Case study·Hard exam skill (4/5)·No calculator

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A 1 kg1\text{ kg} block is pressed against a horizontal spring of force constant 400 N m1400\text{ N m}^{-1}, compressing it by 0.20 m0.20\text{ m}. When released, the block crosses a rough horizontal strip of length 1.0 m1.0\text{ m} where friction is 4 N4\text{ N}, and then climbs a smooth ramp. Take g=10 m s2g=10\text{ m s}^{-2}.
Total: 5 marks

(a) Find the initial elastic potential energy stored in the spring. (1 mark)

(b) Find the speed of the block just after the spring returns to its natural length. (1 mark)

(c) Find the work done by friction on the rough strip. (1 mark)

(d) Find the kinetic energy of the block at the foot of the ramp. (1 mark)

(e) Find the maximum vertical height reached on the smooth ramp. (1 mark)

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