Mini-Golf Windmill: Find Minimum Linear Speed

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In summary, the problem involves a golf ball passing through a windmill with 6 blades rotating at an angular speed of 1.65 rad/s. The ball has a diameter of 4.50x10^-2 m and needs to reach the edge of one blade without getting hit by the next one. The minimum linear speed required for the ball to achieve this is the solution to the problem.
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pmd28
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Homework Statement


A golf ball passing through a windmill at a miniature golf course. The windmill has 6 blades and rotates at an angular speed of 1.65 rad/s. The opening between successive blades is equal to the width of a blade. A golf ball (diameter 4.50x10-2 m) has just reached the edge of one of the rotating blades (see the drawing). Ignoring the thickness of the blades, find the minimum linear speed with which the ball moves along the ground, such that the ball will not be hit by the next blade.


Homework Equations


ω=θ/t
v=m/s


The Attempt at a Solution


I don't know how to start this. I drew out a picture and I still can't see how I can relate the equations.
 
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  • #2
What must the ball do in the problem in order to satisfy the condition specified?
 
  • #3
Go through the hole.
 
  • #4
Bit more specific.
 
  • #5
Go through the hole without getting hit by the windmill?
 
  • #6
Oh, pfft. The golf ball has to go through the hole without getting hit by the windmill with it's slowest possible velocity.
 

1. What is the purpose of finding the minimum linear speed in a mini-golf windmill?

The purpose of finding the minimum linear speed in a mini-golf windmill is to determine the velocity at which a golf ball must travel in order to successfully pass through the windmill without getting stuck or bouncing back. This allows players to strategize and adjust their stroke accordingly, improving their chances of getting a hole-in-one.

2. How is the minimum linear speed calculated in a mini-golf windmill?

The minimum linear speed is calculated by taking into account the dimensions of the windmill blades, the angle at which the ball enters the windmill, and the speed at which the blades are rotating. This calculation involves principles of physics such as projectile motion and rotational dynamics.

3. Can the minimum linear speed vary depending on the design of the windmill?

Yes, the minimum linear speed can vary depending on the design of the windmill. Factors such as the size and shape of the blades, the speed of rotation, and the angle of entry can all affect the minimum linear speed required for the ball to pass through the windmill successfully.

4. How does the minimum linear speed affect the difficulty of a mini-golf course?

The minimum linear speed can greatly affect the difficulty of a mini-golf course. A higher minimum linear speed means that players must hit their shots with more precision and accuracy, making the course more challenging. On the other hand, a lower minimum linear speed may result in easier and more forgiving gameplay.

5. Are there any real-life applications for calculating the minimum linear speed in a mini-golf windmill?

Yes, there are real-life applications for calculating the minimum linear speed in a mini-golf windmill. This concept is similar to calculating the required speed for a car to navigate through a curved road or a cyclist to successfully make a turn. It also has applications in engineering and design, particularly in creating efficient and functional wind turbines.

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