| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Minor (Further Mechanics Minor) |
| Year | 2021 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Verify dimensional consistency |
| Difficulty | Moderate -0.8 This is a straightforward dimensional analysis question requiring only routine application of standard techniques: stating dimensions of force (basic recall), verifying dimensional consistency (mechanical substitution), calculating percentage changes (simple arithmetic), and unit conversion (direct calculation). All parts are standard textbook exercises with no problem-solving insight required. |
| Spec | 6.01a Dimensions: M, L, T notation6.01c Dimensional analysis: error checking |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | −2 |
| MLT | B1 | 1.2 |
| Answer | Marks |
|---|---|
| (b) | ( −1 )2 |
| Answer | Marks | Guidance |
|---|---|---|
| L | M1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| A1 | 2.2a | must see expanded |
| 2 −2 −1 −2 | [2] | −1 2 |
| (c) | = 𝑀𝑀2𝐿𝐿 𝑇𝑇 𝐿𝐿 =𝑀𝑀𝐿𝐿𝑇𝑇 =[𝐿𝐿𝐿𝐿𝐿𝐿] | |
| 1.1 ÷0 .9 | M1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| =1.34444 so 34.4% | A1 | 2.2b |
| Answer | Marks | Guidance |
|---|---|---|
| (d) | 1016×1609÷602 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| =454N | A1 | 1.1 |
Question 1:
1 | (a) | −2
MLT | B1 | 1.2
[1]
(b) | ( −1 )2
M LT
[ ]=
RHS
L | M1 | 3.4 | Using given formula with [m] = M
and [r] = L and [v] = LT–1
A1 | 2.2a | must see expanded
2 −2 −1 −2 | [2] | −1 2
(c) | = 𝑀𝑀2𝐿𝐿 𝑇𝑇 𝐿𝐿 =𝑀𝑀𝐿𝐿𝑇𝑇 =[𝐿𝐿𝐿𝐿𝐿𝐿]
1.1 ÷0 .9 | M1 | 1.1 | Using cor ( r𝐿𝐿e𝑇𝑇ct fo ) rmula with 1.1 and
0.9
=1.34444 so 34.4% | A1 | 2.2b | 34.44444…
[2]
(d) | 1016×1609÷602 | M1 | 1.1 | Condone denominator which is not
squared e.g for the M
mark 3
=454N | A1 | 1.1 | 60 𝑜𝑜𝑜𝑜 60 | 454.0955…
[2]1
\begin{enumerate}[label=(\alph*)]
\item 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
\begin{itemize}
\item $m$ is the constant mass of the car,
\item $v$ is the speed of the car,
\item $r$ is the radius of the circular track.
\item Verify that the formula is dimensionally consistent.
\item 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 $10 \%$.
\end{itemize}
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 $= 1609 \mathrm {~m}$.
\item Determine the number of newtons that are equivalent to 1 Tr .
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2021 Q1 [7]}}