhere between v 1 and v 2.

a gravity  g Falling objects accelerate down at  32 ft/sec m/sec 2 more precisely: at sea level m/sec ft/sec km (  10 miles) above earth’s surface a gravity drops to about 9.75 m/sec km (  20 miles) above earth’s surface a gravity drops to about 9.70 m/sec 2 even skydivers experience a  9.8 m/sec 2 even commercial jet carriers experience a gravity only 1% under the value at sea level!

North Pole a gravity = San Franciscoa gravity = Denver a gravity = The gravitational force on an object decreases by about a millionth for every 3 meter (~10 feet) gain in elevation. An individual with a 50 kilogram mass weighs 500 Newtons (110 pounds) in New York City; but ~0.25 newton (1 ounce) less in mile-high Denver.

If you drop an object (assuming its air resistance is negligible) it accelerates downward at g=9.8 m/sec 2. If instead you throw it downward, its downward acceleration after release is A.<g B.=g C.>g

Inclined Plane A ball rolling down an inclined plane has constant acceleration Is the acceleration of the ball down the ramp 9.8 m/s 2 ? A) yesB) no No! This ball is not in free fall. Gravity alone does not act on it. The inclined plane provides a force of support which affects the motion!

A ball is thrown straight up and falls back to the ground. Which of the following is true about its velocity v and its acceleration a at the highest point in its path? A) v = 0 and a = 0 B) v  0, but a = 0 C) v = 0, but a  0 D) v  0 and a  0 E) cannot be determined At the highest point in its path, the ball momentarily comes to a stop, and so its velocity is zero. However, since the ball is in free fall, its acceleration is g = 9.8 m/s 2 (at every moment).

A ball is dropped from rest, and a bullet shot out of a gun, straight down. Neglecting air resistance, which has the greater acceleration just before hitting the ground? A) the ball B) the bullet C) both have the same acceleration The acceleration of gravity does not depend on the mass or the speed of the object in free fall!

The maximum velocity, v, an object reaches falling freely from rest, is directly proportional to the time, t, of its fall: v  t. 1) TRUE 2) FALSE How fast is an object moving at the end of a one second fall?

How far does an object in freefall drop in one second?