| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Cyclist or runner: find resistance or speed |
| Difficulty | Standard +0.3 This is a straightforward application of P=Fv and F=ma with constant resistance. Part (a) uses P=Fv to find driving force then applies F-R=ma. Part (b) finds constant speed from P=Fv then uses distance=speed×time. Part (c) requires a simple qualitative statement. All steps are standard textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(450/0.5 - 150 = 240a\) | M1 | Using \(F = ma\) with \(m\) substituted in and a force derived from \(P = Fv\) and the resistance force as negative |
| \(a = 3.125\), so maximum acceleration is \(3.13 \text{ ms}^{-2}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(210 = Dv\) | M1 | Use of "\(P = Fv\)" or \(p = \frac{Fd}{t}\) with 210 substituted in |
| Constant speed \(\Rightarrow a = 0 \Rightarrow 210/v = 150\) | M1 | Using \(F = ma\) with \(a = 0\) to deduce the required force. Or \(210 = \frac{150d}{t}\) |
| \(v = 1.4\) | A1 | Or \(t = \frac{150 \times 350}{210}\) |
| \(t = 350/1.4 = 250\) seconds | A1 | 4 minutes 10 seconds |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The model assumes that the power and hence driving force is constant but in practice this will not be the case (since the oars go in and out of the water periodically). Or: Rower may get tired (& reduce power output). Or: Speed may vary, hence power will vary (if the force/resistance is constant). | B1 | Detailed knowledge of the mode of propulsion of a rowing boat is not required. If mentioning change of resistance, force or speed, this must be linked to power output. Allow any response along the lines that any human way of providing power will not in practice be constant. |
# Question 4:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $450/0.5 - 150 = 240a$ | M1 | Using $F = ma$ with $m$ substituted in and a force derived from $P = Fv$ and the resistance force as negative |
| $a = 3.125$, so maximum acceleration is $3.13 \text{ ms}^{-2}$ | A1 | |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $210 = Dv$ | M1 | Use of "$P = Fv$" or $p = \frac{Fd}{t}$ with 210 substituted in |
| Constant speed $\Rightarrow a = 0 \Rightarrow 210/v = 150$ | M1 | Using $F = ma$ with $a = 0$ to deduce the required force. Or $210 = \frac{150d}{t}$ |
| $v = 1.4$ | A1 | Or $t = \frac{150 \times 350}{210}$ |
| $t = 350/1.4 = 250$ seconds | A1 | 4 minutes 10 seconds |
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| The model assumes that the power and hence driving force is constant but in practice this will not be the case (since the oars go in and out of the water periodically). Or: Rower may get tired (& reduce power output). Or: Speed may vary, hence power will vary (if the force/resistance is constant). | B1 | Detailed knowledge of the mode of propulsion of a rowing boat is not required. If mentioning change of resistance, force or speed, this must be linked to power output. Allow any response along the lines that any human way of providing power will not in practice be constant. |
---4 A rower is rowing a boat in a straight line across a lake. The combined mass of the rower, boat and oars is 240 kg . The maximum power that the rower can generate is 450 W .
In a model of the motion of the boat it is assumed that the total resistance to the motion of the boat is 150 N at any instant when the boat is in motion.
\begin{enumerate}[label=(\alph*)]
\item Find the maximum possible acceleration of the boat, according to the model, at an instant when its speed is $0.5 \mathrm {~ms} ^ { - 1 }$.
At one stage in its motion the boat is travelling at a constant speed and the rower is generating power at an average rate of 210 W , which is assumed to be constant. The boat passes a pole and then, after travelling 350 m , a second pole.
\item Determine how long it takes, according to the model, for the boat to travel between the two poles.
\item State a reason why the assumption that the rower's generated power is constant may be unrealistic.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics AS 2023 Q4 [7]}}