QCE Physics Paper 2 free practice questions with answers

Question 1 (5 marks) [Gravitation and orbits]

A 1700 kg lander is on the surface of Mars (mass 6.42 × 10²³ kg, radius 3.39 × 10⁶ m).

(a) What is the escape speed from the surface?

(a) Answer: 5030 m s−¹

• To escape, kinetic energy must equal the magnitude of gravitational potential energy: ½mv² = GMm/R.
• v = √(2GM/R) = √(2 × 6.67 × 10−¹¹ × 6.42 × 10²³ ÷ 3.39 × 10⁶) = 5030 m s−¹

(b) How much energy must be supplied to the lander to escape from the surface?

(b) Answer: 2.15 × 10¹0 J

• Escape energy = |E_p| at the surface = GMm/R.
• E = 6.67 × 10−¹¹ × 6.42 × 10²³ × 1700 ÷ 3.39 × 10⁶ = 2.15 × 10¹0 J

Gravitational potential energy is −GMm/r. To escape, the lander needs kinetic energy equal to GMm/R, giving v_esc = √(2GM/R).