Question

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.

1. Calculate the velocity of the coconut just before it hits the sand.
2. 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 1

Given,

Mass (m) = 1.5 kg

Height of tree (h) = 10 m

Acceleration due to gravity (g) = 10 m s^–2

(i) The coconut's potential energy at the top is transformed into kinetic energy right before it touches the sand.

Using v² = u² + 2gh, with u = 0,

v² = 0 + 2 × 10 × 10 = 200

`v = sqrt(200) = 10sqrt2 ≈ 14.14  "m s"^-1`

Hence, the velocity of the coconut just before it hits the sand is about 14.14 m s^–1.

(ii) The coconut's energy right prior to impact is equal to its kinetic energy and potential energy lost.

Energy = mgh = 1.5 × 10 × 10 = 150 J

The depression is made by using this energy to work against the sand's resistive force.

Resistive force × depth of depression = work done against the resistive force.

Let d be the depression's depth.

3000 × d = 150

`d = 150/3000 = 0.05` m

Hence, the depth of the depression made by the coconut in the sand is 0.05 m (i.e., 5 cm).