OCR 2023 GCE FURTHER MATHEMATICS B MEI Y431/01: MECHANICS MINOR A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

(a) State the dimensions of the following quantities. • Force • Velocity • Density [3] A student investigating the drag force F experienced by an object moving through air conjectures the formula 1 F = ku2^tm 2h3 , where • k is a dimensionless constant • u is the air velocity relative to the moving object • t is the air density • m is the mass of the object. (b) Show that the student’s formula is dimensionally consistent. [2] The student carries out experiments in an airflow tunnel. When the air density is doubled, the drag force is found to double as well, with all other conditions remaining the same. (c) Show that the student’s formula is inconsistent with the experimental observation. [1] The student’s teacher suggests revising the formula as F = kt a u bA c where m has been replaced by A, the cross-sectional area of the object. The constant k is still dimensionless. (d) Use dimensional analysis to determine the values of a, b and c. [3] 3 © OCR 2023 Y431/01 Jun23 Turn over 3 2 A car of mass 1400 kg, travels along a straight horizontal road AB, after which it descends a hill BC inclined at a constant angle of 7° to the horizontal (see diagram). A, B and C all lie in the same vertical plane. Throughout the entire journ