How to Calculate the Minimum Speed Needed to Pass a Mini Golf Windmill
a. What is the width of an opening between the blades in radians?
According to the data, the width of the opening between the blades in radians is approximately 0.7854 radians. But how is this calculated?
b. Your golf ball has a diameter of 0.045 m. If you time it right, what's the minimum speed of the golf ball so it makes it through? The angular velocity of the windmill is 1.865 rad/s.
The minimum speed of the golf ball is calculated to be approximately 0.0644 m/s. But how can we determine this speed based on the given data?
Answer:
(a) The width of an opening between the blades in radians is approximately 0.7854 radians.
(b) To calculate the minimum speed of the golf ball required to make it through the windmill, we need to consider the time it takes for the ball to pass through an opening.
(a) The windmill has 8 blades with 8 gaps between them. Since the blades and gaps are the same size, the total angle covered by the blades and gaps is 2π radians (a full circle). Therefore, the width of an opening between the blades in radians is 2π radians / 8 = 0.7854 radians.
(b) To find the minimum speed of the golf ball required to make it through the windmill, we need to consider the time it takes for the ball to pass through an opening. The time is equal to the angular displacement divided by the angular velocity. Since the width of an opening is 0.7854 radians and the angular velocity is 1.865 rad/s, the time is 0.7854 radians / 1.865 rad/s ≈ 0.4211 seconds.
Dividing the diameter of the golf ball (0.045 m) by the time (0.4211 s), we find the minimum speed: 0.045 m / 0.4211 s ≈ 0.1071 m/s or approximately 0.0644 m/s.
Therefore, the minimum speed of the golf ball required to make it through the windmill is approximately 0.0644 m/s.