Standard +0.3 This is a straightforward moments problem requiring students to identify the pivot point, set up a moment equation about that point when tilting occurs, and solve for the unknown distance. It involves standard mechanics techniques with clear setup and minimal algebraic manipulation, making it slightly easier than average for A-level mechanics.
1
\includegraphics[max width=\textwidth, alt={}, center]{835616aa-0b2b-4e8c-bbbf-60b72dc5ea3e-2_182_843_264_651}
A uniform rigid plank has mass 10 kg and length 4 m . The plank has 0.9 m of its length in contact with a horizontal platform. A man \(M\) of mass 75 kg stands on the end of the plank which is in contact with the platform. A child \(C\) of mass 25 kg walks on to the overhanging part of the plank (see diagram). Find the distance between the man and the child when the plank is on the point of tilting.
\(75g \times 0.9 = 25g \times x + 10g \times 1.1\) (3 term equation)
Two terms correct (unsimplified)
A1
Completely correct (unsimplified)
A1
Distance \(MC = 3.16\) m
A1
4 marks total
> NB: If moments taken about other points, the force of the platform on the plank must be present at the edge of the platform for M1.
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| For taking moments about the edge of the platform | M1 | |
| $75g \times 0.9 = 25g \times x + 10g \times 1.1$ (3 term equation) | | |
| Two terms correct (unsimplified) | A1 | |
| Completely correct (unsimplified) | A1 | |
| Distance $MC = 3.16$ m | A1 | **4 marks total** |
> **NB:** If moments taken about other points, the force of the platform on the plank must be present at the edge of the platform for M1.
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1\\
\includegraphics[max width=\textwidth, alt={}, center]{835616aa-0b2b-4e8c-bbbf-60b72dc5ea3e-2_182_843_264_651}
A uniform rigid plank has mass 10 kg and length 4 m . The plank has 0.9 m of its length in contact with a horizontal platform. A man $M$ of mass 75 kg stands on the end of the plank which is in contact with the platform. A child $C$ of mass 25 kg walks on to the overhanging part of the plank (see diagram). Find the distance between the man and the child when the plank is on the point of tilting.
\hfill \mbox{\textit{CAIE M2 2004 Q1 [4]}}