Finding spring constant k in N/m

In summary, the conversation discusses finding the spring constant, k, for a small mass attached to a spring using the graph of displacement vs. time. The given information includes the mass (16.9 grams), initial displacement (0.43 cm), and period (0.69 seconds). The equation used is F = kx and the attempted solution involves using the formula T = 2pi(m/k)^1/2 for simple harmonic motion. However, the result obtained (38.56 N/m) is incorrect and the individual asks for another method to solve the problem.
  • #1
jimko
2
0

Homework Statement



The graph of displacement vs. time for a small mass at the end of a spring is shown in the figure. At t = 0, x = 0.43 cm. If m = 16.9 gram, find the spring constant, k.

T = 0.69 seconds

Homework Equations



F = kx


The Attempt at a Solution



mg=kx

(.0169 kg)(9.8 m/s^2) / (.0043m) = 38.56

Which is wrong. Is there another way to solve this problem that I'm not seeing?
 
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  • #2
graph please
 
  • #3
There we go.. can you see that?
 

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  • #4
if you have done SHM then:
T=2pi(m/k)^1/2
From the graph T=0.69sec.
After putting the i am getting k=1.39 N/m.
Am I correct.
Can u tell how to upload picture(from mobile). I am new here
 
  • #5



There is another way to solve this problem using the equation T = 2π√(m/k), where T is the period of the oscillation, m is the mass, and k is the spring constant. Rearranging this equation, we get k = (4π^2m)/T^2. Plugging in the given values, we get k = (4π^2)(0.0169 kg)/(0.69 s)^2 = 38.63 N/m. This may be a more accurate solution to the problem. Additionally, it is always important to double check your calculations and units to ensure they are correct.
 

Related to Finding spring constant k in N/m

1. What is the spring constant and why is it important?

The spring constant, denoted as k, is a measure of the stiffness of a spring. It represents the force required to stretch or compress a spring by a certain distance. The spring constant is important because it is used to calculate the force exerted by a spring and is essential in understanding the behavior of springs in various systems.

2. How do you find the spring constant k in N/m?

To find the spring constant, you can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This can be represented by the equation F = -kx, where F is the force, k is the spring constant, and x is the displacement. You can rearrange this equation to solve for k, which will give you the spring constant in units of N/m.

3. What are the units of the spring constant k?

The units of the spring constant k are typically expressed in Newtons per meter (N/m). This unit represents the amount of force (in Newtons) required to stretch or compress a spring by one meter. However, in some cases, the spring constant may also be expressed in units of pounds per inch (lb/in) or kilograms per second squared (kg/s2).

4. Can the spring constant k vary for different types of springs?

Yes, the spring constant can vary for different types of springs. The spring constant is dependent on factors such as the material, shape, and dimensions of the spring. For example, a stiffer and thicker spring will have a higher spring constant than a thinner and more flexible spring. Additionally, the spring constant may also vary for the same type of spring if it is made from different materials with different elastic properties.

5. How does temperature affect the spring constant k?

Temperature can affect the spring constant k as it can cause changes in the elasticity and stiffness of the material used in the spring. In general, as the temperature increases, the spring constant may decrease due to the expansion and softening of the material. However, this effect may vary depending on the type of material and the operating conditions of the spring. It is important to consider the temperature when calculating and using the spring constant in different systems.

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