1.1 Measurements in Physics

Identify the quantity with the SI base units of m³ kg⁻¹ s⁻².

Convert the following measurements to the appropriate unit, and express to an appropriate number of significant figures.   

   90 000 GW = ____________ mW

    45.1 hF = _____________ fF

   0.60 pm = _____________ km

214 minutes = _____________ ms

A sheet of silver has a thickness of 0.671 µm. A silver atom has a radius of 172 pm.

Estimate the number of layers of atoms in this sheet to the nearest thousand.

Identify the variable that has the SI base units kg m² s⁻³ A⁻².

Explain why potential difference is not defined as current × resistance.

Convert 0.01 kWh into PeV.

Tensile stress (σ) is defined as the force applied per unit cross-sectional area on a material. The tensile strength is the maximum amount of tensile stress a material can be subjected to before fracturing, meaning that it is equivalent to the tensile stress at the breaking point.

The humerus bone is approximately cylindrical and has a tensile strength of 0.17 GPa and a diameter of 20 mm. 

Calculate the maximum force on the humerus bone before it fractures.

The femur bone is the strongest bone in the body. It has a tensile strength of 0.135 kN mm^–2. 

Calculate the tensile strength of the femur bone in GPa.

Calculate the number of cubic millimetres (mm³) in 23 km³.

Estimate the time it takes light to cross the nucleus of a hydrogen atom.

Estimate the order of magnitude with an appropriate SI unit and correct prefix for the following quantities.

1 u is the atomic mass unit and a common unit used in nuclear physics.

Show that its value in kg is approximately equal to the mass of a proton in kg.

The cross-sectional area of nuclei are commonly measured in the units barn, which are represented by the symbol b. 1 barn = 100 fm²

Calculate the value of a nano barn (nb) in m².

Pressure at a certain depth in a fluid can be calculated using the value for the density of the fluid, the gravitational field constant g and the depth within the fluid. 

State the following measurements in standard form:

(i)         20 000 kPa

(ii)        0.18 Gm

(iii)       1.15 μg

(iv)       82.6 pN

Pressure is measured in pascals. 

Define 1 Pascal in fundamental SI units.

Atmospheric pressure on Earth is 101 325 Pa. The Mariana trench at the bottom of the western Pacific Ocean has a pressure of around 110 MPa.

Calculate how many times larger the pressure in the Mariana trench is than the atmospheric pressure on Earth.

Pressure changes with depth, as well as force and area.

List the following in order of decreasing pressure:

• Atmospheric pressure at the summit of Mount Everest
• Surface pressure on the Moon
• Atmospheric pressure ~ 101 kPa
• Water pressure of an average garden hose
• The Mariana trench ~ 110 MPa

An electron microscope is used to analyse the arrangement of atoms and their nuclei on a new design for a special sheet of silver foil. The foil is a new material being added to various components in a military medical aircraft. 

Estimate the orders of magnitude with an appropriate fundamental SI unit and correct prefix for the following quantities 

The sheet of silver foil has a thickness of 0.992 µm. A silver atom has a radius of 172 pm. 

Approximate how many layers of atoms there are in this sheet.

Using the electron microscope, the cross–sectional area of the silver nuclei can be measured accurately in units of ‘barn’, with symbol b. 

1 barn = 100 fm² 

Calculate the value of 1 nb in m²

Einstein’s famous equation Energy (J) = Mass (kg) × (Speed of light (m s^–1))²­ demonstrates that energy and matter are interchangeable.

Atomic mass unit, 1 u = 931.5 MeV

1 eV = 1.60 × 10^–19 J

Use this equation to show that the value in kg of 1 u of silver in the foil is approximately equal to the mass of a proton in kg.  

X–ray pulsars are detected by X–ray telescopes on a satellite in low Earth orbit 2000 km above the surface of the Earth. 

Calculate the number of cubic millimetres (mm³) in a volume of 2000 km³.

X–rays from a pulsar travel at the speed of light and are detected on Earth with a wavelength of 8.0 nm. 

Calculate the frequency of the X–rays in PHz. Give your answer to an appropriate number of significant figures. . 

X–rays from the nearest pulsar PSR J0109–1431 take 8.82 Gs to travel to Earth. 

Calculate the number of oscillations of the X–rays from the pulsar to the surface of the Earth. Give your answer to an appropriate number of significant figures.

Show the distance from Earth to PSR J0109–1431 is around 280 light years.

A student conducts an experiment to study the variation of resistance R of a negative temperature coefficient (NCT) thermistor with temperature T. The data from the experiment is shown plotted on the graph.

The electric current through the thermistor for T = 283 K is 0.0078 mA. 

What is the units of resistance R in SI units?

Convert 0.0078 mA to A and write in standard form.

Calculate the ratio  when T = 291 K. Write your answer in fundamental SI units to an appropriate number of significant figures.

Estimate the resistance of the thermistor at a temperature of 335 K