OCR MEI
Further Mechanics Minor
2021
November
— Question 1
Exam Board
OCR MEI
Module
Further Mechanics Minor (Further Mechanics Minor)
Year
2021
Session
November
Topic
Dimensional Analysis
1
State the dimensions of force.
The force \(F\) required to keep a car moving at constant speed on a circular track is given by the formula
$$\mathrm { F } = \frac { \mathrm { mv } ^ { 2 } } { \mathrm { r } }$$
where
\(m\) is the constant mass of the car,
\(v\) is the speed of the car,
\(r\) is the radius of the circular track.
Verify that the formula is dimensionally consistent.
Determine the percentage increase in force required to keep a car moving on a circular track if the speed of the car were to increase by \(10 \%\) and if the track radius were to decrease by \(10 \%\).
It is proposed that a new unit of force, the trackforce (Tr), should be adopted in motor-racing. 1 Tr is defined as the amount of force required to accelerate a mass of 1 ton at a rate of 1 mile per hour per second.
It is given that 1 ton \(= 1016 \mathrm {~kg}\) and 1 mile \(= 1609 \mathrm {~m}\).
Determine the number of newtons that are equivalent to 1 Tr .