Calculate the speed of a ball tied to a string of length 1.5 m making 4.6 revolutions every second.
Va = 4.6 rev/s * 6.28 rad/rev = 28.9 rad/s = Angular velocity.
C = pi*D = 3.14 * (2*1.5) = 9.42 m.
V = 4.6 rev/s * 9.42 m/rev = 43.4 m/s.
= Linear speed.
To calculate the speed of the ball, we can use the formula for the circumference of a circle, which is C = 2πr, where r is the radius of the circle. In this case, the radius is equal to the length of the string, which is 1.5 meters.
Now, let's calculate the distance traveled by the ball in one revolution. Since the circumference of a circle is equal to the distance traveled in one revolution, we can use the formula C = 2πr. Plugging in the values, we get:
C = 2π(1.5) = 3π ≈ 9.42 meters
Therefore, the distance traveled by the ball in one revolution is approximately 9.42 meters.
Next, we need to calculate the total distance traveled by the ball in one second. Given that the ball makes 4.6 revolutions every second, we can multiply the distance traveled in one revolution by the number of revolutions per second:
Total distance traveled in one second = 9.42 meters/rev × 4.6 rev/sec ≈ 43.32 meters/sec
Hence, the speed of the ball is approximately 43.32 meters per second.