a) A dimensionless quantity is a physical quantity that has no associated physical units. It is expressed as…

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a) A dimensionless quantity is a physical quantity that has no associated physical units. It is expressed as a pure number, often derived from a ratio of two quantities with the same units, causin

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Here's the solution to question 1:

a) A dimensionless quantity is a physical quantity that has no associated physical units. It is expressed as a pure number, often derived from a ratio of two quantities with the same units, causing the units to cancel out.

b) To show that the coefficient of friction, $\mu$ , is dimensionless, we will analyze the units of the given formula $f = \mu mg$ .

Rearrange the formula to solve for $\mu$ .
$f = \mu mg$ $\mu = \frac{f}{mg}$
Determine the SI units for each variable.
- The unit of force ( $f$ ) is Newtons ( $\text{N}$ ), which is equivalent to $\text{kg} \cdot \text{m} \cdot \text{s}^{-2}$ .
- The unit of mass ( $m$ ) is kilograms ( $\text{kg}$ ).
- The unit of acceleration due to gravity ( $g$ ) is meters per second squared ( $\text{m} \cdot \text{s}^{-2}$ ).
Substitute the units into the expression for $\mu$ .
$\text{Units of } \mu = \frac{\text{Units of } f}{\text{Units of } m \times \text{Units of } g}$ $\text{Units of } \mu = \frac{\text{kg} \cdot \text{m} \cdot \text{s}^{-2}}{\text{kg} \cdot (\text{m} \cdot \text{s}^{-2})}$ $\text{Units of } \mu = \frac{\text{kg} \cdot \text{m} \cdot \text{s}^{-2}}{\text{kg} \cdot \text{m} \cdot \text{s}^{-2}}$
Cancel out the units.
All the units in the numerator and denominator cancel each other out.
$\text{Units of } \mu = 1$
Since $\mu$ has no units, it is a dimensionless quantity.

A) A dimensionless quantity is a physical quantity that has no associated physical units. It is expressed as a pure number, often derived from a ratio of two quantities with the same units, causin

Step-by-step solution

Rearrange the formula to solve for $\mu$ .

Determine the SI units for each variable.

Substitute the units into the expression for $\mu$ .

Cancel out the units.

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