on If What this forces trunk isact moved

on If. What this forces trunk isact moved this storage trunk? across the floor at constant velocity, Push Friction Support of floor (distributed among the 4 casters it sits on) Weight 1. the man’s PUSH must exceed the trunk’s WEIGHT. 2. the man’s PUSH must exceed the total friction forces. 3. all the above forces must exactly balance.

Forces all balance for constant velocity.

Imagine the work involved in sliding this crate from the loading dock to the center of the machine shop floor. Compare that to the task of pushing over to the far wall (TWICE AS FAR)… TWICE AS MUCH …or to the task of pushing WORK! two identical crates together to the center of the room (TWICE AS MUCH).

Consider the work involved in lifting this heavy box to the bottom storage shelf. 2 h compare this to h doing it twice (once for each box) doing it once with BOTH boxes together TWICE lifting a single box to the AS MUCH upper shelf (TWICE AS FAR) WORK? HALF What about: half as high? AS MUCH half the weight? WORK?

Work Force used in performing it. Work distance over which work is done. Lifting weights is definitely work even by this physics definition! What about lowering weights back down? When lowering an object, the force you apply to support it (and keep it from dropping too fast) is NOT in the same direction as its motion. In fact it is OPPOSITE. Instead we think in terms of the weight of the object (gravity’s pull downward) is moving you. When you LIFT weights you do work on them. When you lower them, they (gravity, actually) do work on you.

How much work is being done balancing this tray in place? What distance does it move in the direction of the force on it? Work was done picking this briefcase up from the floor. How much work is being done in holding it still? Does it move UP at all in the direction of the applied force?

How much work does the cable do in supporting the bowling ball? T How much work does a crane do in holding its load in place above ground? When holding this load steady in place, how much energy must the crane’s motor consume? Notice it could be shut off, and hold the weight still. If no energy is required there’s no real work performed.

Work = Force distance If there is no unbalanced force, no work is done! If the pushed object doesn’t even move no work is done! If the pushed object doesn’t move in the direction of the force, no work is being done on it! If the object moves (despite an applied force) in a direction opposite to the force, we say: its doing work on the person trying to push Or that the person pushing does NEGATIVE work.

The crane lifts its load up at constant speed. 1. It lifts with a force > the load’s weight. 2. It lifts with a force = the load’s weight. 3. It lifts with a force < the load’s weight.

B C A D Work is done on the box during which stage(s)? A. Lifting box up from floor. B. Holding box above floor. C. Carrying box forward across floor. D. Setting box down gently to floor. E. At all stages: A, B, C, D. F. At stages A and C. G. At stages A and D H. At none of the stages illustrated.

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

Which of the following geometric shapes are “similar”? A B 1. A and C 3. D and F 5. C and G C D E F G 2. A and C and G 4. A, C, E, and G 6. they are all polygons and thus similar

A B C D E Only C and D above are geometrically similar. The geometric definition of “similar” requires more than that the shapes are all triangles. …more than that the triangles be the same “type” isosceles triangles (A and E) or right triangles (B, C, D) They need to “look alike”, but not be exactly alike (that’s CONGRUENT, remember? )

1. 35 inch D inch 2. 25 inch 7 1. 47 ch 2 in 2. 46 C 1 inch 0. 6 in The dimensions of figure C are in the same proportion as the corresponding sides in figure D. anyway you look at it: Triangle D is 0. 6 the size of triangle C

1. 35 inch ch D 7 in 1 inch 1. 47 C ch 2 in 2. 46 2. 25 inch You may also remember 0. 6 in Ratios of any two sides within one figure are in the same proportion as the corresponding ratio of any similar figure. Each triangle is 2. 25 as tall as it stands wide. A description that applies equally to each.

Quantities are in proportion when they simply scale with one another. An object’s weight scales with its mass: weight = 2. 20462 lb/kg mass Similarly, the weight of a liquid scales with its volume weight = 2204. 62 lb/m 3 volume density (of water) The charge built up in a capacitor scales with the voltage across its leads: charge = C coul/volts voltage its capacitance The cost of filling your tank scales with the number of gallons of gasoline cost = $2. 34/gal number of gallons

cost = $2. 34/gal number of gallons Cost (in dollars) $30 $25 $20 $15 $10 $5 5 10 15 Gallons (of gasoline) Twice as much gas costs twice as much money! Ten times as much gas costs 10 the money! No gas costs nothing! We say Cost Gallons

Not all relationships are proportions: o. F Temperature conversion follows: 9 F = C + 32 5 o. C y = mx + b Notice: the graph of F vs C does not go through (0, 0)! This means while 0 o C = 32 o F doubling (or tripling) both gives 0 o C and 64 o (or 96 o) F which is no kind of proportion! also: not all relationships are even linear!

A little geometry: A line cutting across a pair of parallel lines, creates alternating congruent angles

A little geometry: Whenever any two lines cross the opposite angles formed are congruent. Since the sum of all the “interior” angles of every triangle add up to 360 o…

A little geometry: B A C D F E …these two triangles are similar! Look carefully to see which are the “corresponding” (matching) sides.

Proportionalities B A D F E C The ratio of lengths of side A to side C is in the same proportion as: 1. E/F A = ? C 2. F/E 3. D/F 4. F/D 5. E/D 6. D/E

Proportionalities A B D C A = ? z 1. A/w 2. A/x 3. B/x 4. C/x 5. D/x 6. D/w y w x z

s a r The ratio of surface areas A = ? a 1. R/r 2 2. R 2/r 2 3. R 2/r 4. R/r 5. r/R R A S

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

To scale proportionally height, h weight, W And this double-sized block weighs 1. 2 W 2. 4 W 3. 6 W 4. 8 W 5. 10 W 6. 12 W

More generally, 2 L 2 w h L w 2 h original =hw. L volume new =(2 h)(2 w)(2 L) volume = ( 8 )hw. L =(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 = 1. 03 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

SOME ANSWERS Question 1 2. It lifts with a force We already demonstrated in class that I lifting requires, = the load’s weight. on average, a force simply equal to a load’s weight. Question 2 A only! A. Lifting box up from floor. requires positive work B. Holding box above floor. requires NO work C. Carrying box forward across floor. No work if lifting force perpendicular to direction of boxes motion! D. Setting box down gently to floor. Involves NEGATIVE work! Question 3 5. C and G Question 4 4. F/D Question 5 5. D/x Question 6 2. Question 7 4. 8 W “Similar” shapes have all their corresponding (‘matching”)angles congruent, i. e. , they can be lined up so that all their corners are matched identically. It makes all similar shapes “look alike” (like perfectly scaled models of one another). A, the shortest side of the larger triangle corresponds to F, the shortest of the 2 nd triangle. C is the middlesized side so corresponds to D. 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 2/r 2 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. Twice as wide…twice as tall…twice as thick… means 2 2 2=8 times the volume (and mass).