An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 1000 m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?
A) 0.25
B) 0.50
C) 1.00
D) 2.00
E) 4.00

Question

Quizplus · Accepted Answer

The centripetal acceleration is given by:

ac = v^2/r

where v is the speed of the plane, and r is the radius of the circle.

When the plane flies in the first circle, with a speed of 150 m/s and a radius of 500 m, its centripetal acceleration is:

ac1 = (150 m/s)^2 / 500 m = 45 m/s^2

When the plane flies in the second circle, with a speed of 300 m/s and the same radius of 500 m, its centripetal acceleration is:

ac2 = (300 m/s)^2 / 500 m = 180 m/s^2

The factor by which the centripetal acceleration changes is:

ac2/ac1 = 180 m/s^2 / 45 m/s^2 = 4

Therefore, the centripetal acceleration would increase by a factor of 4 if the plane were to fly in the same circle at a speed of 300 m/s instead of 150 m/s.

An Airplane Flies in a Horizontal Circle of Radius 500