Question

An elephant is located on Earth’s surface at a latitude λ. Calculate the centripetal acceleration of the elephant resulting from the rotation of Earth around its polar axis. Express your answer in terms of λ, the radius RE of Earth, and time T for one rotation of Earth. Compare your answer with g for λ=40°.

a) 0 m/s²
b) g/2
c) g
d) 3g/2

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Answer 1

To calculate the centripetal acceleration of an elephant on Earth at a latitude λ, use the formula a_c = ω^2 × r, with ω being the angular velocity and r the distance from the axis of rotation, adjusted for latitude. At λ = 40°, compare this with the acceleration due to gravity, g. Option c is the correct answer.

Step-by-step explanation:

The question involves calculating the centripetal acceleration of an elephant standing on the Earth's surface at a given latitude λ due to Earth's rotation about its polar axis. To solve for this, we can use the formula for centripetal acceleration: a_c = ω^2 × r, where ω is the angular velocity and r is the radius of the circular motion.

Since Earth makes one rotation every T seconds, its angular velocity is ω = 2π/T. The radius r is the distance from the axis of rotation, which at a latitude λ is r = R_E × cos(λ). So, the centripetal acceleration formula for our scenario becomes:

a_c = (2π/T)^2 × R_E × cos(λ)

At latitude λ = 40°, we can compare the calculated centripetal acceleration with the acceleration due to gravity, g. The exact answer can be computed using the given values for T, R_E, and g.