Britney asked in Science & MathematicsPhysics · 7 months ago

# A 3-kg rock swings in a circle of radius 5 m. making one complete trip every 2 seconds. What is the centripetal acceleration of the rock?

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• oubaas
Lv 7
7 months ago

ω = 2PI/T = 2PI/2 = PI rad/sec

ac = ω^2*r = 3.1416^2*5 = 49.35 m/sec^2

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• 7 months ago

Centripetal acceleration = v^2 ÷ r

During the two seconds, the rock moves a distance of the circumference of a circle that has a radius.5 meters..

d = 2 * π * 5 = 10 * π meters

v = d ÷ t = 10 * π ÷ 2 = 5 * π

The speed of the rock is approximately 15.7 m/s.

Centripetal acceleration = 25 * π^2 ÷ 5 = 5 * π^2

This is approximately 49.3 m/s^2. I hope this is helpful for you.

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• 7 months ago

Centripetal acceleration is v²/r where v is velocity given by time taken to traverse the circumference in one rotation which is 2π*5 / 2 m/s = 5π² m/s.

So we substitute (5π)² /5 to get Centripetal acceleration is 5π² m/s²

Given that the mass of the rock is 3 kg, we may determine the force due to centripetal acceleration using the formula Force = mass x acceleration

F = ma, = 3*5π² = 148.0 m/s²

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• 7 months ago

The radius is 5 m, so the circumference is:

C = 2πr

C = 10π

The rock completes one revolution in 2 seconds, so its velocity is:

v = C / t

v = 10π / 2

v = 5π

We can now find the centripetal acceleration:

a = v² / r

a = (5π)² / 5

a = 5π²

a ≈ 49.3 m/s²

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