Spring Constant Calculation for Compressed Spring with Mass

In summary, the conversation is about calculating the spring constant for a compressed mass on a light spring. The mechanical energy of the spring is converted into gravitational potential energy when the mass reaches the top of its trajectory. The correct equation to use is 1/2kx^2=mgy, where x is the distance the spring moves and y is the distance the mass travels vertically. The final answer for the spring constant is approximately 3.1E3 N/m.
  • #1
michlip
1
0
1. Homework Statement
The left side of the figure shows a light (`massless') spring of length 0.340 m in its relaxed position. It is compressed to 67.0 percent of its relaxed length, and a mass M= 0.250 kg is placed on top and released from rest (shown on the right).

The mass then travels vertically and it takes 1.50 s for the mass to reach the top of its trajectory. Calculate the spring constant, in N/m. (Use g=9.81 m/s2). Assume that the time required for the spring to reach its full extension is negligible.


2. Homework Equations
EK=1/2mv2=1/2 * 0.25 * V2
K=-0.5mv2/x

3. The Attempt at a Solution
-0.5mv2/x
v=14.715
x=11.22
m=0.250
I plugged in the variables, but it still isn't right.
 
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  • #2
The mechanical energy of the spring will be converted into gravitational potential energy at the top of the trajectory. You have used kinetic energy instead.
 
  • #3
im really confused by this same type of question...
i found U(y) now how do i use that to find K?
 
  • #4
As someone above said, you should be converting mechanical energy into gravitational potential energy, rather than using kinetic. 1/2kx^2=mgy is the proper conversion of energy. Hope that helps
 
  • #5
is x = .2278 m like above? and y = the distance the mass traveled in the air? because i have been using those and gettting the wrong answer
 
  • #6
^

The x i used in my equation is the distance that the spring moves from its "position of relaxation". You need to find the distance that the object goes vertically, and plug that in for y in the equation

1/2kx^2=mgy >>>>> k= (mgy)/(.5x^2)

Once you have y you can solve
 
  • #7
If you can confirm that the asnwer is roughly 3.1E3 N/m , I will tell you how i got it.

I believe in the equation x= x(initial) + Velocity(Initial)*time + .5gt^2 you forgot to account for the .5gt^2, which equals roughly 22 m. Added to the 11 m you found using the middle term of the equation above, you have solved for the correct height. You were only a step off from getting it.
 

1. What is a spring constant?

A spring constant, also known as a force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

2. How is the spring constant calculated?

The spring constant is calculated by dividing the applied force by the displacement of the spring. It can also be calculated by dividing the elastic potential energy stored in the spring by the distance the spring is stretched or compressed.

3. What is the unit of measurement for spring constant?

The unit of measurement for spring constant is Newtons per meter (N/m) in the SI system, or pounds per inch (lb/in) in the imperial system.

4. How does the spring constant affect the behavior of a spring?

The spring constant determines the stiffness of a spring and how much it will stretch or compress when a force is applied. A higher spring constant means a stiffer spring that requires more force to stretch or compress, while a lower spring constant means a more flexible spring that requires less force.

5. Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material of the spring, the dimensions of the spring, and the temperature. The spring constant for a specific spring is not a constant value, but rather a characteristic of the spring's properties and the conditions in which it is used.

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