OCR M3 2007 January — Question 1 6 marks

Exam BoardOCR
ModuleM3 (Mechanics 3)
Year2007
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 2
TypeVertical circle: tension at specific point
DifficultyStandard +0.3 This is a standard vertical circle problem requiring energy conservation to find speed at the top, then applying Newton's second law with centripetal force. The calculation is straightforward with given values, though it requires careful handling of the energy equation and force balance—slightly above average due to the multi-step nature but still a textbook exercise.
Spec6.02i Conservation of energy: mechanical energy principle6.05e Radial/tangential acceleration

1 A particle \(P\) of mass 0.6 kg is attached to a fixed point \(O\) by a light inextensible string of length 0.4 m . While hanging at a distance 0.4 m vertically below \(O , P\) is projected horizontally with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and moves in a complete vertical circle. Calculate the tension in the string when \(P\) is vertically above \(O\).

Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(\frac{1}{2}(0.6)5^2 - \frac{1}{2}(0.6)v^2 = 0.6g(2\times0.4)\) \([v^2 = 9.32]\)M1, A1 For using the principle of conservation of energy
\([T + 0.6g = 0.6a]\)M1 For using Newton's second law
\([a = 9.32/0.4]\)M1 For using \(a = v^2/r\)
\(T + 0.6g = 0.6 \times 9.32/0.4\)A1ft ft incorrect energy equation
Tension is \(8.1\text{N}\)A1 Total: 6
# Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{1}{2}(0.6)5^2 - \frac{1}{2}(0.6)v^2 = 0.6g(2\times0.4)$ $[v^2 = 9.32]$ | M1, A1 | For using the principle of conservation of energy |
| $[T + 0.6g = 0.6a]$ | M1 | For using Newton's second law |
| $[a = 9.32/0.4]$ | M1 | For using $a = v^2/r$ |
| $T + 0.6g = 0.6 \times 9.32/0.4$ | A1ft | ft incorrect energy equation |
| Tension is $8.1\text{N}$ | A1 | **Total: 6** |

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1 A particle $P$ of mass 0.6 kg is attached to a fixed point $O$ by a light inextensible string of length 0.4 m . While hanging at a distance 0.4 m vertically below $O , P$ is projected horizontally with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and moves in a complete vertical circle. Calculate the tension in the string when $P$ is vertically above $O$.

\hfill \mbox{\textit{OCR M3 2007 Q1 [6]}}