A-LevelMathematicsMechanics9709/51 · Oct/Nov 2017 · Q37 Marks
One end of a light inextensible string of length 0.4 m is attached to a fixed point A which is above a smooth horizontal surface. A particle P of mass 0.6 kg is attached to the other end of the string. P moves in a circle on the surface with constant speed v m s⁻¹, with the string taut and making an angle of 60° with the horizontal (see diagram).
- (i)Given that v = 0.5, calculate the magnitude of the force that the surface exerts on P.[4]
- (ii)Find the greatest possible value of v for which P remains in contact with the surface.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [M1] Tsin60 + R = 0.6g Resolves vertically.
- [M1] Tcos60 = 0.6 × 0.5²/(0.4cos60) Uses Newton's Second Law horizontally.
- [A1] T = 1.5
- [A1] R = 4.7(0) N
- [M1] Tsin60 = 0.6g (leads to T = 6.9282...) Resolve vertically. Note R = 0.
- [M1] 6.9282...cos60 = 0.6 v² /(0.4cos60) Use Newton's second Law horizontally.
- [A1] v = 1.07 Greatest value.
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →