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The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s2. Use 1 ft = 30.48 cm to express this acceleration in units of m/s2. (c) The density of water is 1.0 g/cm3. Convert this density to units of kg/m3.

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cjmejiab

To solve this exercise we will define the units of conversion between each of the variables given to facilitate the calculation in each section.

[tex]1 mile = 5280ft[/tex]

[tex]1h = 3600s[/tex]

[tex]1 ft = 30.48cm[/tex]

[tex]1 m = 100cm[/tex]

[tex]1kg = 1000g[/tex]

PART A ) For this part we have 60mph to ft/s, then

[tex]60mph = 60\frac{miles}{hour} (\frac{5280ft}{1mile})(\frac{1h}{3600s})[/tex]

[tex]60mph = 88ft/s[/tex]

PART B) Convert from [tex]ft/s^2[/tex] to [tex]m/s^2[/tex]

[tex]32ft/s^2 = 32 \frac{ft}{s^2} (\frac{30.48cm}{1ft})(\frac{1m}{100cm})[/tex]

[tex]32ft/s^2 = 9.7536m/s^2[/tex]

PART C) Convert [tex]g/cm^3[/tex] to [tex]kg/m^3[/tex]

[tex]1 g/cm^3 = 1\frac{g}{cm^3}(\frac{1kg}{1000g})(\frac{100cm}{1m})^3[/tex]

[tex]1 g/cm^3 = 1000kg/m^3[/tex]

mickymike92

Based on the conversion factors,  the conversions are as follows:

  • 60 mph = 88 ft/s
  • 32 ft/s² = 9.75 m/s²
  • 1 g/cm³ = 1000 Kg/m³

What are the conversions for the given units?

Conversions are used when converting between different units measuring the same quantity.

a. To convert 60 mph to ft/s:

  • 1 mi = 5280 ft
  • 1 h = 3600

60 mph = 60 * 5280/3600

60 mph = 88 ft/s

b. To convert 32 ft/s² to m/s

1 ft = 30.48 cm = 0.3048 m

32 ft/s² = 32 * 0.3034

32 ft/s² = 9.75 m/s²

c. To convert g/cm³ to kg/m³

1 g = 0.001 kg

1 cm³ = 0.000001 m³

1.0 g/cm3 = 1.0 * 0.001 kg/0.000001 m³

1 g/cm³ = 1000 Kg/m³

Therefore, the conversions are as follows:

  • 60 mph = 88 ft/s
  • 32 ft/s² = 9.75 m/s²
  • 1 g/cm³ = 1000 Kg/m³

Learn more about unit conversions at: https://brainly.com/question/174910

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