A particle of mass 0.8kg lies on a rough plane which is inclined at an angle of 28° to the horizontal. The particle is kept in equilibrium by a force of magnitude TN. This force acts at an angle of 35° above a line of greatest slope of the plane (see diagram). The coefficient of friction between the particle and the plane is 0.2 . Find the least and greatest possible values of T.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [M1] 3 relevant terms; allow sign errors; allow sin/cos mix; allow g missing; m = 0.8 must be used; correct angles must be used.
2. [A1]
3. [M1] 3 relevant terms; allow sign errors; allow sin/cos mix; allow g missing; m = 0.8 must be used; correct angles must be used.
4. [A1] May use their F.
5. [A1] May use their F.
6. [DM1] Dependent on previous 2 M marks. May be implied by correct T value. Allow g missing. If resolved equations incorrect and no working seen, then this mark is implied by the correct T value for their equations.
7. [A1] 5.534499898 AWRT 5.53 from correct work. Allow 5.54 from correct work.
8. [A1] 3.326141531 AWRT 3.33 from correct work. Allow 3.32 from correct work.