Solve Spring Constant: 40g Mass, 20N/m

In summary, a mass of 40.0 grams is attached to a vertical spring with a spring constant k = 20.0 N/m. The spring is lowered slowly until it stops stretching. To determine the amount of spring stretch, the weight of the mass can be calculated using F = mg, where g is the acceleration due to gravity. The acceleration is assumed to be slower than gravity since the spring is lowered slowly.
  • #1
ajmCane22
33
0

Homework Statement


A mass of 40.0 grams is attached to a vertical spring with a spring constant k = 20.0 N/m and lowered slowly until the spring stops stretching. How much is the spring stretched?


The Attempt at a Solution


I assume I have to use F = -kx? But I don't know the force so how would I figure this out? I am really stuck. Please help.
 
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  • #2
Hint: How much does the mass weigh?
 
  • #3
40.0 grams, but how is that a hint? F = ma and I don't know acceleration, so how does the mass help?
 
  • #4
Given a mass 'm', how do you figure out its weight? What gravitational force acts on it?
 
  • #5
Would it be F = mg? It said the spring was lowered slowly so I assumed the acceleration was slower than gravity.
 
  • #6
ajmCane22 said:
Would it be F = mg?
Yes!
It said the spring was lowered slowly so I assumed the acceleration was slower than gravity.
mg gives the weight of an object regardless of its acceleration. (If the object were dropped, so that the only force acting was gravity, then its acceleration would be g.)
 
  • #7
Thanks! :)
 

Related to Solve Spring Constant: 40g Mass, 20N/m

1. What is the formula for calculating spring constant?

The formula for calculating spring constant is k = F/x, where k is the spring constant (measured in N/m), F is the applied force (measured in N), and x is the displacement of the spring from its equilibrium position (measured in m).

2. How do you calculate the spring constant using a mass and applied force?

To calculate the spring constant using a mass and applied force, you can use the equation k = (m * g)/x, where k is the spring constant (measured in N/m), m is the mass (measured in kg), g is the acceleration due to gravity (9.8 m/s^2), and x is the displacement of the spring from its equilibrium position (measured in m).

3. Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material of the spring, the length of the spring, and the temperature. It is important to note that the spring constant is only constant for a specific spring under specific conditions.

4. Why is it important to know the spring constant?

Knowing the spring constant allows us to understand the relationship between the force applied to a spring and the resulting displacement. This is essential in many areas of science, such as engineering, physics, and materials science.

5. How can you determine the spring constant experimentally?

The spring constant can be determined experimentally by using Hooke's law, which states that the force applied to a spring is directly proportional to the resulting displacement. By measuring the force and displacement for different values, you can plot a graph and calculate the slope, which represents the spring constant.

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