10 - University Physics with Modern Physics

Question

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.

Step-by-Step Solution

Answer

(a) The velocity in ft/s is 88 ft/s.

(b) The acceleration in m/s² is 18.3 m/s².

(c) The density in kg/m³ is 1000 kg/m³.

Conversion in ft/s

Part (a)

The conversion in ft/s is shown below,

$$\begin{gathered} 60 mph=60 \frac{mi}{h}\times \frac{5280 ft}{1 mile}\times \frac{1 h}{3600 s} \\ 60 mph= 88 ft/s \end{gathered}$$

 Thus, the value in ft/s is 88 ft/s.

Conversion in m/s 2

Part (b)

The conversion in m/s² is shown below,

$$\begin{gathered} 32 ft/s^2=60\frac{ft}{h}\times \frac{30.48 cm}{1 ft}\times \frac{1 m}{100 cm} \\ 32 ft/s^2=18.3 m/s^2 \end{gathered}$$

Thus, the value in m/s² is 18.3 m/s²

Conversion in m/s 2

Part (c)

The conversion in kg/m³ is shown below,

$$\begin{gathered} 1 g/c{m}^3=1\frac{g}{c{m}^3}\times {\left(\frac{100 cm}{1 m}\right)}^3\times \frac{1 kg}{1000 g} \\ 1 g/c{m}^3=1000 kg/m^3 \end{gathered}$$

 

Thus, the value of density in kg/m³ is 1000 kg/m³.