A ball is placed on the spring and launched vertically, Find k

In summary, the conversation discusses the purpose of placing a ball on a spring and launching it vertically, which is to determine the spring constant or k value. The k value can be calculated by measuring the displacement of the spring and is affected by factors such as air resistance, friction, and human error. The k value determines the behavior of the spring, including its stiffness and oscillation frequency, and can change if the physical properties of the spring are altered. However, it should remain constant under constant conditions, although it may vary slightly due to external factors.
  • #1
Alexanddros81
177
4

Homework Statement


14.28 The spring of stiffness k is undeformed in the position shown. The 30-g ball
is placed on the spring and launched vertically by compressing the spring 150mm and
releasing it. If the ball reaches an elevation of 14.25m above A, determine the value of
k.

Fig P14_28.jpg


Homework Equations

The Attempt at a Solution



Pytels_Dynamics113.jpg

[/B]
The solution given is 36.7 N/M. So is it my mistake or the book is wrong?
Can you check my solution?
 

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  • #2
I believe your solution is correct. I suspect that the answer provided is a misprint.
 
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Related to A ball is placed on the spring and launched vertically, Find k

1. What is the purpose of placing a ball on a spring and launching it vertically?

The purpose of this experiment is to determine the spring constant, or k value, of the spring. This constant represents the stiffness of the spring and is an important factor in understanding the behavior of the spring.

2. How is the k value of the spring calculated?

The k value of the spring can be calculated by measuring the displacement of the spring when the ball is placed on it and released. This displacement, along with the mass of the ball and the acceleration due to gravity, can be used to calculate the spring constant using the equation k = (mg)/x, where m is the mass of the ball, g is the acceleration due to gravity, and x is the displacement of the spring.

3. What factors can affect the accuracy of the k value calculation?

The accuracy of the k value calculation can be affected by factors such as air resistance, friction in the spring, and human error in measurement. These factors can cause slight variations in the displacement of the spring and ultimately affect the calculated k value.

4. How does the k value affect the behavior of the spring?

The k value of the spring determines how much force is required to compress or stretch the spring. A higher k value indicates a stiffer spring, meaning more force is needed to produce the same displacement compared to a spring with a lower k value. This also affects the spring's oscillation frequency and period.

5. Can the k value of a spring change?

The k value of a spring can change if the physical properties of the spring, such as its length or material, are altered. However, under constant conditions, the k value of a spring should remain the same. It is important to note that the k value of a spring may vary slightly due to factors such as temperature and aging of the material.

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