| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Engine power on road constant/variable speed |
| Difficulty | Standard +0.3 This is a standard M2 work-energy-power question with two parts: (i) uses P=Fv with forces in equilibrium (routine show-that), (ii) applies work-energy principle with variable acceleration. Both parts follow textbook methods with straightforward arithmetic, though part (ii) requires integrating P=Fv·dt which is slightly above basic recall but well within standard M2 technique. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Driving Force \(= 10000/20\ (= 500)\) | B1 | |
| \(cv(10000/20) - 1300 + 800g\sin\alpha = 0\) | M1 | Attempt at N2L with 3 terms |
| A1 | ||
| \(\sin\alpha = 5/49\) | A1 | AG at least one more line of correct working (at least e.g. \(-800 + 800g\sin\alpha = 0\)); allow verification (e.g. \(500 - 1300 + 800 = 0\)) |
| [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(800(22.1)g\sin\alpha\) | B1 | Work done against weight; Need a value for \(\sin\alpha\) or \(\alpha\) |
| \(800(22.1)g\sin\alpha + 1300(22.1) + \frac{1}{2}(800)(8^2)\) | M1 | Total work done, 3 terms needed |
| A1 | Need a value for \(\sin\alpha\) or \(\alpha\); (72010 J) | |
| M1 | Time = work done (from at least one correct energy term)/power | |
| \(t = 3.6(0)\) s | A1 | 'Exact' is 3.6005 |
| [5] |
## Question 5:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Driving Force $= 10000/20\ (= 500)$ | B1 | |
| $cv(10000/20) - 1300 + 800g\sin\alpha = 0$ | M1 | Attempt at N2L with 3 terms |
| | A1 | |
| $\sin\alpha = 5/49$ | A1 | **AG** at least one more line of correct working (at least e.g. $-800 + 800g\sin\alpha = 0$); allow verification (e.g. $500 - 1300 + 800 = 0$) |
| **[4]** | | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $800(22.1)g\sin\alpha$ | B1 | Work done against weight; Need a value for $\sin\alpha$ or $\alpha$ |
| $800(22.1)g\sin\alpha + 1300(22.1) + \frac{1}{2}(800)(8^2)$ | M1 | Total work done, 3 terms needed |
| | A1 | Need a value for $\sin\alpha$ or $\alpha$; (72010 J) |
| | M1 | Time = work done (from at least one correct energy term)/power |
| $t = 3.6(0)$ s | A1 | 'Exact' is 3.6005 |
| **[5]** | | |
---5 (i) A car of mass 800 kg is moving at a constant speed of $20 \mathrm {~ms} ^ { - 1 }$ on a straight road down a hill inclined at an angle $\alpha$ to the horizontal. The engine of the car works at a constant rate of 10 kW and there is a resistance to motion of 1300 N . Show that $\sin \alpha = \frac { 5 } { 49 }$.\\
(ii) The car now travels up the same hill and its engine now works at a constant rate of 20 kW . The resistance to motion remains 1300 N . The car starts from rest and its speed is $8 \mathrm {~ms} ^ { - 1 }$ after it has travelled a distance of 22.1 m . Calculate the time taken by the car to travel this distance.
\hfill \mbox{\textit{OCR M2 2014 Q5 [9]}}