Question

A 200 – g object is tied to the end of a cord and it is turning in horizontal circle of radius 1.20 Cm at the constant 3 rev/sec. Calculate the centripetal acceleration of the object.

Answer 1

To calculate the centripetal acceleration of the object, first find the linear velocity and then apply the centripetal acceleration formula. The centripetal acceleration of the object is approximately 4.26 m/s².

Step-by-step explanation:

The question involves calculating the centripetal acceleration of an object moving in a horizontal circle with a known radius and rotational speed. To find the centripetal acceleration, we can use the formula ac = v2 / r, where v is the linear velocity and r is the radius of the circle.

First, convert revolutions per second to linear velocity using: v = 2 π r f, where f is the frequency in revolutions per second. In this case, f is 3 rev/sec and r is 1.20 cm which is 0.012 m.

The linear velocity v is 2 π × 0.012 m × 3 rev/sec, which equals approximately 0.22619 m/s. Substituting v and r into the centripetal acceleration formula gives: ac = (0.22619 m/s)2 / 0.012 m, which equals approximately 4.26 m/s2.

Answer 2

At angular speed of 3 rev/s, the object moves a distance equal to 3 times the circumference of the circle each second, or a distance of 3 • 2π (1.20 cm) ≈ 22.6 cm.

So, with a linear speed of 22.6 cm/s = 0.226 m/s, the object has a centripetal acceleration a of

a = (0.226 m/s)² / (0.012 m) ≈ 18.8 m/s²

directed toward the center of the circle.