A machine for driving a nail into a block of wood causes a hammerhead to drop vertically onto the top of a nail. The mass of the hammerhead is 1.2kg and the mass of the nail is 0.004kg (see diagram). The hammerhead hits the nail with speed vms⁻¹ and remains in contact with the nail after the impact. The combined hammerhead and nail move immediately after the impact with speed 40ms⁻¹.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] Attempt at conservation of momentum [1.2v = (1.2 + 0.004) × 40]
2. [A1] v = 602/15 oe
3. [M1] Use of a 'suvat' method to get an equation in a. Allow sign errors. Allow ±20000. Do not allow 4 in place of 0.04. Allow use of 40.1 or 602/15 for velocity in place of 40. (e.g., 0² = (40)²+2×0.04×a [a=-20000] or 0.04 = (0+40)/2 -t gets t = 0.002, so 0=40+0.002a[a=-20000])
4. [M1] Attempt to use Newton's Second Law vertically. Must have the correct number of relevant terms. Allow sign errors, but terms including masses must be effectively added. Do not allow any mass other than (1.2 + 0.004). (e.g., [-R+(1.2+0.004)g=(1.2+0.004)×a] [-R+12.04=1.204a])
5. [A1] R = 24 100 N [24 092.04 = 602301/25] WWW. Note: use of wrong sign for g leads to answers 24 067.96 which gets max M1M1A0. Note: Missing weight term gets 24 080 which gets Max M1M0A0.
6. [B1] [Alternative method using energy for Question 2(b)] [Change in PE =] 1.204g×0.04[=0.4816] or [change in KE =] (1/2)×1.204×(40)² [=963.2]
7. [M1] Attempt at work energy equation. Must have correct number of relevant terms. dimensionally correct; allow sign errors. Do not allow 4 in place of 0.04. Allow use of 40.1 or 602/15 for velocity in place of 40. (e.g., 1.204g×0.04+ (1/2)×1.204×(40)² = 0.04R)
8. [A1] R = 24 100 N [24 092.04 = 602301/25] WWW Note: use of wrong sign for g leads to answers 24 067.96 which gets max B1M1A0. Note: Missing potential energy term gets 24 080, which gets maximum of B1M0A0.