SI Units (CIE A Level Physics)

Define the following quantities and state their SI base units

The pressure due to a liquid of density  is related to the depth by the expression   

where  is the acceleration of free fall.

Use this expression to determine the derived units of pressure .

The speed  of a sound wave through a gas of pressure  and density  is given by the equation

where  is a constant.

Show that the constant  has no unit.

Derive the SI base unit of force.

As a spherical object of radius moves through the air at speed , it experiences a force due to air resistance.

The resistive force is given by 

Where  is a constant.

Derive the SI base unit of the constant .

Fig 1.2 shows a turbine that is used to generate electrical power P from wind travelling with velocity v.

The useful power output P of the turbine is given by

Where L is the length of each blade, ρ is the density of air, v is the wind velocity and C_P is a constant.

Show that the constant C_P has no units.

A local council is looking into building wind turbines to supply power to 2500 households in a village. The average energy consumption of a household in the village is 3000 kWh a year.

Fig. 1.3. shows an image from a catalogue detailing the different sizes and power outputs of available wind turbines.

They decide to build 8 of the same wind turbine to supply the entire village with electricity. 

Convert the following measurements

The frequency f of a stationary wave on a string is given by 

where L is the length of the string, T is the tension in the string, m is the mass per unit length of the string and k is a dimensionless constant.

By considering the homogeneity of the equation, determine the value of k.

The current through a semiconductor diode given by 

where is the initial current, q is the charge of an electron, V is the applied potential difference, T is the temperature and n is a constant.

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

A foil made from gold has a thickness of 0.132 µm. A gold atom has a radius of 146 pm.

The atomic mass unit u is a common unit used in nuclear physics. 1u is equivalent to 931.5 MeV c^–2

Show that 1u is approximately equal to the mass of a proton in kg.

An acre is a unit of land measurement approximately equal to 4050 m² which is roughly equivalent to the size of a football field.

An Astronomical Unit, or 1 AU, is defined as the average distance between the Earth and the Sun and is approximately equal to 150 million km.