Solving for Maximum Speed: Object on Spring with Force Constant of 19.6N/m

In summary, the object moves at a maximum speed of 0.28m/s when connected to a light spring with a force constant of 19.6N/m.
  • #1
mizzy
217
0

Homework Statement


A 0.40kg object connected to a light spring with a force constant of 19.6N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest, determine (a) the maximum speed of the object.


Homework Equations



F = -kx

The Attempt at a Solution



Does this involve kinetic energy?
 
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  • #2


Yes, you need to use the conservation of mechanical energy principle.
 
  • #3


so KE + KEs = 0

1/2mv^2 + 1/2kx^2 = 0

solve for v?
 
  • #4


Close, but the spring has no kinetic energy only the attached mass. The spring can store what type of energy? Also set it up so its all the energy at state 1 equal to all the energy at state 2 (the point of interest).
 
  • #5


sorry not kinetic energy but potential energy.
 
  • #6


Yes so you should arrive at:
PEs = KE
which would give the same result as if you used the work kinetic energy theorm:
Ws = KE2-KE1
where Ws is the work done by the spring on the block and is equal to the integral of the spring force with respect to x or:
Ws = integral of Fdx = (1/2)kx^2
 
  • #7


kjohnson said:
Yes so you should arrive at:
PEs = KE
which would give the same result as if you used the work kinetic energy theorm:
Ws = KE2-KE1
where Ws is the work done by the spring on the block and is equal to the integral of the spring force with respect to x or:
Ws = integral of Fdx = (1/2)kx^2

so 1/2mv^2 = 1/2kx^2
v = square root (kx^2/m)
 
  • #8


correct.
 
  • #9


k. i got the answer, the max speed is 0.28m/s.

The next part of the question is, for what value of x does the speed equal one-half the maximum speed.

What i did was to solve for x with v = 1/2(max speed)

I got the answer wrong.

Can someone point out where i went wrong?
 
  • #10


Again use the conservation of energy. Is your energy at state 1 (the compressed state) any different from part a? Then what forms of energy are present at state 2?
 
  • #11


at state 2, is it half the compressed state?
 
  • #12


No, that distance x is the unknown you are asked to solve for. At state 1 the only energy is potential energy which you know. At state two you know the kinetic energy of the mass because you know v=vmax/2, but you don't know the potential energy of the spring=(1/2)kx^2...
 
  • #13


So in state 1 there is potential energy, no kinetic energy. State 2 there's kinetic energy, where v is half of the max speed and there's potential energy and that's when we solve for x.
 
  • #14


correct.
 
  • #15


Thanks for you help! =)
 

1. How do I calculate the amount of compression needed for a spring?

To calculate the amount of compression needed for a spring, you will need to know the spring constant (k) and the force applied to the spring (F). The formula is: Δx = F/k, where Δx is the amount of compression in meters.

2. What factors affect the compression of a spring?

There are several factors that can affect the compression of a spring, including the material of the spring, the diameter and length of the spring, and the amount of force applied to the spring. The type of end attachments and any external factors, such as temperature, can also impact the compression of a spring.

3. How do I choose the right spring for my project?

Choosing the right spring for your project depends on several factors, including the required load or force, the amount of space available, the desired amount of compression, and the environment in which the spring will be used. It is important to consult with a spring manufacturer or engineer to determine the best spring for your specific needs.

4. Can I adjust the compression of a spring?

Yes, the compression of a spring can be adjusted by changing the amount of force applied to the spring or by altering the spring's dimensions, such as its length or diameter. However, it is important to note that adjusting a spring's compression can affect its overall performance and should be done carefully.

5. How do I know if a spring is compressed too much?

If a spring is compressed too much, it can become permanently deformed or lose its ability to return to its original shape. Signs that a spring is compressed too much include a decrease in its spring rate, uneven compression, or visible damage to the spring. It is important to follow the manufacturer's guidelines for the maximum compression limit of a spring to avoid these issues.

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