| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | SUVAT simultaneous equations: find u and a |
| Difficulty | Standard +0.3 This is a straightforward SUVAT problem requiring systematic application of s=ut+½at² at two time points to form simultaneous equations, followed by standard mechanics calculations for angle (using g sin θ = 4) and mass (using R = mg cos θ). All steps are routine M1 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.03f Weight: W=mg3.03i Normal reaction force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Single equation with one unknown from two equations | M1 | Candidates using \(s\) or \(x\) instead of \(d\) can be given marks BoD |
| \(2d = 120\) leading to \(d = 60\) | A0 | From their SE |
| \(2d = 120\) with no further work | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Value for mass assumed or wrong | M1A0 | Fortuitous |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Candidates using cos in (ii) and sin in (iii) | M1A0 | Fortuitously correct mass |
## Question 5(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Single equation with one unknown from two equations | M1 | Candidates using $s$ or $x$ instead of $d$ can be given marks BoD |
| $2d = 120$ leading to $d = 60$ | A0 | From their SE |
| $2d = 120$ with no further work | A1 | |
## Question 5(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Value for mass assumed or wrong | M1A0 | Fortuitous |
## Question 5(iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Candidates using cos in (ii) and sin in (iii) | M1A0 | Fortuitously correct mass |
---5 A particle $P$ is projected with speed $u \mathrm {~ms} ^ { - 1 }$ from the top of a smooth inclined plane of length $2 d$ metres. After its projection $P$ moves downwards along a line of greatest slope with acceleration $4 \mathrm {~ms} ^ { - 2 }$. At the instant 3 s after projection $P$ has moved half way down the plane. $P$ reaches the foot of the plane 5 s after the instant of projection.\\
(i) Form two simultaneous equations in $u$ and $d$, and hence calculate the speed of projection of $P$ and the length of the plane.\\
(ii) Find the inclination of the plane to the horizontal.\\
(iii) Given that the contact force exerted on $P$ by the plane has magnitude 6 N , calculate the mass of $P$.
\hfill \mbox{\textit{OCR M1 2013 Q5 [10]}}