• POD Solutions

    Mr. Neff

    North Allegheny School District

     

    POD

    ANSWER

    1

    Answers vary

    2

    Hypothesis should use preexisting knowledge of this scenario.

    3

    The sky is blue.  Dogs bark.  Ice floats.  You can smell a candle from across a room.

    4

    For hypothesis to be ¡°scientific,¡± there must be a way to prove it wrong if it is indeed wrong. This hypothesis is not scientific because if it is wrong, there is no way to know it.  Hence it does not lend itself to an experiment and is not scientific.

    5

    The fossil is still 3 000 000 years old since the uncertainty on the 3 000 000 says the fossil is really between 2 000 000 and 4 000 000 years old.  When you add the years since 1993 to the 3 000 000 and round to the least significant place, you still get 3 000 000.

    6

    Since you are their frame of reference, which they mistakenly take for granted as stopped relative to the ground and they think they are moving.

    7

    19 spots and 29 spots

    8

    6.2     19.4

    8.1

    4.8     10     5     56

     

    8.2

    61 stretch units      108 stretch units

    9

    4.8     10

    5         56

    11

    .045 mi/min or 2.7 mi/hr

    15

    10. m/s    5.4 m/s   70. min

    16

    Avg vel = 3.75 mi/h West (or .0625 mi/min)  avg speed = 13.8 mi/h  (or .229 mi/min)

    17

    Story should start by moving away from some starting location.  Then, story will pause for a time at some location.  Then story will go back to the starting point at a much slower rate than at the beginning.  The story must begin and end in the same place.

    18.5

    Distances: 180.m   320.m  420.m    Displacements: +180.m    +40.m   +140.m

    19

    Answers vary, but should be based on Vince using minimal accelerations and a smoother ride (Mr. Neff¡¯s Choice of Driver), Jason doing very abrupt accelerations and turning around, and Norman¡¯s extreme acceleration to pull out

    20

    .56 sec

    22

    +1.6 m/s   +17.6 m/s   34 m

    23

    3.08 sec and 13.7 sec

    25

    23 sec

    26

    They hit the ground at the same time.  They have the same shape so experience the same amount of air resistance.

    27

    9.8 m/s/s down    24.5 m/s down   120. m

    28

    1.5 sec up, 1.5 sec down    -15.0 m/s   0    9.8 m/s/s down

    29

    180 000 m/s/s

    29¡¯

    31.9 m-25.0 m/s

    33

    		17 blocks
    33dx (12 bl) + dy (5.0 bl) = 17 blocks
    34
    Use Pythagorean Theorem and Inverse Tangent
    8.1 m/s @ 68¡Ædownstream from straight across
    362.0 N Left + 7.0 N Down = 7.3 N @74¡Æ below the - x-axis
    38
    a) larger left force, smaller up force
    b) larger down force, smaller left force
    39
    Resolve 160 mph at 20¡Æ S¨¬E into 150.35 mph E and 54.7232 mph S; then add 60 mph E
    217 mph @ 15¡Æ S¨¬E
    40
    Add x-components for Harry (1.026 N) and Tommy ( 7.3724 N)
    Since F left (8.3984 N) < F right (10.0N), Jimmy wins!
    41
    Add y-components for two scales: Left (61.905 lbs) + Right (203.00 lbs) = 264.906 lbs, which also equals the weight of the shark (because of equilibrium).
    42
    Find right component of first quadrant force (14.518296 N) and set up an expression for second quadrant force (A Cos 28¡Æ).  Set these equal (because of equilibrium).  A = 16.442987 N
    Find up component of first quadrant force (19.9827 N) and second quadrant force (7.7195 N).  These are equal (because of equilibrium) to the force pointing directly down the -y-axis (27.702 N).
    43
    Since x-velocity is independent of y-velocity, the additional x-velocity of ball 2 will have no effect on how long it takes to hit the floor.  Since gravity affects all object in the same manner, both will hit the floor at the same time (Using dy=viyt + 1/2 at^2; t=.65776 sec).  Ball 2 will land 3.3 m out (dx = vx t).
    44
    Each ball has an identical x-velocity vector, which points to the right in this case. The first ball has no y-velocity (since it has not yet fallen).  Successive vy's get larger from left to right. These obviously point down.
    Follow up questions: 1.  No because equal vx's  2. Yes because vy's get longer and longer  3. Yes for two reasons: velocity vectors (vector sum of vx and vy on each ball): 1. get longer and longer and 2.  change direction.
    48
    He will not make it.  By the time he falls the the level of the other rooftop (gets a y-displacement of -40 ft or -12.192 m), 1.577 seconds elapse.  In that time, he travels out only 12.619 m, which is less than the 48 ft (14.6m).
    51
    The monkey will still be shot.  The bullet will fall from the straight line path the same amount as the monkey will fall from rest, so they will meet somewhere below the monkey's original position.
    57
    Yes, the balls will collide because they have the same vx, and when the top ball leaves the table and begins to fall, the falling (vy) will not change the vx.
    They will .12 m
    60Using the chain rule: tongueVfly=776 cm/s south
    69
    1.  Air's natural place is above the water, so the air takes the person with it.
    2.  When heated, the balloon has fire put into it.  Since fire's natural place is above the air, the balloon rises.
    3.  Liquid mercury would be a combination of water and earth, so it would tend to stay between the water and the earth.
    73
    Mass and wieght are very different, but related.  Mass is the amount of matter in an object, while weight is how strongly gravity pulls on that mass.  Mass is a scalar quantity, while weight is a vector quantity.  Since mass is determined by factors coming from inside the object itself and not upon external influences, we say mass is a fundamental quantity.  Conversely, weight depends on both interal and external factors, and can even change as the object moves from place to place and so it is not a fundamental quantity.  You can have mass without weight, but there is no weight without mass.
    Mass : Matter :: Weight : Pull of Gravity on an Object
    74.1
    20. N     5.6 kg     60.5 kg   133 pounds     319 N     780. N
    74.2
    The force will acclerate the smaller mass more than it will acclerate the larger mass because accleration is inversely proportional to mass.
    The larger force will accelerate the object more because acceleration is directly proportional to net force.
    75
    Tension  Friction  Normal Force  Weight
    6 m/s/s right
    79
    1. T  2. T  3. F  4. F  5. T  6. F  7. F  8. F
    80.5
    1.6 m/s/s clockwise; 29 N
    82
    The faster someone goes, the more air molecules they encouter every second.  So, the faster someone goes, the more air resistance they encounter. 
    Terminal velocity is a condition where air resistance matches a falling object's weight, producing no net force and no accleration.  If the object falls far enough and fast enough, air resistance can get great enough to balance the force of gravity.  At this point, the object will no longer accelerate, but rather maintain its speed. 
    Compared to the smaller parachutest, the larger parachutest will have to travel farther, accelerate longer, and achieve a higher speed until a speed is finally reached sufficient to produce an air resistance capable of balancing out the force of gravity.   Consequently, the larger parachutest lands first because of her higher terminal velocity and greater average velocity. The larger parachutest goes faster and accelerates longer.
    83
    The swing with angled strings has a greater chance of breaking.  In both cases, a weight force pulls the monkey and the boy down equally.  These weight forces must be balanced by the two tension forces on each rope.  In the monkey's swing, the tension in each string just equals half the weight.  In the boy's swing, the force of gravity is being balanced by the y-components of the tension forces.  If those y-components each equal half the boy's weight, the tension in each rope must be greater than half the boy's weight (since components are always smaller than the vectors from which they come).  Consequently, the boy's strings are under greater tension and are more likely to break.
    84
    They are action and reaction and so they are the same.
    d.  Rockets acclerate in space because they push backwards on exhaust gasses, which push forward on the rocket.
    b.  They expereince an equal force ,but the difference in mass creates a difference in acceleration.
    84'
    750 N  750 N  750 N  900 N  520 N
    86
    Action and reaction forces could never cancel out.  Consider two objects: A and B.  A force of object A on object B could be considered an action.  The corresponding equal and opposite reaction would be the force of object B back on object A.  Since these two forces act on different objects, they cannot cancel each other. 
    88
    It does, but the force of the hotdog on the earth is only able to produce an insignificant acceleration on the earth's large mass.
    903.3 m/s/s CW  Ft = 15 N
    92
    Since Fg|| is greater than Fg2 the system will certainly not move clockwise, but will accelerate counterclockwise if it accelerates at all.  This allows us to draw the friction up the incline.  Since fs max is greater than the difference between Fg|| and Fg2, the object will not accelerate at all. 
    So, a = 0 and Ft = 22.54N.
     
    Now if you want to challenge yourself, make the surface more slippery, say µs   = .10 and µk = .050, then the static friction will not be adequate to hold it and the system will accelerate counterclockwise at 0.60 m/s/s and Ft = 24 N. 
    98It will accelerate because the critical angle is only 21.8˚.  The acceleration will be 1.477 m/s/s down the incline.
    100
    Answers vary, but generally, "gaining momentum" means that a person, object, or team is gaining some type of ability, whether it is to succeed, win, or just to be able to do something it could not do before.
    This is often heard on sportscasts.
    102
    540 kg m/s East; 20 000 kg m/s West; 80. kg m/s South
    104
    a.  40 000 units    b.  60 000 units      c.  40 000 units       d.  80 000 units
    106
    The truck has a momentum of 1600 kg x .1m/s = 160 kg m/s
    The bicycle and rider have a momentum of 92.3 kg x 13.4 m/s = 1240 kg m/s
    The bicycle and rider have WAY more momentum and will launch the bale further.
    108
    1.  Case A (+5 --> -4 is greater than +5 --> 0)
    2.  Case A (m x big change in veloctity) > (m x little change in velocity)
    3.  Case A (Impulse = change in momentum)
    4.  Case A (Careful!  This is only true because it was given that times were the same!)
    112
    Ft = change in p  -->  F = (pf - pi)/t 
    a.  F = (60)(25)/.400  = 3750 N
    b.  F = (60)(25)/.001  = 1 500 000 N
    113
    All momenta in kg m/s:
    A: +1.2   B: -10.8    C: -2.8    D: +13.2      E: +17.4
    114
    1.  a. +40   b.  +30     c.  +40
    2.  a.  0      b.  -5000  c.  0
    116
    4 m/s
    120
    4 m/s
    126
    p before =p after
    p = (-.13 kg m/s x-hat + 1.45 kg m/s y-hat) or (1.45 kg m/s @ 84¡Æ above the neg x-axis)
    128
    1.47 m (=2.1 x .70)   1.03 m (= 1.47 x .70)
    .21 m (=2.1 x .10)     .021 m (.21 x .10)
    Either they don't exist (so you'd want none) or they do and you'd want as many as you could possibly purchase!
    1305.3 m/s
    150
    Neither person is doing work.  If they do not displace the wall, they do not put it into a state which would allow it (the wall) to do more work itself than before. 
    152
    No-see note on pod 150
    Yes-Gravity causes the displacement
    No-The tray is worked upon when it is picked up, and the tray is worked upon when it is initially set into horizontal motion, but after it is up to speed, its energy is not changing (it is not getting more and more capable of doing work itself).  Also, when carring the tray, the waiter's force is up, while the displacement is forward.  Up forces cannot have forward effects, so there is no cause. 
    154
    10 812.81 J 
    Since humans are 10% efficient on average, the actual work in (food burned) is 108 128.1 J .  Since there are 4184 J in each Calorie, the work in is 25.8 Calories.
    158
    Just more than 2 pushups (.49 J of work on each pushup)
    Since P = W/t = 1.0 J / 4.0 s = .25 Watts
    160
    800. m
    162
    6.4 N/m  4.8 N
    163
    Though there are similarites, stretching a spring is very different from sliding an object against friction. The two scenarios are similar in that a force is being applied causing  displacement.  However, while an approximately constant force is adequate to slide an object against friction, an ever increasing force is required to stretch a spring.
    164
    203 N cm (cJ) or 2.03 J
    314.75 N cm or 3.1475 J
    172
    It is tough to show bars here, so I'll put numbers on their heights to quantify them:
    A: GPE= 10  KE= 0    EPE= 0
    B: GPE= 8    KE= 2    EPE= 0
    C: GPE= 6    KE= 4    EPE= 0
    D: GPE=  3   KE=  5   EPE= 2 (EPE is not half but a quarter of what it will end up: W = 1/2 kx^2)
    E: GPE=  1   KE= 0    EPE= 9
    178
    1492 W x .45 = 671.4 W or 671.4 J/s
    Work = F d --> d = Work / F = 671.4 Nm / 20 000 N = .03357 m
    180
    Since Win = Wout-->Fin din = Fout dout -->Fin (1.8) = (10 000g) (.20)-->Fin = 10 888.89 N
    MA = Fout / Fin = (10 000 g)/(10 888.89) = 9.0 (no unit on MA)
    182
    Fin = 101.35 N     TMA=2.467   AMA = 1.613  eff=65.4%
    192
    These are "ballpark" numbers: Nailclipper: 3.6   Crowbar: 3   See-Saw: 1    Catapult: 0.5
    200
    T = 2.06 seconds  (T = time to complete that many revolutons / # revolutions)
    f = .49 Hz (f = 1/T = # revolutions / time to complete that many revolutons)
    201
    2.0 m    Fc = mv2/r
    202
    Points along the radius of a wheel all have the same period (T) because they cover one circle in the same amount of time.  They have different tangential velocities (v) however, because they travel different circumferences in that amount of time.  A real-life example of this is two adjacent horses on a merry-go-round.  They have equal peroids but different circumferences so different tangential velocities. 
    2053.1 m/s = vcrit =  square root of (gr)
    206
    Astronauts are no more weightless than you are when you jump off of the high dive.  To orbit the Earth, you move sideways fast, so that when you fall to the Earth, you move sideways far enough to miss the surface.  The bottom line though: the astronauts are still falling, and so, the feel weightless.
    21020 m/s = vcrit =  square root of (gr)
    211No.  Since f = Fg then Coeff = 1.56 which is way too high to be realistic.

     

     
Last Modified on December 8, 2011