Calculate the period of a ball tied to a string
of length 1.7 m making 3.6 revolutions every
second.
Answer in units of s
Calculate the speed of the ball.
Answer in units of m/
Why did the ball bring a calculator to its physics class? Because it wanted to calculate its period and speed!
To calculate the period of the ball, we can use the formula T = 1/f, where T represents the period and f represents the frequency. Since the ball is making 3.6 revolutions every second, the frequency is 3.6 Hz. Therefore, the period is T = 1/3.6 = 0.2778 seconds.
Now, let's move on to the speed of the ball. We can use the formula v = (2πr/T), where v represents the speed, r represents the radius (which is the length of the string), and T represents the period.
Since the length of the string is 1.7 meters, the radius (r) of the circular path the ball takes is also 1.7 meters. Plugging the values into the formula, we get v = (2π(1.7))/0.2778 = 38.656 m/s.
So, the period of the ball is approximately 0.2778 seconds, and the speed of the ball is approximately 38.656 m/s.
To calculate the period of the ball, we can use the formula:
Period (T) = 1 / Frequency (f)
Given that the ball makes 3.6 revolutions every second, the frequency is 3.6 Hz.
Therefore, the period of the ball is:
T = 1 / 3.6 Hz
T ≈ 0.2778 s
The period of the ball is approximately 0.2778 seconds.
To calculate the speed of the ball, we can use the formula:
Speed (v) = (2 * π * radius) / Period (T)
The length of the string is given as 1.7 m. Since the ball is tied to the string, the radius of the circular motion is equal to the length of the string. So, the radius is also 1.7 m.
Using the period value calculated earlier, we can find the speed of the ball:
v = (2 * π * 1.7 m) / 0.2778 s
v ≈ 32.49 m/s
The speed of the ball is approximately 32.49 m/s.
To calculate the period of a ball tied to a string, we can use the formula:
Period (T) = 1 / Frequency (f)
Given that the ball makes 3.6 revolutions every second, the frequency is 3.6 Hz (revolutions per second). Therefore, the period can be calculated as:
T = 1 / 3.6 = 0.2778 s
So, the period of the ball is 0.2778 s.
To calculate the speed of the ball, we need to know the formula for speed. In this case, the speed can be calculated using the formula:
Speed (v) = 2πr / T
where r is the radius (string length) and T is the period of the ball.
Given that the length of the string is 1.7 m, the radius will be half of the length, which is 0.85 m. Substituting these values into the formula, we get:
v = 2π * 0.85 / 0.2778 ≈ 19.194 m/s
So, the speed of the ball is approximately 19.194 m/s.
period = 1/frequency = 1/3.6 = 0.2777 s
circumference = 2pi*r = 10.7m
speed = distance/time (or, distance * frequency) = 10.7*3.6 = 38.5m/s