| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | October |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Maximum or minimum mass |
| Difficulty | Moderate -0.3 This is a standard M1 moments question requiring equilibrium conditions and taking moments about a point. Part (a) involves finding when one tension becomes zero (limiting case), and part (b) is straightforward application of moment equilibrium. The setup is clear, methods are routine, and it's slightly easier than average due to being a textbook-style two-part question with no geometric complexity or novel insight required. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks |
|---|---|
| 2(a) | 3 a 2 a |
| Answer | Marks |
|---|---|
| 5 | M1A1 |
| Answer | Marks |
|---|---|
| 3 | A1 (3) |
| 2(a) | M1 For an equation (or inequality, „ ) in X , M and a only (allow |
| Answer | Marks |
|---|---|
| 2(b) | 1 3 a 2 a |
| Answer | Marks |
|---|---|
| 5 2 5 | M1A1 |
| Answer | Marks |
|---|---|
| 10 | A1 (3) |
| Answer | Marks |
|---|---|
| 2(b) | M1 For an equation in Tc , M , g and a only (allow consistent missing |
Question 2:
--- 2(a) ---
2(a) | 3 a 2 a
M ( D ) , X g = M g
5 5
Other possible equations:
( ) T = M g + X g
D
7 a
M ( A M ) , g a + X g a 2 = T
D
5
a 3
M ( B M ) , g a = T T would then need to be eliminated
D D
5
3 a a 8
M ( C M ) , g X g + = T a
D
5 5
a 2
M ( G X ) , g a = T
D
5 | M1A1
2M
X = , 0.67 M or better
3 | A1 (3)
2(a) | M1 For an equation (or inequality, „ ) in X , M and a only (allow
consistent missing a’s) with correct no. of terms.
Allow if one g is missing.
N.B. M0 if Tc appears and never becomes zero
A1 Correct equation or inequality
A1 cao
--- 2(b) ---
2(b) | 1 3 a 2 a
M ( D ) T, a + M g = M g
C
2 5 5
Other possible equations:
1
()T +T =Mg+ Mg
C D
2
1 2a 7a
M(A), Mga+ Mg2a =T +T
C D
2 5 5
8a 3a
M(B), Mga=T +T T would need eliminating
C 5 D 5 D
3a 1 8a
M(C), Mg + Mg =T a
D
5 2 5
3a 1 2a
M(G), T + Mga =T
C D
5 2 5 | M1A1
1
T = Mg oe
C
10 | A1 (3)
(6)
Notes for question 2
2(b) | M1 For an equation in Tc , M , g and a only (allow consistent missing
a’s or if g(’s) missing) with correct no. of terms
M0 if they assume that T =T or if they assume their X value from
C D
(a).
A1 Correct equation
A1 cao\includegraphics{figure_1}
A uniform rod $AB$ has length $2a$ and mass $M$. The rod is held in equilibrium in a horizontal position by two vertical light strings which are attached to the rod at $C$ and $D$, where $AC = \frac{2}{5}a$ and $DB = \frac{3}{5}a$, as shown in Figure 1.
A particle $P$ is placed on the rod at $B$.
The rod remains horizontal and in equilibrium.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $M$, the largest possible mass of the particle $P$ [3]
Given that the mass of $P$ is $\frac{1}{2}M$
\item Find, in terms of $M$ and $g$, the tension in the string that is attached to the rod at $C$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2022 Q2 [6]}}