The diagram shows the vertical cross-section XYZ of a rough slide. The section YZ is a straight line of length 2 m inclined at an angle of α to the horizontal, where sin α = 0.28. The section YZ is tangential to the curved section XY at Y, and X is 1.8 m above the level of Y. A child of mass 25 kg slides down the slide, starting from rest at X. The work done by the child against the resistance force in moving from X to Y is 50J.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] PE lost = mgh = 25g×1.8[=450].
2. [M1] For work energy equation. Must have correct number of terms. Allow sign errors. Dimensionally correct. Must use 25, not m. Candidates who try to use constant acceleration can only score B1.
3. [A1] 25g×1.8 - 50 = (1/2)×25v². OE. Must be correct.
4. [A1] v = 4√2 [ms⁻¹] or 5.66 [5.6568...]. Allow √32.
5. [B1FT] PE gained/lost = ±25g×2×0.28[=±140] or KE gained/lost = ±(1/2)×25(their 4√2)². [KE = ± 400]. For either. FT from their v for KE. Must have a substituted for PE. Allow 25g×2sin16.26° or 25g×2sin16.3°.
6. [*M1] For work energy equation. Must have correct number of terms. Allow sign errors. Dimensionally correct. Allow sin/cos mix. Do not allow with WD instead of F×2. Must have substituted a and v.
7. [A1FT] F×2 = 25g×2×0.28 + (1/2)×25(4√2)². [⇒ F = 270]. FT their v² or v.
8. [B1] R = 25g×0.96 [= 240]. Allow 25gcos16.26° or 25gcos16.3°.
9. [DM1] Use of F = µR to form an equation in µ only. Must be from 3 term F, dimensionally correct and single term R. Allow sin/cos mix but must be different components of weight. F and R must be numerical expressions.
10. [A1] µ = 9/8. CAO. Allow 1 1/8, but no other answer.