Physics 221 Chapter 1

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Physics 221Chapter 1
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Problem 1 . . . Pizza Party -)

• A 6 inch round pizza can comfortably serve one
  student. How many students can a 12 inch round
  pizza with the same crust thickness serve?

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Linear and Non-Linear Thinking!

• Does the braking distance of a car double when
  you double the speed?
• Does a 12 inch pizza serve twice as many people
  as a 6 inch pizza?

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Solution 1 . . . Pizza Party -)

• If a 6 inch pizza can comfortably serve one
  student, then a 12 inch pizza with the same crust
  thickness will serve a party of 4
  
  

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Powers of 10

• 1,560 1.56x103
• 4,200,000 4.2x106
• 103 1,000
• 106 1,000,000 1M 1 Million
• 2.5GB 2.5x109 2.5 Giga Bytes 2.5 Billion
  Bytes
• 0.007 7x10 -3 7 parts in a thousand

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Sig Figs (Significant Figures)

• Measurements in science always entail
  UNCERTAINTIES.
• For example, a measurement of 2.4 cm is likely to
  be actually between 2.3 and 2.5 cm you never
  know!
• So our uncertainty is 0.1 cm. In other words, we
  may express our measurement as 2.4?0.1

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Sig Figs . . . continued!

• So you see 2.4 and 2.40 are not the same! 2.4 has
  2 sig figs and 2.40 has 3 sig figs
• 2.4 means that the number is probably between 2.3
  and 2.5
• On the other hand, 2.40 means that the number is
  probably between 2.39 and 2.41

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Problem 2 . . . sig figs

• What is the area of a circle whose radius is
  measured to be 2 .5 cm?
• A. 19.634954 cm2
• B. 19.634954 cm
• C. 20 cm2
• D. 7.8 cm

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Hint Sig Figs Problem . . .

• 6.5 has 2 sig figs
• 7.28 has 3 sig figs
• 65.142 has 5 sig figs
• 2.3547681 has 8 sig figs
• Unless specified otherwise, in this class we will
  report our answers using 2 sig figs

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Solution 2 . . . sig figs

• What is the area of a circle whose radius is
  measured to be 2 .5 cm?
• A. 19.634954 cm2
• B. 19.634954 cm
• C. 20 cm2
• D. 7.8 cm

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SI (metric) Units

• 1 meter (m) 100 cm
• 1 kilogram (kg) 1000 g
• 1 kilometer (km) 1000 m
• 1 liter (L) 1000 cm3
• 1 in. 2.5 cm
• 1 mi. 1.6 km
• 1 kg 2 pounds
• 1 gallon 4 L

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Problem 3 . . . unit conversion

• Convert 55 mph to km / h and m / s

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Solution 3 . . . unit conversion

• 55 miles / h x 1.6 km / 1 mi. 88 km / h
• 88 km / h x 1000 m / 1 km 88,000 m / h
• 88, 000 m / h x 1 h / 3600 s 24 m /s

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Density

• Density Mass / Volume
• ? m / V

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Problem 4

• The density of water is 1 g /cm3. A teaspoon is
  about 5 cm3. A cup is about 250 cm3 . A quart
  is approximately equal to a liter (1000 cm3). So
  a cm3 equals a mL. The density of water,
  expressed in kg/m3 (metric or SI units) would be
  most nearly
• A. 100,000
• B. 1000
• C. 100
• D. 0.001

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Solution 4

• 1 g /cm3 1000 kg / m3
• Density of water 1 g /cm3 or 1000 kg / m3

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Problem 5

• Which is heavier, a pound of lead or a pound of
  aluminum?

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Solution 5

• They weigh the same!
• -)

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Problem 6 . . . Pb or Al?

• Which has the larger volume, a pound of lead or a
  pound of aluminum?

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Solution 6 . . . Pb or Al?

• Lead (Pb) has the smaller volume because it has
  the greater density.

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Problem 7 . . . Buddha in Bamiyan!

• The density of gold (Au) is approximately twice
  the density of copper (Cu). Suppose we have two
  statues of Buddha, one made of gold and the other
  made of copper. They look very similar in size
  and shape except that the gold one is very shiny
  (like gold) and the copper one has a copper tone.
  
• Which statue has the greater volume?
• Which statue has the greater mass?
• Which statue has the greater density?

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Solution 7 . . . Buddha in Bamiyan!

• If they have the same size and shape, they must
  have the same volume!
• If they have the same volume then the one with
  the greater density must have the greater mass.
  Recall that density mass/volume
• Gold (Au) has the greater density thats what
  the problem says!

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Dimensional Analysis

• What is the formula for the volume of a sphere?
• 4 / 3 ? r 3
• or
• 4 ? r 2

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Dimensional Analysis

• The units for volume MUST be meter cubed so the
  correct formula for volume is
• 4 / 3 ? r 3
• Folks, there is more to physics than simply
  memorizing formulas -)

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Problem 8 . . . Lets get REAL!

• A cylindrical tank has a height h and radius r.
  The tank is full of a liquid of density ? . The
  mass of the liquid in the tank is
• A. 4/3 ? r 3 ?
• B. ? r2 ? h
• C. 2? r ? h
• D. ? r h

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Solution 8 . . . Lets get REAL!

• B. ? r2 ? h
• Volume of the liquid ? r2 h
• Mass of the liquid volume x density ? r2 h x
  ?
• Note Check for dimensional consistency!

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• Thats all Folks!