| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Constant power on inclined plane |
| Difficulty | Standard +0.3 This is a straightforward application of P=Fv and F=ma on an incline. Students must resolve forces (weight component down slope), use the power equation to find driving force, then apply Newton's second law. While it requires multiple steps and careful sign conventions for uphill/downhill cases, the techniques are standard M1 content with no novel problem-solving required. |
| Spec | 3.02h Motion under gravity: vector form3.03d Newton's second law: 2D vectors6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Driving force = 400/4 | B1 | |
| M1 | For using Newton's second law (either case) – 3 terms needed | |
| \(DF - 80g\sin2° = 80a\) (i) or \(DF + 80g\sin2° = 80a\) (ii) | A1 | |
| Acceleration is \(0.9\text{ ms}^{-2}\) (i) or Acceleration is \(1.6\text{ ms}^{-2}\) (ii) | A1 | Accept 0.90 or 0.901 and 1.60 |
| Acceleration is \(1.6\text{ ms}^{-2}\) (ii) and Acceleration is \(0.9\text{ ms}^{-2}\) (i) | B1ft | [5] ft Ans (i) + (ii) = 2.5 |
| Answer | Marks |
|---|---|
| Driving force = 400/4 | B1 |
| M1 | For using Newton's second law (either case) – 3 terms needed |
| \(a = -8.74\) (i) and \(a = 11.2\) (ii) | A1 |
Driving force = 400/4 | B1 |
| M1 | For using Newton's second law (either case) – 3 terms needed
$DF - 80g\sin2° = 80a$ (i) or $DF + 80g\sin2° = 80a$ (ii) | A1 |
Acceleration is $0.9\text{ ms}^{-2}$ (i) or Acceleration is $1.6\text{ ms}^{-2}$ (ii) | A1 | Accept 0.90 or 0.901 and 1.60
Acceleration is $1.6\text{ ms}^{-2}$ (ii) and Acceleration is $0.9\text{ ms}^{-2}$ (i) | B1ft | [5] ft Ans (i) + (ii) = 2.5
**SR(max. 3/5)** for candidates who have sin and cos interchanged
Driving force = 400/4 | B1 |
| M1 | For using Newton's second law (either case) – 3 terms needed
$a = -8.74$ (i) and $a = 11.2$ (ii) | A1 |
---2 A cyclist, working at a constant rate of 400 W , travels along a straight road which is inclined at $2 ^ { \circ }$ to the horizontal. The total mass of the cyclist and his cycle is 80 kg . Ignoring any resistance to motion, find, correct to 1 decimal place, the acceleration of the cyclist when he is travelling\\
(i) uphill at $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$,\\
(ii) downhill at $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M1 2010 Q2 [5]}}