| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Modelling assumptions and limitations |
| Difficulty | Moderate -0.5 This is a straightforward M1 question testing understanding of modelling assumptions and basic force calculations. Part (a) requires stating a standard assumption (no air resistance), part (b)(i) is a simple F=ma calculation, and the remaining parts ask for qualitative descriptions of resistance forces rather than complex mathematical derivations. While it requires understanding of mechanics concepts, the mathematical demands are minimal and the question structure is highly scaffolded. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03g Gravitational acceleration6.06a Variable force: dv/dt or v*dv/dx methods |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| No air resistance / Only gravity or weight | B1 | Acceptable assumption |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(0.2\times8=0.2\times9.8-R\) | M1 | Three term equation of motion |
| \(R=0.36\text{ N}\) | A1 | Correct equation |
| A1 | Correct magnitude of the resistance force |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Increases as the speed increases | B1 | Correct explanation |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(\pm9.8\text{ ms}^{-2}\) | B1 | CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Decreases towards zero | B1 | Correct explanation |
## Question 5:
**Part (a)**
| Working | Marks | Guidance |
|---------|-------|----------|
| No air resistance / Only gravity or weight | B1 | Acceptable assumption |
**Part (b)(i)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $0.2\times8=0.2\times9.8-R$ | M1 | Three term equation of motion |
| $R=0.36\text{ N}$ | A1 | Correct equation |
| | A1 | Correct magnitude of the resistance force |
**Part (b)(ii)**
| Working | Marks | Guidance |
|---------|-------|----------|
| **Increases** as the speed increases | B1 | Correct explanation |
**Part (c)(i)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $\pm9.8\text{ ms}^{-2}$ | B1 | CAO |
**Part (c)(ii)**
| Working | Marks | Guidance |
|---------|-------|----------|
| **Decreases** towards zero | B1 | Correct explanation |
---5 A sphere of mass 200 grams is released from rest and allowed to fall vertically.
\begin{enumerate}[label=(\alph*)]
\item A student states that the acceleration of the sphere is $9.8 \mathrm {~ms} ^ { - 2 }$ while it is falling. What modelling assumption is this student making?
\item The student conducts an experiment and finds that the acceleration of the ball is in fact $8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. He formulates a model for the motion that assumes a constant resistance force acts on the ball as it is falling.
\begin{enumerate}[label=(\roman*)]
\item Calculate the magnitude of this resistance force based on this assumption.
\item Describe how the resistance force would vary in reality.
\end{enumerate}\item In a revised model the resistance force is assumed to be proportional to the speed of the sphere.
\begin{enumerate}[label=(\roman*)]
\item State the initial acceleration of the sphere.
\item State what would happen to the acceleration of the sphere if it were able to fall for a long period of time.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA M1 2005 Q5 [7]}}