| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | November |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Motion with friction on horizontal surface |
| Difficulty | Moderate -0.3 This is a standard M1 mechanics question involving resolving forces, friction, and kinematics. Parts (a) and (b) require routine application of Newton's laws with force resolution at an angle, while part (c) uses basic SUVAT equations. The multi-step nature and need to link parts together makes it slightly below average difficulty, but all techniques are standard textbook exercises requiring no novel insight. |
| Spec | 3.03e Resolve forces: two dimensions3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks |
|---|---|
| 7 (a) | R 150 |
| Answer | Marks |
|---|---|
| (ii) | T |
Question 7:
--- 7 (a) ---
7 (a) | R 150
0.2R R(↑) R + 150 sin 20 = 30g M1 A1
30g ⇒ R ≈ 243 N A1
(3)
R(→): 150 cos 20 – 0.2R = 30a M1 A1
⇒ a ≈ 3.08 m s–2 A1
S (3)
F
S = 30g ⇒ F = 0.2 x 30g M1 A1
30g
30a’ = (–) 0.2 x 30g ⇒ a’ = (–) 0.2g (= 1.96) M1 A1
0 = 122 – 2 x 0.2g x s (using new a’) M1
⇒ s ≈ 36.7 m A1
(6)
8 (a)
(b)
(c) (i)
(ii) | T
R
F R(perp. to slope): R = 20g cos 60 (= 10g = 98 N) M1 A1
F = 0.4R (used) B1
20g R(parallel to slope): T + F = 20g cos 30 M1 A2, 1, 0
↓
T = 10√3 g – 4g ≈ 131 or 130 N M1 A1
T R (8)
R = 10g as before B1 √
F T – 0.4R = 20g cos 30 M1 A1
20g
T = 10√3 g + 4g ≈ 209 or 210 N A1
(4)
Friction acts down slope (and has magnitude 0.4R) B1
Net force on package = 0 (or equivalent), or ‘no acceleration’ B1
(2)
________________________________________________________________________________\includegraphics{figure_3}
A sledge has mass 30 kg. The sledge is pulled in a straight line along horizontal ground by means of a rope. The rope makes an angle $20°$ with the horizontal, as shown in Figure 3. The coefficient of friction between the sledge and the ground is 0.2. The sledge is modelled as a particle and the rope as a light inextensible string. The tension in the rope is 150 N. Find, to 3 significant figures,
\begin{enumerate}[label=(\alph*)]
\item the normal reaction of the ground on the sledge, [3]
\item the acceleration of the sledge. [3]
\end{enumerate}
When the sledge is moving at $12 \text{ m s}^{-1}$, the rope is released from the sledge.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find, to 3 significant figures, the distance travelled by the sledge from the moment when the rope is released to the moment when the sledge comes to rest. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q7 [12]}}