| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Maximum speed on incline vs horizontal |
| Difficulty | Standard +0.3 This is a straightforward power-speed-force problem requiring the standard formula P = Fv and resolution of forces on an incline. Students must apply the equation twice (up and down) with correct force directions, but the method is direct with no conceptual subtleties or multi-step problem-solving required. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = 250/v\) | B1 (AO 1.1) | Used in the solution in either direction; do not award if equating \(D\) with \(Fr\) |
| Up: \((\pm)F - 80g\sin4° - 70 = 0\) | M1 (AO 1.1) | N1L (or balancing forces); opposing forces must be in same direction; allow sin/cos confusion; allow 40° instead of 4° confusion |
| \(v =\) awrt \(2.00\) | A1 (AO 1.1) | \(2.004987...\); accept 2 m/s but not e.g. 2.01; NB 2.005 to 4sf; do not accept negative value unless clearly justified e.g. if downwards is defined as negative |
| Down: \(F + 80g\sin4° - 70 = 0\) | M1 (AO 1.1) | N1L (or balancing forces); \(F = 15.310...\) |
| \(v =\) awrt \(16.3\) | A1 [5] (AO 1.1) |
# Question 4:
$F = 250/v$ | B1 (AO 1.1) | Used in the solution in either direction; do not award if equating $D$ with $Fr$
Up: $(\pm)F - 80g\sin4° - 70 = 0$ | M1 (AO 1.1) | N1L (or balancing forces); opposing forces must be in same direction; allow sin/cos confusion; allow 40° instead of 4° confusion
$v =$ awrt $2.00$ | A1 (AO 1.1) | $2.004987...$; accept 2 m/s but not e.g. 2.01; NB 2.005 to 4sf; do not accept negative value unless clearly justified e.g. if downwards is defined as negative
Down: $F + 80g\sin4° - 70 = 0$ | M1 (AO 1.1) | N1L (or balancing forces); $F = 15.310...$
$v =$ awrt $16.3$ | A1 [5] (AO 1.1) |
---4 A cyclist is riding a bicycle along a straight road which is inclined at an angle of $4 ^ { \circ }$ to the horizontal. The cyclist is working at a constant rate of 250 W . The combined mass of the cyclist and bicycle is 80 kg and the resistance to their motion is a constant 70 N .
Determine the maximum constant speed at which the cyclist can ride the bicycle
\begin{itemize}
\item up the hill, and
\item down the hill.
\end{itemize}
\hfill \mbox{\textit{OCR Further Mechanics AS 2022 Q4 [5]}}