| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Lifting objects vertically |
| Difficulty | Easy -1.2 This is a straightforward application of basic work-energy formulas (W = Fd, P = W/t) with constant forces and vertical motion. Requires only direct substitution into standard formulas after identifying that the crane must overcome both weight (mg) and resistance, making it easier than average A-level questions which typically involve multi-step problem-solving or conceptual challenges. |
| Spec | 6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| PE gain \(= 50g \times 3.5 \ (=1750)\) | B1 | |
| \([WD = 50g \times 3.5 + 25 \times 3.5]\) | M1 | For using \(WD = \text{PE gain} + WD\) against resistance |
| Work done \(= 1837.5\text{ J}\) or \(1840\text{ J}\) | A1 | [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([P = 1837.5/2]\) or \([P/v = 50g + 25\) and \(3.5 = 2v]\) | M1 | For using \(P = WD/t\) or for using \(P = Fv\) and \(s = vt\) |
| Power \(= 919\text{ W}\) | A1 | [2] |
# Question 1:
## Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| PE gain $= 50g \times 3.5 \ (=1750)$ | B1 | |
| $[WD = 50g \times 3.5 + 25 \times 3.5]$ | M1 | For using $WD = \text{PE gain} + WD$ against resistance |
| Work done $= 1837.5\text{ J}$ or $1840\text{ J}$ | A1 | [3] |
## Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[P = 1837.5/2]$ or $[P/v = 50g + 25$ **and** $3.5 = 2v]$ | M1 | For using $P = WD/t$ or for using $P = Fv$ and $s = vt$ |
| Power $= 919\text{ W}$ | A1 | [2] |
---1 A crane is used to raise a block of mass 50 kg vertically upwards at constant speed through a height of 3.5 m . There is a constant resistance to motion of 25 N .\\
(i) Find the work done by the crane.\\
(ii) Given that the time taken to raise the block is 2 s , find the power of the crane.
\hfill \mbox{\textit{CAIE M1 2016 Q1 [5]}}