OCR MEI
Further Mechanics Minor
2024
June
— Question 2
Exam Board
OCR MEI
Module
Further Mechanics Minor (Further Mechanics Minor)
Year
2024
Session
June
Topic
Dimensional Analysis
2
State the dimensions of force.
Use the following metric-imperial conversion factors for the rest of this question.
\(1 \mathrm {~kg} = 2.2 \mathrm { lb }\) (pounds)
\(1 \mathrm {~m} = 39.4 \mathrm { in }\) (inches)
A unit of force used in the imperial system is the pound-force (lbf). 1 lbf is defined as the gravitational force exerted on 1 lb on the surface of the Earth.
Show that 1 lbf is approximately equal to 4.45 N .
The pascal (Pa) is a unit of pressure equivalent to 1 Newton per square metre. Pressure can also be measured in pound-force per square inch (psi).
A diver, at a depth of 40 m , experiences a typical pressure of \(5 \times 10 ^ { 5 } \mathrm {~Pa}\).
Determine whether this is greater or less than the pressure in a bicycle tyre of 80 psi .
In various physical contexts, energy density is the amount of energy stored in a given region of space per unit volume.
Show that energy density and pressure are dimensionally equivalent.