| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2019 |
| Session | Specimen |
| Marks | 4 |
| Topic | Work done and energy |
| Type | Motion on rough inclined plane |
| Difficulty | Moderate -0.5 This is a straightforward energy conservation problem requiring a single application of the work-energy principle. Students must equate initial energy plus work done by gravity to final energy plus work done against friction, then solve for F. While it involves multiple energy terms, the setup is standard and the algebra is simple, making it slightly easier than average. |
| Spec | 6.02a Work done: concept and definition6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle |
**Question 7**
$\frac{1}{2} \times 20 \times 2^2 + 20 \times 8 \times 10$ [M1]
$= \frac{1}{2} \times 20 \times 6^2 + F \times 16$ All signs correct for A1 [M1A1]
Solve to get $F = 80$ [A1]
**Total: 4 marks**7 A child of mass 20 kg slides down a rough slope of length 16 m against a constant frictional force $F \mathrm {~N}$. Starting with an initial speed of $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at a point 8 m above the ground, she reaches the ground with a speed of $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find the value of $F$.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2019 Q7 [4]}}