Final answer:
The period of the ball’s motion is 0.5 seconds. The frequency is 2 Hertz. The tension in the string, which acts as the centripetal force, is calculated at 2.367 Newtons.
Step-by-step explanation:
To calculate the period, frequency, tangential speed, centripetal acceleration, and tension of the ball attached to a string, we'll go through each step one by one.
1) Period (T)
The period is the time it takes for one complete revolution. Since the ball makes 30 revolutions in 15 seconds:
T = total time / number of revolutions = 15s / 30 = 0.5s
2) Frequency (f)
Frequency is the number of revolutions per second, which is the inverse of the period.
f = 1 / T = 1 / 0.5s = 2 Hz
3) Tangential Speed (v)
The tangential speed is the linear speed of the ball along its circular path.
v = 2πr / T = 2π * 3m / 0.5s = 37.70 m/s
4) Centripetal Acceleration (ac)
Centripetal acceleration can be defined as the speed that is directed toward the center of the circular path.
ac = v² / r = (37.70 m/s)² / 3m = 473.4 m/s²
5) Tension in the String (T)
The tension is defined as the centripetal force needed to keep the ball moving in a circle.
T = m * ac = 0.005 kg * 473.4 m/s2 = 2.367 N
Following are the answers for each part of the question:
a) Period: 0.5s, frequency 2 Hertz, tangential speed 37.70 m/s, centripetal acceleration 473.4 m/s², tension 2.367 N.
b) The period is 0.5 seconds,
c) The frequency is 2 Hertz,
d) The tension in the string is 2.367 Newtons.