Question

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the speed remained the same, by what factor would its centripetal acceleration change?

Answer 1

The centripetal acceleration changed by a factor of 0.5

Step-by-step explanation:

Given;

first radius of the horizontal circle, r₁ = 500 m

speed of the airplane, v = 150 m/s

second radius of the airplane, r₂ = 1000 m

Centripetal acceleration is given as;

`a = (v^2)/(r)`

At constant speed, we will have;

`v^2 =ar\\\\v = √(ar)\\\\at \ constant\ v;\\√(a_1r_1) = √(a_2r_2)\\\\a_1r_1 = a_2r_2\\\\a_2 = (a_1r_1)/(r_2) \\\\a_2 = (a_1*500)/(1000)\\\\a_2 = (a_1)/(2) \\\\a_2 = (1)/(2) a_1`

a₂ = 0.5a₁

Therefore, the centripetal acceleration changed by a factor of 0.5