Identifying limit of puck height

In summary, the conversation discusses the use of a formula from a book on hockey physics to determine if a 100 mph shot from 30 feet away can hit the crossbar. The modified formula takes into account drag and lift, but it seems that the puck will not rise above 48 inches. The speaker mentions that this could be due to the lift coefficient peaking near 25 degrees or the limitations of the formula. They also provide their calculations and suggest comparing the model with real-life conditions.
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Homework Statement



This homework isn't for a course. There is a book on hockey physics with a section discussing puck drop below intended target. When I use the book's formula modified for drag and lift, it seems to show that a 100 mph shot, taken from 30 feet from the net, can not hit the crossbar. The puck height reaches a maximum height of 46.63652463 inches with an initial puck angle of 24 degrees. Changing to 23 and 25 degrees reduce the final puck height. I guess this result is either because of the lift coefficient peaking near 25 degrees as mentioned on page 78 or because on the bottom of page 77 it is mentioned that formula 3.7 which includes a simple fit to data is only valid to within 20 percent.

I'm wondering why the puck won't rise above 48 inches.

I think I’ve seen high school kids, whom I doubt can shoot 100 mph, hit the crossbar from 30 feet away.

Homework Equations



Are provided in order below.

The Attempt at a Solution

Here is my work, in case I’ve made some mistakes.Formula 3.3 to determine puck drop below target without air resistance:gx2

________________2v2 cos2θg = 9.80665 m/s2x = 30’ = 9.144 metersv = 100 mph = 44.704 m/sθ = 24 degrees = 0.4188790205 radians
Formula 3.3 with drag:Formula 3.5 = velocity dropVelocity drop = -6.3 * (1/10/10/10) * 44.704 * 9.144 = -2.575272269Velocity at end = 44.704 + -2.575272269 = 42.12872773Average velocity = (44.704 + 42.12872773) / 2 = 43.41636387Formula 3.3 using average velocity:(9.80665 * (9.144 * 9.144)) / (2 * (43.41636387 * 43.41636387) * (cos(0.4188790205) * cos(0.4188790205))) = 0.2606128904 meters puck drop from target0.2606128904 meters = 10.16390273 inchesPuck height would be 48 - 10 = 38 inchesFormula 3.3 with drag and lift:Formula 3.7 (This is the simple fit to data):(4 * (1/10/10/10/10/10) * 24 degrees -7.8 * (1/10/10/10/10/10/10/10) * 24 degrees * 24 degrees = 0.00051072Formula 3.6 lift:0.00051072 from formula 3.7 * 44.704 initial velocity * 44.704 initial velocity = 1.020647166 liftNew gravity = gravity minus (lift / mass) (from bottom paragraph of page 79):Puck Mass: Page 85 shows puck mass as 170 grams. However, to get the calculations in the bottom paragraph of page 79 to end up at 32 inches I used 0.138 for puck mass. Using .170097 for puck mass gave me an answer of 33.5 inches.9.80665 gravity - (1.020647166 lift / 0.138 mass) = 2.40465604348 revised gravityFormula 3.3 with drag and lift:(2.40465604348 gravity revised for lift * (9.144 distance in meters * 9.144 distance in meters)) / ( 2 * (43.41636387 avg velocity * 43.41636387 average velocity) * (COS(0.4188790205 puck angle in radians) * COS(0.4188790205 puck angle in radians))) = 0.06 meters puck drop.06 meters puck drop = 2.498475371 inches puck drop below target[/B]
 
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  • #2
Youd have to compare the conditions irl with the model the textbook uses.
 

1. What is the purpose of identifying the limit of puck height?

The purpose of identifying the limit of puck height is to determine the maximum height at which a puck can be thrown or hit with a stick before it falls back to the ground. This information is important for understanding the physics of the game and for setting rules and regulations.

2. How is the limit of puck height determined?

The limit of puck height is determined through experiments and calculations. Scientists use tools such as motion sensors and high-speed cameras to track the trajectory of a puck and analyze its motion. They also consider factors such as air resistance and the force applied by the stick to determine the limit.

3. What factors affect the limit of puck height?

The limit of puck height can be affected by various factors such as the weight and size of the puck, the force applied by the stick, the angle at which the puck is hit, and external factors such as air resistance and gravity. Surface friction and temperature can also play a role in the limit of puck height.

4. Why is the limit of puck height important in hockey?

The limit of puck height is important in hockey because it affects the strategy and gameplay of the sport. It also helps to ensure the safety of players and prevents the puck from flying too high and potentially causing injury. Additionally, the limit of puck height can be used to determine penalties or rule violations.

5. Can the limit of puck height change?

Yes, the limit of puck height can change depending on various factors such as changes in equipment, playing conditions, or rules and regulations. It can also vary among different levels of play, such as amateur versus professional hockey. Scientists continue to study and improve their understanding of the limit of puck height in order to accurately determine and enforce it in the game of hockey.

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