| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics A AS (Further Mechanics A AS) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done against friction/resistance - inclined plane or slope |
| Difficulty | Standard +0.3 This is a straightforward application of energy methods and power calculations with standard mechanics formulas. Part (a) uses work-energy principle with one unknown, (b) is a 'show that' calculation combining work and power, (c) applies P=Fv at maximum speed, and (d) is unit conversion. All parts follow routine procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings6.02k Power: rate of doing work6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | Let the distance travelled be x m. |
| 12 2 4 0 3 2 + 2 4 0 g 2 5 − 1 2 0 x = 12 2 4 0 1 8 2 | B1 | |
| M1 | 1.1 | |
| 3.4 | One correct term. |
| Answer | Marks | Guidance |
|---|---|---|
| x = 1 7 5 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | Let the engine do E J of work from B to A. | |
| E − 1 2 0 1 7 5 = 12 2 4 0 7 2 + 2 4 0 g 2 5 ( E = 8 5 6 8 0 ) | M1 | 3.3 |
| correct amount of work done. | Using their x | |
| Average power =8568030=2856W | A1 | 2.2a |
| Answer | Marks |
|---|---|
| (c) | Let the snowmobile have driving force D N. When travelling |
| Answer | Marks | Guidance |
|---|---|---|
| (𝐷 =) 240𝑔sin12°+120 (= 609) | M1 | 3.3 |
| 6 0 0 0 = D v | M1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| v = 9 .8 5 2 0 8 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (d) | Work done in lifting the mass | |
| = ( 5 5 0 2 .2 ) 9 .8 ( 1 3 .2 8 ) | M1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 7 4 7 W | A1 | 2.2b |
Question 4:
4 | (a) | Let the distance travelled be x m.
12 2 4 0 3 2 + 2 4 0 g 2 5 − 1 2 0 x = 12 2 4 0 1 8 2 | B1
M1 | 1.1
3.4 | One correct term.
Attempt at WEP with correct
number of terms (condone sign
errors).
x = 1 7 5 | A1 | 1.1
[3]
(b) | Let the engine do E J of work from B to A.
E − 1 2 0 1 7 5 = 12 2 4 0 7 2 + 2 4 0 g 2 5 ( E = 8 5 6 8 0 ) | M1 | 3.3 | Must have equation which gives
correct amount of work done. | Using their x
Average power =8568030=2856W | A1 | 2.2a | AG, so must see reference to work
done 30 (e.g. 30P = 85680)
[2]
(c) | Let the snowmobile have driving force D N. When travelling
at maximum speed v ms-1, acceleration up the slope is zero.
(𝐷 =) 240𝑔sin12°+120 (= 609) | M1 | 3.3 | M0 if g omitted
6 0 0 0 = D v | M1 | 3.4 | Applying P = Fv with P=6000 and
Fis driving force (or force down the
slope) stated or implied
v = 9 .8 5 2 0 8 | A1 | 1.1
[3]
(d) | Work done in lifting the mass
= ( 5 5 0 2 .2 ) 9 .8 ( 1 3 .2 8 ) | M1 | 1.1 | Using mgh with attempts to convert
550 lb and 1 ft. Condone
conversion factors misapplied.
M0 if g omitted
M1A0 if KE is considered as well
7 4 7 W | A1 | 2.2b
[2]4 The diagram shows two points A and B on a snowy slope. A is a vertical distance of 25 m above B.\\
\includegraphics[max width=\textwidth, alt={}, center]{d1ec7861-dc8b-450b-8e05-c70479ab0dc2-5_220_1376_306_244}
A rider and snowmobile, with a combined mass of 240 kg , start at the top of the slope, heading in the direction of $B$. As the snowmobile passes $A$, with a speed of $3 \mathrm {~ms} ^ { - 1 }$, the rider switches off the engine so that the snowmobile coasts freely. When the snowmobile passes B, it has a speed of $18 \mathrm {~ms} ^ { - 1 }$.
The resistances to motion can be modelled as a single, constant force of magnitude 120 N .
\begin{enumerate}[label=(\alph*)]
\item Calculate the distance the snowmobile travels from A to B.
The rider now turns the snowmobile around and brings it back to B, so that it faces up the slope. Starting from rest, the snowmobile ascends the slope so that it passes A with a speed of $7 \mathrm {~ms} ^ { - 1 }$. It takes 30 seconds for the snowmobile to travel from B to A. The resistances to motion can still be modelled as a single, constant force of magnitude 120 N .
\item Show that the snowmobile develops an average power of 2856 W during this time.
The snowmobile can develop a maximum power of 6000 W . At a later point in the journey, the rider and snowmobile reach a different slope inclined at $12 ^ { \circ }$ to the horizontal. The resistances to motion can still be modelled as a single, constant force of magnitude 120 N .
\item Determine the maximum speed with which the rider and snowmobile can ascend.
The power developed by a vehicle is sometimes given in the non-SI unit mechanical horsepower $( \mathrm { hp } ) .1 \mathrm { hp }$ is the power required to lift 550 pounds against gravity, starting and ending at rest, by 1 foot in 1 second.
\item Given that 1 metre $\approx 3.28$ feet and $1 \mathrm {~kg} \approx 2.2$ pounds, determine the number of watts that are equivalent to 1 hp .
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics A AS 2022 Q4 [10]}}