OCR M2 2006 June — Question 2 5 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2006
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeVertical drop and bounce
DifficultyModerate -0.8 This is a straightforward application of impulse-momentum theorem with standard kinematics. Students need to find velocities before and after impact using v² = u² + 2as (routine), then calculate impulse as change in momentum. It's a standard M2 textbook exercise requiring only direct application of well-practiced formulas with no problem-solving insight or geometric complexity.
Spec6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form
2 A small sphere of mass 0.3 kg is dropped from rest at a height of 2 m above horizontal ground. It falls vertically, hits the ground and rebounds vertically upwards, coming to instantaneous rest at a height of 1.4 m above the ground. Ignoring air resistance, calculate the magnitude of the impulse which the ground exerts on the sphere when it rebounds.
Question 2:
AnswerMarks Guidance
WorkingMark Guidance
\(v^2 = 2gh\)M1 kinematics or energy
\(u = \sqrt{4g}\) or \(\sqrt{39.2}\) or \(6.26\)A1 speed of impact \((\pm)\)
\(v = \sqrt{2.8g}\) or \(\sqrt{27.44}\) \((5.24)\)A1 speed of rebound \((\pm)\)
\(I = \mathbf{?}\ 0.3(6.26 + 5.24)\)M1 must be sum of magnitudes of velocities
\(3.45\) NsA1\(\checkmark\) 5 marks total; \(\checkmark\) must be positive 
# Question 2:

| Working | Mark | Guidance |
|---------|------|----------|
| $v^2 = 2gh$ | M1 | kinematics or energy |
| $u = \sqrt{4g}$ or $\sqrt{39.2}$ or $6.26$ | A1 | speed of impact $(\pm)$ |
| $v = \sqrt{2.8g}$ or $\sqrt{27.44}$ $(5.24)$ | A1 | speed of rebound $(\pm)$ |
| $I = \mathbf{?}\ 0.3(6.26 + 5.24)$ | M1 | must be sum of magnitudes of velocities |
| $3.45$ Ns | A1$\checkmark$ | 5 marks total; $\checkmark$ must be positive |

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2 A small sphere of mass 0.3 kg is dropped from rest at a height of 2 m above horizontal ground. It falls vertically, hits the ground and rebounds vertically upwards, coming to instantaneous rest at a height of 1.4 m above the ground. Ignoring air resistance, calculate the magnitude of the impulse which the ground exerts on the sphere when it rebounds.

\hfill \mbox{\textit{OCR M2 2006 Q2 [5]}}
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