Edexcel M3 — Question 1 7 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicWork done and energy
TypeParticle on smooth curved surface
DifficultyStandard +0.8 This M3 energy conservation problem requires setting up and solving a quadratic equation involving elastic potential energy, gravitational potential energy, and kinetic energy across multiple positions. While the physics concepts are standard A-level, the multi-step calculation with careful tracking of datum points and solving the resulting equation elevates it slightly above average difficulty.
Spec6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle
A light spring, of natural length 30 cm, is fixed in a vertical position. When a small ball of mass 0.4 kg rests on top of it, the spring is compressed by 10 cm. The ball is then held at a height of 15 cm vertically above the top of the spring and released from rest. Calculate the maximum compression of the string in the resulting motion. [7 marks]
AnswerMarks
\(\frac{\lambda}{0.3} \times 0.1 = 0.4 \times 9.8\)M1 A1
\(\lambda = 11.76 \text{ N}\)M1 A1 A1
Energy: \(0.4 \times 9.8 \times (0.15 + x) = \frac{11.76}{2 \times 0.3}x^2\)M1 A1 A1
\(0.06 + 0.4x = 2x^2\)
\(10x^2 - 20x - 3 = 0\)M1 A1
\((10x + 1)(10x - 3) = 0\)
\(x = 0.3 \text{ m}\)M1 A1
Total: 7 marks
$\frac{\lambda}{0.3} \times 0.1 = 0.4 \times 9.8$ | M1 A1 | 

$\lambda = 11.76 \text{ N}$ | M1 A1 A1 |

Energy: $0.4 \times 9.8 \times (0.15 + x) = \frac{11.76}{2 \times 0.3}x^2$ | M1 A1 A1 |

$0.06 + 0.4x = 2x^2$ |  |

$10x^2 - 20x - 3 = 0$ | M1 A1 |

$(10x + 1)(10x - 3) = 0$ |  |

$x = 0.3 \text{ m}$ | M1 A1 |

**Total: 7 marks**
A light spring, of natural length 30 cm, is fixed in a vertical position. When a small ball of mass 0.4 kg rests on top of it, the spring is compressed by 10 cm. The ball is then held at a height of 15 cm vertically above the top of the spring and released from rest.

Calculate the maximum compression of the string in the resulting motion. [7 marks]

\hfill \mbox{\textit{Edexcel M3  Q1 [7]}}
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