| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find acceleration on incline given power |
| Difficulty | Standard +0.3 This is a straightforward M2 mechanics question requiring standard application of P=Fv and F=ma with resolving forces on an incline. Part (i) is direct substitution, part (ii) requires combining driving force equation with Newton's second law on a slope—routine for M2 students with no novel problem-solving required. |
| Spec | 6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(20000/32\) | B1 | |
| \(R = 20000/32\) | M1 | |
| \(R = 625\) N | A1 | cao |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(F + 1500g\sin 2 - 625 = 1500 \times 0.1\) | M1, A1ft | Using Newton 2, all forces used; ft their \(R\) from (i); SC \(F - 1500g\sin 2 - 625 = 1500 \times 0.1\) |
| Power \(= 32 \times F\) | M1 | Using their \(F\) |
| Power \(= 8380\) W or \(8.38\) kW | A1 | \(8383.27\ldots\) SC \(41200\) W or \(41.2\) kW |
| [4] |
## Question 2:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $20000/32$ | B1 | |
| $R = 20000/32$ | M1 | |
| $R = 625$ N | A1 | cao |
| **[3]** | | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $F + 1500g\sin 2 - 625 = 1500 \times 0.1$ | M1, A1ft | Using Newton 2, all forces used; ft their $R$ from (i); SC $F - 1500g\sin 2 - 625 = 1500 \times 0.1$ |
| Power $= 32 \times F$ | M1 | Using their $F$ |
| Power $= 8380$ W or $8.38$ kW | A1 | $8383.27\ldots$ SC $41200$ W or $41.2$ kW |
| **[4]** | | |
---2 The power developed by the engine of a car as it travels at a constant speed of $32 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ on a horizontal road is 20 kW .\\
(i) Calculate the resistance to the motion of the car.
The car, of mass 1500 kg , now travels down a straight road inclined at $2 ^ { \circ }$ to the horizontal. The resistance to the motion of the car is unchanged.\\
(ii) Find the power produced by the engine of the car when the car has speed $32 \mathrm {~ms} ^ { - 1 }$ and is accelerating at $0.1 \mathrm {~ms} ^ { - 2 }$.
\hfill \mbox{\textit{OCR M2 2013 Q2 [7]}}