| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Energy method - driving force up incline, find work done by engine/force |
| Difficulty | Moderate -0.3 This is a straightforward application of standard energy methods and kinematics. Part (a) is direct KE calculation, part (b) uses work-energy theorem with simple geometry for PE change, and part (c) is routine constant acceleration motion. All steps are textbook procedures with no problem-solving insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03f Weight: W=mg6.02d Mechanical energy: KE and PE concepts6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Decrease in \(KE = \frac{1}{2} \times 4 \times (12^2 - 8^2)\) | M1 | |
| \(160\ \text{J}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(PE\) gained \(= 4g \times 10\sin30\ (= 200)\) | B1 | |
| Total work done \(= 200 - 160\) | M1 | |
| Total work done \(= 40\ \text{J}\) | A1 FT |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(-4g\sin30 = 4a\) | M1 | |
| \(a = -5\) | A1 | |
| \(-10 = 8t - \frac{1}{2} \times 5t^2\) | M1 | |
| \(t = 4.16\ \text{s}\) | A1 |
## Question 5(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Decrease in $KE = \frac{1}{2} \times 4 \times (12^2 - 8^2)$ | M1 | |
| $160\ \text{J}$ | A1 | |
## Question 5(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $PE$ gained $= 4g \times 10\sin30\ (= 200)$ | B1 | |
| Total work done $= 200 - 160$ | M1 | |
| Total work done $= 40\ \text{J}$ | A1 FT | |
## Question 5(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| $-4g\sin30 = 4a$ | M1 | |
| $a = -5$ | A1 | |
| $-10 = 8t - \frac{1}{2} \times 5t^2$ | M1 | |
| $t = 4.16\ \text{s}$ | A1 | |
---5 A block $B$ of mass 4 kg is pushed up a line of greatest slope of a smooth plane inclined at $30 ^ { \circ }$ to the horizontal by a force applied to $B$, acting in the direction of motion of $B$. The block passes through points $P$ and $Q$ with speeds $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. $P$ and $Q$ are 10 m apart with $P$ below the level of $Q$.
\begin{enumerate}[label=(\alph*)]
\item Find the decrease in kinetic energy of the block as it moves from $P$ to $Q$.
\item Hence find the work done by the force pushing the block up the slope as the block moves from $P$ to $Q$.
\item At the instant the block reaches $Q$, the force pushing the block up the slope is removed. Find the time taken, after this instant, for the block to return to $P$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q5 [9]}}