| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Variable resistance: find k or constants |
| Difficulty | Moderate -0.3 This is a straightforward M2 mechanics problem requiring application of the power equation P=Fv and resolution of forces at constant speed. Part (i) involves setting up one equation with driving force balancing resistance plus weight component, then solving for k. Part (ii) uses the same k value in a simpler scenario. Standard bookwork with clear method and no conceptual surprises, making it slightly easier than average. |
| Spec | 6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| i | \(21000/25\) | B1 |
| \(0 = 21000/25 - 25k - 1250\sin 2\) | M1 | 3 terms |
| \(k = 16.5\) | A1 | \(cv(21000/25)\) |
| A1 | ||
| [4] | ||
| ii | \(21000/v = 16.5v\) | M1 |
| \(v = 35.7 \text{ ms}^{-1}\) | A1 | |
| [3] |
| **Part** | **Answer/Working** | **Marks** | **Guidance** |
|----------|-------------------|----------|-------------|
| i | $21000/25$ | B1 | Use of force = power/speed |
| | $0 = 21000/25 - 25k - 1250\sin 2$ | M1 | 3 terms |
| | $k = 16.5$ | A1 | $cv(21000/25)$ |
| | | A1 | |
| | | [4] | |
| ii | $21000/v = 16.5v$ | M1 | $ft$ on $cv(k)$ |
| | $v = 35.7 \text{ ms}^{-1}$ | A1 | |
| | | [3] | |2 A car of mass 1250 kg travels along a straight road inclined at $2 ^ { \circ }$ to the horizontal. The resistance to the motion of the car is $k v \mathrm {~N}$, where $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the speed of the car and $k$ is a constant. The car travels at a constant speed of $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ up the slope and the engine of the car works at a constant rate of 21 kW .\\
(i) Calculate the value of $k$.\\
(ii) Calculate the constant speed of the car on a horizontal road.
\hfill \mbox{\textit{OCR M2 2011 Q2 [7]}}