Answer:
approximately 1.007 * 10^8 m/s^2
Step-by-step explanation:
To find the ball's centripetal acceleration, we can use the formula a = v^2 / r, where a is the centripetal acceleration, v is the tangential velocity of the ball (the speed at which it moves around the circle), and r is the radius of the circle (the length of the piece of string).
First, we need to find the tangential velocity of the ball. The ball makes 159 complete turns each minute, which means it makes 159 * 2 * pi = 998.46 radians per minute. Since the ball is moving at a constant speed, the tangential velocity is equal to the angle it travels in radians per unit of time, so the tangential velocity of the ball is 998.46 radians per minute.
Next, we need to find the radius of the circle. The length of the piece of string is 0.735 m, and since the ball is swinging in a horizontal circle, the radius of the circle is equal to the length of the piece of string. Therefore, the radius of the circle is 0.735 m.
Now that we have the tangential velocity and the radius of the circle, we can plug these values into the formula to find the centripetal acceleration:
a = v^2 / r
= 998.46^2 / 0.735
= 1.007 * 10^8 m/s^2
Therefore, the ball's centripetal acceleration is approximately 1.007 * 10^8 m/s^2.