| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Difficulty | Standard +0.3 This is a straightforward mechanics problem requiring resolution of forces, application of equilibrium conditions (constant speed means zero net force), and basic work-energy calculations. The given cosine values simplify calculations, and the method is standard textbook material with no novel insight required. Slightly above average difficulty due to multiple steps and careful bookkeeping of components. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03v Motion on rough surface: including inclined planes6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(WD = 30 \times 20 \times 0.6 + 40 \times 20 \times 0.8\) | M1 | For using \(WD = Fd\cos\theta\) |
| Work done is \(1000\) J | A1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For applying \(F = \mu W\) and Newton's 2nd law with \(a = 0\) | |
| \(30 \times 0.6 + 40 \times 0.8 - 0.625W = 0\) | A1 | |
| Weight is \(80\) N | A1 [3] |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $WD = 30 \times 20 \times 0.6 + 40 \times 20 \times 0.8$ | M1 | For using $WD = Fd\cos\theta$ |
| Work done is $1000$ J | A1 [2] | |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For applying $F = \mu W$ and Newton's 2nd law with $a = 0$ |
| $30 \times 0.6 + 40 \times 0.8 - 0.625W = 0$ | A1 | |
| Weight is $80$ N | A1 [3] | |
---2\\
\includegraphics[max width=\textwidth, alt={}, center]{3e58aa5a-3789-4aaf-8656-b5b98cd7f693-2_385_389_918_879}
A block $B$ lies on a rough horizontal plane. Horizontal forces of magnitudes 30 N and 40 N , making angles of $\alpha$ and $\beta$ respectively with the $x$-direction, act on $B$ as shown in the diagram, and $B$ is moving in the $x$-direction with constant speed. It is given that $\cos \alpha = 0.6$ and $\cos \beta = 0.8$.\\
(i) Find the total work done by the forces shown in the diagram when $B$ has moved a distance of 20 m .\\
(ii) Given that the coefficient of friction between the block and the plane is $\frac { 5 } { 8 }$, find the weight of the block.
\hfill \mbox{\textit{CAIE M1 2013 Q2 [5]}}