Physical Quantities and Units

Explain what is meant by the accuracy of a measured value.

Show that the calculated density of the material of cube A is $8.7 \times 10^{3}\ \text{kg m}^{-3}$.

Calculate the percentage uncertainty in the density of the material of cube A.

percentage uncertainty = ______ %

The density of the material of cube B is determined to be $9.2 \times 10^{3}\ \text{kg m}^{-3} \pm 6\%$.

State and explain whether cube A and cube B could be made from the same material.

Table 1.1 lists some SI quantities. Complete the table by indicating with a tick (✓) which rows are SI base quantities.

Table 1.1

Use the definition of power to determine its SI base units.

SI base units = ______

A light meter is used to measure the intensity of light in a classroom. Daylight is incident normally on the sensor of the meter. The sensor has an area of $2.2\ \text{cm}^2$. The reading on the meter is $950\ \text{W m}^{-2}$.

Calculate the power of the daylight incident on the sensor.

power = ______ $\text{W}$

Compare scalar and vector quantities.

the radius, in cm, of the sphere

radius = ______ $\text{cm}$

the percentage uncertainty in the radius of the sphere.

percentage uncertainty = ______ $\%$

Table 1.1 lists some physical quantities. Complete the table by placing a tick (✓) next to the scalar quantities.

Table 1.1

Calculate the percentage uncertainties in $D$ and $L$. Write your answers in Table 1.2.

Calculate the density of the cylinder. Give your answer to three significant figures.

density = ______ $\text{kg m}^{-3}$

Calculate the percentage uncertainty in the density.

percentage uncertainty = ______ $\%$

In the following list, underline all units that are SI base units.

ampere degree Celsius kilogram newton

Calculate the percentage uncertainty in the value of $E$.

percentage uncertainty = ______ $\%$

Use your answer in (b)(i) to determine the value of $E$, with its absolute uncertainty, to an appropriate number of significant figures.

$E$ = ( ______ $\pm$ ______ ) $\times 10^9\ \text{Pa}$

The boxes in Fig. 1.1 contain terms on the left-hand side and examples of these terms on the right-hand side.

Draw a line between each term on the left and the correct example on the right.

precise

not accurate.

Calculate the percentage uncertainty in $v$.

percentage uncertainty = ______ %

The value of $v$ is $15.0\ \text{m s}^{-1}$.

Calculate the absolute uncertainty in $v$.

absolute uncertainty = ______ $\text{m s}^{-1}$

Use information in Table 1.1 to show that the SI base unit of $\alpha$ is $\text{s}^{-1}$.

Show that the percentage uncertainty in $\alpha$ is $15\%$.

Calculate $\alpha$ with its absolute uncertainty. Give your answer to an appropriate number of significant figures.

$\alpha$ = ( ______ $\pm$ ______ ) $\times 10^7\ \text{s}^{-1}$

State two other scalar quantities and two other vector quantities.

scalar quantities: ______ and ______
vector quantities: ______ and ______

State two properties that are possessed by both scalar and vector physical quantities.

1. ______
2. ______

Determine the magnitudes of the components of the velocity of the ship in the north and the east directions.

north component of velocity = ______ $\text{m s}^{-1}$
east component of velocity = ______ $\text{m s}^{-1}$

The ship now experiences a tidal current. The water in the sea moves with a velocity of $2.7\ \text{m s}^{-1}$ to the west.

Calculate the resultant velocity component of the ship in the east direction.

resultant east component of velocity = ______ $\text{m s}^{-1}$

Use your answers in (b)(i) and (b)(ii) to determine the magnitude of the resultant velocity of the ship.

magnitude of resultant velocity = ______ $\text{m s}^{-1}$

Use your answers in (b)(i) and (b)(ii) to determine the angle between north and the resultant velocity of the ship.

angle = ______ $^{\circ}$

A unit may be stated with a prefix that represents a power-of-ten multiple or submultiple.

Complete Table 1.1 to show the name and symbol of each prefix and the corresponding power-of-ten multiple or submultiple.

Table 1.1

In the following list, underline all the units that are SI base units.

ampere coulomb metre newton

the percentage uncertainty

percentage uncertainty = ______ $\%$

the absolute uncertainty.

absolute uncertainty = ______ $\Omega\ \text{m}$

Length, mass and temperature are all SI base quantities.

State two other SI base quantities.

1. ______
2. ______

Calculate the acceleration of free fall $g$.

$g$ = ______ $\text{m s}^{-2}$

Determine the percentage uncertainty in $g$.

percentage uncertainty = ______ $\%$

Use your answers in (b)(i) and (b)(ii) to determine the absolute uncertainty of the calculated value of $g$.

absolute uncertainty = ______ $\text{m s}^{-2}$