| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Difficulty | Moderate -0.8 This is a straightforward mechanics problem requiring basic work-energy calculations. Part (i) uses W = Fs cos θ with given values, and part (ii) applies work-energy principle with simple arithmetic. Both parts are standard textbook exercises with no problem-solving insight required, making it easier than average. |
| Spec | 6.02b Calculate work: constant force, resolved component6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(WD = 35\cos 20 \times 12\) | M1 | Uses \(WD = Fd\cos\theta\) |
| \(395\) J | A1 | |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| *EITHER:* | ||
| \(WD\) against resistance \(= 15 \times 12\) | (B1) | |
| \(35\cos20 \times 12 = 15 \times 12 + \frac{1}{2}(25v^2)\) | M1 | Uses \(WD_{man} = WD_{resistance} + KE\) gain |
| \(v = 4.14 \text{ ms}^{-1}\) | A1) | |
| *OR:* | ||
| \(35\cos20 - 15 = 25a \quad [a = 0.716]\) | (B1) | Applies Newton's Second Law |
| \(v^2 = 2 \times 0.7155 \times 12\) | M1 | Uses \(v^2 = u^2 + 2as\) |
| \(v = 4.14 \text{ ms}^{-1}\) | A1) | |
| Total: 3 |
## Question 1:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $WD = 35\cos 20 \times 12$ | M1 | Uses $WD = Fd\cos\theta$ |
| $395$ J | A1 | |
| **Total: 2** | | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| *EITHER:* | | |
| $WD$ against resistance $= 15 \times 12$ | (B1) | |
| $35\cos20 \times 12 = 15 \times 12 + \frac{1}{2}(25v^2)$ | M1 | Uses $WD_{man} = WD_{resistance} + KE$ gain |
| $v = 4.14 \text{ ms}^{-1}$ | A1) | |
| *OR:* | | |
| $35\cos20 - 15 = 25a \quad [a = 0.716]$ | (B1) | Applies Newton's Second Law |
| $v^2 = 2 \times 0.7155 \times 12$ | M1 | Uses $v^2 = u^2 + 2as$ |
| $v = 4.14 \text{ ms}^{-1}$ | A1) | |
| **Total: 3** | | |
---1 A man pushes a wheelbarrow of mass 25 kg along a horizontal road with a constant force of magnitude 35 N at an angle of $20 ^ { \circ }$ below the horizontal. There is a constant resistance to motion of 15 N . The wheelbarrow moves a distance of 12 m from rest.\\
(i) Find the work done by the man.\\
(ii) Find the speed attained by the wheelbarrow after 12 m .\\
\hfill \mbox{\textit{CAIE M1 2017 Q1 [5]}}