Question

An apparatus is designed to study insects at an acceleration of magnitude 934 m/s2. The apparatus consists of a 1.70-m rod with insect containers at either end. The rod rotates about an axis perpendicular to the rod and at its center. where L = 1.70 m. How fast does an insect move when it experiences a radial acceleration of 934 m/s2?

Answer 1

The radial acceleration (centripetal acceleration) of an object moving in a circle of radius "r" at a constant speed "v" is given by the formula:

a = v² / r

In this case, the rod is rotating about an axis at its center, so the radius "r" is half of the length of the rod: r = L / 2.

Given the radial acceleration "a" as 934 m/s² and the length of the rod "L" as 1.70 m, we can rearrange the formula to solve for the speed "v":

v = √(a * r)

Substitute the values:

v = √(934 m/s² * (1.70 m / 2))

Calculate the value inside the square root:

v = √(934 m²/s² * 0.85 m)

v = √793.9 m²/s²

v ≈ 28.2 m/s

The insect moves at a speed of approximately 28.2 meters per second when it experiences a radial acceleration of 934 m/s².