| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string with compression (spring) |
| Difficulty | Standard +0.8 This is a Further Mechanics energy conservation problem requiring careful setup of elastic potential energy with Hooke's law (modulus λ), gravitational PE, and initial KE. The algebra to reach the given quadratic is non-trivial, requiring correct handling of the compression distance and natural length. While methodical, it demands more sophistication than standard A-level mechanics and involves multiple energy terms with potential for sign errors. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) | 1 10800x2 |
| Answer | Marks |
|---|---|
| 300x2(cid:16)49x(cid:16)255(cid:32)0 | M1 |
| Answer | Marks |
|---|---|
| [5] | 3.3 |
| Answer | Marks |
|---|---|
| 2.1 | Attempt at conservation of energy |
| Answer | Marks |
|---|---|
| step | GPE is Gravitational Potential |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (ii) | x(cid:32)(cid:16)0.8438977...(cid:31)0 so not valid |
| x(cid:32)1.01 | B1 |
| Answer | Marks |
|---|---|
| [2] | 2.3 |
| 3.4 | e |
| Answer | Marks | Guidance |
|---|---|---|
| and not given as a final answer | 1.007231… | |
| 2 | (iii) | e.g. g (cid:32)9.8 is not precise enough, use g(cid:32)9.81 |
| Answer | Marks |
|---|---|
| multiple springs | E1 |
| Answer | Marks |
|---|---|
| [2] | i3.5b |
| c3.5c | m |
Question 2:
2 | (i) | 1 10800x2
75g(6.2)(cid:14) (cid:11)75(cid:12)(2)2 (cid:32)75g(1.2(cid:16)x)(cid:14)
2 2(1.2)
300x2(cid:16)49x(cid:16)255(cid:32)0 | M1
A1
A1
A1
E1
[5] | 3.3
1.1
1.1
1.1
2.1 | Attempt at conservation of energy
GPE term(s)
KE term
EPE term
www; AnG must show intermediate
step | GPE is Gravitational Potential
Energy
KE is Kinetic Energy
EPE is Elastic Potential Energy
2 | (ii) | x(cid:32)(cid:16)0.8438977...(cid:31)0 so not valid
x(cid:32)1.01 | B1
B1
[2] | 2.3
3.4 | e
The negative value of x must be seen
and not given as a final answer | 1.007231…
2 | (iii) | e.g. g (cid:32)9.8 is not precise enough, use g(cid:32)9.81
e.g. the army recruit is not a particle, model as a
rigid body
e.g. the mat is not a single spring, model as
multiple springs | E1
E1
e
[2] | i3.5b
c3.5c | m
For one assumption and a sensible
refinement2 As part of a training exercise an army recruit of mass 75 kg falls a vertical distance of 5 m before landing on a mat of thickness 1.2 m . The army recruit sinks a distance of $x \mathrm {~m}$ into the mat before instantaneously coming to rest. The mat can be modelled as a spring of natural length 1.2 m and modulus of elasticity 10800 N and the army recruit can be modelled as a particle falling vertically with an initial speed of $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Show that $x$ satisfies the equation $300 x ^ { 2 } - 49 x - 255 = 0$.\\
(ii) Calculate the value of $x$.\\
(iii) Ignoring the possible effect of air resistance, make
\begin{itemize}
\item one comment on the assumptions made and,
\item suggest a possible refinement to the model.
\end{itemize}
\hfill \mbox{\textit{OCR Further Mechanics Q2 [9]}}