Work done against resistance - penetration into material

An object (ball, pebble, stone) hits a soft surface (ground, sand, liquid) and continues moving through it; the resistance force or work done against it during penetration is found using energy methods.

3 questions · Moderate -0.1

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Edexcel M2 2017 January Q6
5 marks Standard +0.3
6. A ball of mass 0.6 kg is projected vertically upwards with speed \(22.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point which is 1.5 m above horizontal ground. The ball moves freely under gravity until it reaches the ground. The ground is soft and the ball sinks 2.5 cm into the ground before coming to rest. The ball is modelled as a particle and the ground is assumed to exert a constant resistive force of magnitude \(R\) newtons on the ball. Using the work-energy principle, find, to 3 significant figures, the value of \(R\).
(5)
OCR MEI Paper 1 2024 June Q9
7 marks Moderate -0.3
9 A child throws a pebble of mass 40 g vertically downwards with a speed of \(6 \mathrm {~ms} ^ { - 1 }\) from a point 0.8 m above a sandy beach.
  1. Calculate the speed at which the pebble hits the beach. The pebble travels 3 cm through the sand before coming to rest.
  2. Find the magnitude of the resistance force of the sand on the pebble, assuming it is constant. Give your answer correct to \(\mathbf { 3 }\) significant figures.
Edexcel M2 Q1
7 marks Moderate -0.3
  1. A bullet of mass 25 g is fired directly at a fixed wooden block of thickness 4 cm and passes through it. When the bullet hits the block, it is travelling horizontally at \(200 \mathrm {~ms} ^ { - 1 }\). The block exerts a constant resistive force of 8000 N on the bullet.
    1. Find the work done by the block on the bullet.
    By using the Work-Energy principle,
  2. show that the bullet emerges from the block with speed \(120 \mathrm {~ms} ^ { - 1 }\).