| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Session | Specimen |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Projectile motion after leaving circle |
| Difficulty | Standard +0.8 This is a multi-part Further Mechanics question combining circular motion with energy conservation and projectile motion. Part (i) requires energy conservation setup (standard but FM-level), part (ii) involves projectile motion from the lowest point (straightforward application), and part (iii) requires relating tension to angle using both energy and circular motion equations. While systematic, it demands fluency with multiple FM concepts and careful algebraic manipulation across several steps, placing it moderately above average difficulty. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (i) | 1 |
| Answer | Marks |
|---|---|
| v2 (cid:32)4g(cid:11)2cos(cid:84)(cid:16)1(cid:12) | M1 |
| Answer | Marks |
|---|---|
| [5] | 3.3 |
| Answer | Marks |
|---|---|
| 2.1 | Attempt at conservation of mechanical |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (ii) | When (cid:84)(cid:32)0 , v (cid:32)2 g |
| Answer | Marks |
|---|---|
| (cid:84)(cid:32)50.8 below the horizontal | B1 |
| Answer | Marks |
|---|---|
| [5] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | e |
| Answer | Marks |
|---|---|
| H | 6.260990… |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (iii) | p |
| Answer | Marks |
|---|---|
| (cid:84)(cid:32)33.6 | B1 |
| Answer | Marks |
|---|---|
| [5] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | May appear anywhere in answer |
| Answer | Marks |
|---|---|
| BC | N2L is Newton’s second law |
Question 4:
4 | (i) | 1
35g(cid:11)5(cid:12)(cid:16) (cid:11)35(cid:12)v2 (cid:32)...
2
...35g(cid:11)7(cid:16)4cos(cid:84)(cid:12)
v2 (cid:32)4g(cid:11)2cos(cid:84)(cid:16)1(cid:12) | M1
A1
A1
A1
E1
[5] | 3.3
1.1
1.1
1.1
2.1 | Attempt at conservation of mechanical
energy
PE term on lhs
KE term on rhs
n
www; AG must show an intermediate
step
4 | (ii) | When (cid:84)(cid:32)0 , v (cid:32)2 g
H
v 2 (cid:32)2g(3)
V
v(cid:32)9.90 so speed is 9.90ms-1
(cid:84)(cid:32)50.8 below the horizontal | B1
B1
M1
e
A1
A1
[5] | 3.3
3.3
3.4
i
c
1.1
1.1 | e
m
Use of either v2 (cid:32)v 2 (cid:14)v 2 or
V H
v
tan(cid:84)(cid:32) V
v
H | 6.260990…
9.8994949…
50.768479…
4 | (iii) | p
Tension when (cid:84)(cid:32)60 is 17.5gN
S
T (cid:16)35gcos(cid:84)(cid:32)35(cid:11)4g(cid:11)2cos(cid:84)(cid:16)1(cid:12)(cid:12)
4
(cid:84)(cid:32)33.6 | B1
*M1
A1
dep*
M1
A1
[5] | 1.1
3.1b
1.1
1.1a
1.1 | May appear anywhere in answer
Attempt to use N2L radially with
v2
a(cid:32)
r
Substituting 3(cid:117)their(T) into their
N2L attempt and solving for (cid:84)
BC | N2L is Newton’s second law
33.55730…4 A light inextensible taut rope, of length 4 m , is attached at one end $A$ to the centre of the horizontal ceiling of a gym. The other end of the rope $B$ is being held by a child of mass 35 kg . Initially the child is held at rest with the rope making an angle of $60 ^ { \circ }$ to the downward vertical and it may be assumed that the child can be modelled as a particle attached to the end of the rope. The child is released at a height 5 m above the horizontal ground.\\
(i) Show that the speed, $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, of the child when the rope makes an angle $\theta$ with the downward vertical is given by $v ^ { 2 } = 4 g ( 2 \cos \theta - 1 )$.\\
(ii) At the instant when $\theta = 0 ^ { \circ }$, the child lets go of the rope and moves freely under the influence of gravity only. Determine the speed and direction of the child at the moment that the child reaches the ground.\\
(iii) The child returns to the initial position and is released again from rest. Find the value of $\theta$ when the tension in the rope is three times greater than the tension in the rope at the instant the child is released.
\hfill \mbox{\textit{OCR Further Mechanics Q4 [15]}}