| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done against friction/resistance - inclined plane or slope |
| Difficulty | Moderate -0.8 This is a straightforward multi-part mechanics question requiring standard application of work-energy formulas (W = Fd, PE = mgh) with basic trigonometry. All steps are routine calculations with no problem-solving insight needed—easier than average A-level. |
| Spec | 6.02a Work done: concept and definition6.02d Mechanical energy: KE and PE concepts |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(WD = 40 \times 36 = 1440\) J | B1 | [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| M1 | Using \(PE = mgh\) | |
| \(PE = 25 \times g \times 36 \sin 20 = 3080\) J | A1 | [2] \([PE = 3078.18]\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| WD by pulling force \(=\) (i) \(+\) (ii) | M1 | For using WD by pulling force \(=\) Gain in \(PE\) + WD against \(F\) |
| \(WD = 4520\) J | A1 | [2] \([WD = 4518.18]\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \([(25g \sin 20 + 40) \times 36]\) | M1 | For attempting to find the pulling force and multiply by 36 to find the work done |
| \(WD = 4520\) J | A1 | [2] \([WD = 4518.18]\) |
## Question 2:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $WD = 40 \times 36 = 1440$ J | B1 | [1] |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| | M1 | Using $PE = mgh$ |
| $PE = 25 \times g \times 36 \sin 20 = 3080$ J | A1 | [2] $[PE = 3078.18]$ |
### Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| WD by pulling force $=$ (i) $+$ (ii) | M1 | For using WD by pulling force $=$ Gain in $PE$ + WD against $F$ |
| $WD = 4520$ J | A1 | [2] $[WD = 4518.18]$ |
**Alternative for (iii):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $[(25g \sin 20 + 40) \times 36]$ | M1 | For attempting to find the pulling force and multiply by 36 to find the work done |
| $WD = 4520$ J | A1 | [2] $[WD = 4518.18]$ |
---2 A box of mass 25 kg is pulled, at a constant speed, a distance of 36 m up a rough plane inclined at an angle of $20 ^ { \circ }$ to the horizontal. The box moves up a line of greatest slope against a constant frictional force of 40 N . The force pulling the box is parallel to the line of greatest slope. Find\\
(i) the work done against friction,\\
(ii) the change in gravitational potential energy of the box,\\
(iii) the work done by the pulling force.
\hfill \mbox{\textit{CAIE M1 2016 Q2 [5]}}