Daily Exam Challenge: Physics (Higher)
Mark Scheme — 21 marks total
Higher TierMarking Instructions
- • Accept equivalent answers unless the mark scheme states otherwise.
- • M marks are for method — award even if the final answer is wrong.
- • A marks are for accuracy — only award if the method mark has been earned.
- • B marks are independent and can be awarded without other marks.
- • Where a range of answers is acceptable, this is indicated in the mark scheme.
A student investigates how the extension of a spring varies with the force applied. The spring constant is 50 N/m. The elastic limit is reached at a force of 8 N. (a) Calculate the extension at the elastic limit. (b) Calculate the elastic potential energy stored at the elastic limit. (c) The spring is used to launch a 0.02 kg ball vertically. Calculate the maximum height the ball could reach, assuming all stored energy is transferred to gravitational potential energy.
Acceptable Answer
(a) F = ke → e = F/k = 8/50 = 0.16 m (b) Ee = ½ke² = ½ × 50 × 0.16² = ½ × 50 × 0.0256 = 0.64 J (c) Ee = GPE → 0.64 = mgh → h = 0.64/(0.02 × 10) = 0.64/0.2 = 3.2 m
A transformer has 200 turns on the primary coil and 50 turns on the secondary coil. The input voltage is 240V and the current in the primary coil is 0.5A. (a) Calculate the output voltage. (b) Assuming the transformer is 100% efficient, calculate the current in the secondary coil. (c) In practice, transformers are not 100% efficient. Explain two reasons why energy is lost in a real transformer.
Acceptable Answer
(a) Vp/Vs = Np/Ns → 240/Vs = 200/50 → Vs = 240 × 50/200 = 60V (b) VpIp = VsIs (100% efficient) → 240 × 0.5 = 60 × Is → Is = 120/60 = 2A (c) 1) Resistance in the coils — current flowing through the wire causes heating (I²R losses), wasting energy as thermal energy. 2) Eddy currents induced in the iron core — these circulating currents cause heating. This is minimised by using a laminated core.
A 1500 kg car travelling at 20 m/s collides with a stationary 1000 kg car. After the collision, they move together. (a) Calculate the velocity after the collision. (b) Show that kinetic energy is not conserved and calculate the energy lost. (c) Explain what has happened to the lost kinetic energy.
Acceptable Answer
(a) Conservation of momentum: 1500 × 20 + 0 = 2500 × v → v = 30000/2500 = 12 m/s (b) KE before = ½ × 1500 × 20² = 300,000 J. KE after = ½ × 2500 × 12² = 180,000 J. Energy lost = 120,000 J. KE is not conserved (inelastic collision). (c) The lost kinetic energy has been transferred to: thermal energy (heating of the cars and surroundings due to deformation), sound energy (noise of the collision), and deformation of the car bodies (work done in crumpling metal).