Question

A 0.100 kg mass is attached to a string 0.75m long and swings in a horizontal circle,

revolving once every 0.80 s.
Calculate:
the centripetal acceleration of the mass.

Answer 1

The centripetal acceleration of the mass is 46.14 m/s², calculated using the formula ac = v² / r, where v is the linear velocity of the mass swinging in the horizontal circle.

Step-by-step explanation:

The question involves calculating the centripetal acceleration of a mass swinging in a horizontal circle. To find the centripetal acceleration (ac), we use the formula: ac = v² / r, where v is the linear speed and r is the radius of the circle. The linear speed can be found by first determining the circumference of the circle (C = 2πr) and then using the period of revolution (T), which gives us v = C / T. Given the radius (r) as 0.75 m and the period (T) as 0.80 s, we have:

C = 2π(0.75 m) = 4.71 m

v = 4.71 m / 0.80 s = 5.89 m/s

Substituting these values into the centripetal acceleration formula:

ac = (5.89 m/s)² / 0.75 m = 46.14 m/s²

Hence, the centripetal acceleration is 46.14 m/s².