A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. Class 9
A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. Class 9
Question 1.
A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. The height of the tree is 10 m. On impact, the coconut comes to rest by making a depression in the sand. Class 9
(i) Calculate the velocity of the coconut just before it hits the sand.
(ii) Assume that the average resistive force of sand is 3000 N and all of the coconut’s energy is used to create the depression in the sand. Calculate the depth of the depression the coconut makes in the sand. Assume g = 10 m s-2.
Answer:
(i) Using conservation of energy (PE at top = KE just before impact): mgh = 1/2mv² → v² = 2gh = 2 × 10 × 10 = 200 m² s-2v = [latex]\sqrt {200}[/latex] = 10 [latex]\sqrt {2}[/latex] ≈ 14.14 m s-1
(ii) KE just before impact = 1/2 mv² = 1/2 × 1.5 × 200 = 150 J. All this energy is used against the resistive force of sand to create depression of depth d: Work done against sand = Force × depth = 3000 × d = 150 Jd 150/3000 = 0.05 m = 5 cm