| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | June |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Motion with friction on horizontal surface |
| Difficulty | Standard +0.3 This is a standard M1 mechanics question involving connected particles with friction. Parts (a)-(c) require routine application of Newton's second law and friction formulas with straightforward calculations. Parts (d)-(e) add a time-based element after string breaks, requiring SUVAT equations but following predictable problem structure. The multi-part nature and 17 marks indicate moderate length, but each step uses standard M1 techniques without requiring novel insight or complex problem-solving. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks |
|---|---|
| 7 | R R |
Question 7:
7 | R R
1 2
F F 40
1 2
4g 6g
(a) F = 2 x 4g (= 11.2) or F = 2 x 6g (= 16.8) B1
1 7 2 7
System: 40 – 2 x 4g – 2 x 6g = 10a (equn in a and not T) M1 A1
7 7
⇒ a = 1.2 m s–2 (*) A1
(4)
(b) P: T – 8 g = 4 x 1.2 or Q: 40 – T – 12g = 6 x 1.2 M1 A1
7 7
⇒ T = 16 N A1
(3)
(c) Accelerations of P and Q are same B1
(1)
(d) v = 1.2 x 7 = 8.4 B1
P: (–) 8 g = 4a ⇒ a = (–) 2 g = 2.8 M1 A1
7 7
↓
0 = 8.4 – 2.8t ⇒ t = 3 s (*) M1 A1
(5)
(e) Q: 40 – 12 g = 6a (⇒ a ≈ 3.867) M1 A1
7
↓
v = 8.4 + 3.867 x 3 = 20 m s–1 M1 A1
(4)
(a) 1st A1 requires values for the F’s. (Allow M1 with just ‘F’’s)
(b) Allow M1 A1 for one of these equations wherever seen (e.g. in (a))
(c) extra statement about tensions being equal (with the correct ans): B0
(d) allow verification
No g: allow 1st M1 in each of parts (a), (b), (d), (e) as f.t. but other A’s are cao\includegraphics{figure_4}
Two particles $P$ and $Q$, of mass $4$ kg and $6$ kg respectively, are joined by a light inextensible string. Initially the particles are at rest on a rough horizontal plane with the string taut. The coefficient of friction between each particle and the plane is $\frac{2}{5}$. A constant force of magnitude $40$ N is then applied to $Q$ in the direction $PQ$, as shown in Fig. 4.
\begin{enumerate}[label=(\alph*)]
\item Show that the acceleration of $Q$ is $1.2$ m s$^{-2}$. [4]
\item Calculate the tension in the string when the system is moving. [3]
\item State how you have used the information that the string is inextensible. [1]
\end{enumerate}
After the particles have been moving for $7$ s, the string breaks. The particle $Q$ remains under the action of the force of magnitude $40$ N.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Show that $P$ continues to move for a further $3$ seconds. [5]
\item Calculate the speed of $Q$ at the instant when $P$ comes to rest. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q7 [17]}}