Solving Spring Force Problems: Showing Maximum Displacement & Velocity

In summary, the conversation discusses a problem involving a spring with a non-ideal force function and a mass attached to it. The goal is to find the maximum downward displacement and maximum velocity of the mass. The conversation also provides a hint to start by deriving the spring potential energy as a function of displacement.
  • #1
aboutguava
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I'm just having some trouble with this problem. Any help would really be appreciated. I'm not even sure where to start.

A spring (not ideal) supplies a force given by F = zx^2, where x is measured from the equilibrium position and z is a constant. A mass m is attached to the spring and then released from rest at x = 0 (non-stretched spring)

a) show that the maximum downward displacement of the mass will be (3mg/z)^(1/2)
b) At what displacement will the mass have its maximum velocity

Thank you
 
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  • #2
Start by deriving the spring potential energy as a function of displacement x. (Hint: How much work is required to stretch the spring?)
 

1. What is spring force and how does it affect displacement and velocity?

Spring force refers to the force exerted by a spring when it is stretched or compressed. It follows Hooke's Law, which states that the force is directly proportional to the displacement from its equilibrium position. This means that the more the spring is stretched or compressed, the greater the force it exerts. This force also affects the velocity of the object attached to the spring, as it is responsible for accelerating or decelerating the object as it moves.

2. How do I calculate the maximum displacement and velocity of an object attached to a spring?

To calculate the maximum displacement, you will need to know the spring constant (k) and the maximum force exerted by the spring (Fmax). The maximum displacement (xmax) can be calculated using the formula: xmax = Fmax / k. To calculate the maximum velocity, you will need to know the mass (m) of the object and the maximum force (Fmax) exerted by the spring. The maximum velocity (vmax) can be calculated using the formula: vmax = √(2Fmax / m).

3. How do I show the calculations for solving spring force problems?

The best way to show the calculations for solving spring force problems is by using a step-by-step approach. This involves clearly stating the given information, identifying the relevant formulas, plugging in the values, and showing the calculations. It is also helpful to include diagrams or illustrations to visualize the problem and make it easier to understand.

4. What are some common mistakes to avoid when solving spring force problems?

Some common mistakes to avoid when solving spring force problems include using the wrong formula, not converting units correctly, and not considering the direction of the force. It is important to carefully read and understand the problem, double-check the given values, and pay attention to units and directions. It is also helpful to check your answer using a different method or by plugging it back into the original formula.

5. How can I apply the concept of spring force to real-life situations?

The concept of spring force can be applied to various real-life situations, such as in the design of suspension systems for vehicles, in the construction of buildings and bridges, and in sports equipment like trampolines and pogo sticks. It can also be used in medical devices like prosthetics and braces, as well as in everyday objects like door hinges and retractable pens. Understanding spring force can help in predicting and controlling the behavior of these systems and ensuring their safety and efficiency.

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