| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Horizontal force on slope |
| Difficulty | Standard +0.3 This is a standard mechanics problem requiring resolution of forces and Newton's second law. Students must find sin α and cos α from tan α, resolve forces horizontally and vertically, calculate friction, then find acceleration. Part (b) requires conceptual understanding of how normal reaction affects friction. While multi-step, it follows a routine procedure with no novel insight required, making it slightly easier than average. |
| Spec | 3.03a Force: vector nature and diagrams3.03c Newton's second law: F=ma one dimension3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form3.03s Contact force components: normal and frictional3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| Resolve vertically | M1 | 3.1b |
| \(R + 40\sin\alpha = 20g\) | A1 | 1.1b |
| Resolve horizontally | M1 | 3.1b |
| \(40\cos\alpha - F = 20a\) | A1 | 1.1b |
| \(F = 0.14R\) | B1 | 1.2 |
| \(a = 0.396\) or \(0.40\) (m s\(^{-2}\)) | A1 | 2.2a |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| Pushing will increase \(R\) which will increase available \(F\) | B1 | 2.4 |
| Increasing \(F\) will decrease \(a\) * GIVEN ANSWER | B1* | 2.4 |
## Question 7:
### Part (a):
| Working/Answer | Mark | Guidance |
|---|---|---|
| Resolve vertically | M1 | 3.1b |
| $R + 40\sin\alpha = 20g$ | A1 | 1.1b |
| Resolve horizontally | M1 | 3.1b |
| $40\cos\alpha - F = 20a$ | A1 | 1.1b |
| $F = 0.14R$ | B1 | 1.2 |
| $a = 0.396$ or $0.40$ (m s$^{-2}$) | A1 | 2.2a |
**Notes:**
- M1: Resolve vertically with usual rules applying
- A1: Correct equation. Neither $g$ nor $\sin\alpha$ need to be substituted
- M1: Apply $F = ma$ horizontally, with usual rules
- A1: Neither $F$ nor $\cos\alpha$ need to be substituted
- B1: $F = 0.14R$ seen (e.g. on diagram)
- A1: Either answer
### Part (b):
| Working/Answer | Mark | Guidance |
|---|---|---|
| Pushing will increase $R$ which will increase available $F$ | B1 | 2.4 |
| Increasing $F$ will decrease $a$ * GIVEN ANSWER | B1* | 2.4 |
**Notes:**
- B1: Pushing increases $R$ which produces an increase in available (limiting) friction
- B1: $F$ increase produces a decrease in $a$ (need to see this)
- N.B. It is possible to score B0 B1 but for the B1, some "explanation" is needed to say why friction is increased e.g. by pushing into the ground
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7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{65e4b254-fb7b-45c2-9702-32f034018193-20_264_698_246_685}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
A wooden crate of mass 20 kg is pulled in a straight line along a rough horizontal floor using a handle attached to the crate.\\
The handle is inclined at an angle $\alpha$ to the floor, as shown in Figure 1, where $\tan \alpha = \frac { 3 } { 4 }$\\
The tension in the handle is 40 N .\\
The coefficient of friction between the crate and the floor is 0.14\\
The crate is modelled as a particle and the handle is modelled as a light rod.\\
Using the model,
\begin{enumerate}[label=(\alph*)]
\item find the acceleration of the crate.
The crate is now pushed along the same floor using the handle. The handle is again inclined at the same angle $\alpha$ to the floor, and the thrust in the handle is 40 N as shown in Figure 2 below.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{65e4b254-fb7b-45c2-9702-32f034018193-20_220_923_1457_571}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
\item Explain briefly why the acceleration of the crate would now be less than the acceleration of the crate found in part (a).
\end{enumerate}
\hfill \mbox{\textit{Edexcel Paper 3 2018 Q7 [8]}}