Solve Halfway Measures: Find KE at 7cm

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In summary, the conversation involves discussing a physics problem involving a mass-spring system. The work required to stretch the spring is calculated and used to determine the kinetic energy of the system at different points. The correct formula for calculating the total energy stored in the system is also discussed.
  • #1
anyone1979
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[SOLVED] Halfway measures

Am I doing this right?

You stretch the spring of a certain mass-spring system 14.0 cm from its relaxed state; this requires 21.2J of work. You then release the system. What is its Kinetic energy when the stretch of the spring is 7 cm?

W = F*s
21.2 = F(.14)
F = 151.4N

W = 151.4(.07)
W = 10.6J
W = change in KE
KE = 10.6J
 
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  • #2
No, you cannot assume that the spring force is constant, which is what you are doing when you set the work equal to F*s. Hint: What's the energy stored in a stretched spring? (Look it up or derive it.)
 
  • #3
Is this close?

W = 1/2(kx^2)
21.2 = (1/2)k(.14^2)
21.2(2) = k(.14^2)
k = 216.3J

W = (1/2)(216.3)(.07^2)
W = .053J
KE = .053J
 
  • #4
anyone1979 said:
Is this close?

W = 1/2(kx^2)
21.2 = (1/2)k(.14^2)
21.2(2) = k(.14^2)
k = 216.3J
Much better. (You are close.)

You have a typo (or arithmetic error) in that last step: k = 2163 J.

Realize that this is the total energy stored in the system. After you release it, some of that initial spring potential energy will be transformed to KE. But at all times, Total energy = KE + PE.
 
  • #5
Thanks for replying.
I do not see the error though. I changed it from cm to meters.

21.2 = (1/2)k(0.14^2)
21.2(2) = k(0.196)
((21.2)(2))/(0.196) = k am I calculating wrong?

U1 = (1/2)k(x1^2)
U2 = (1/2)k(x2^2)
KE1 = (1/2)mv1^2
KE2 = (1/2)mv2^2

KE2 = KE1 + U1 - U2

Is that the right Idea?
 
  • #6
anyone1979 said:
Thanks for replying.
I do not see the error though. I changed it from cm to meters.

21.2 = (1/2)k(0.14^2)
21.2(2) = k(0.196)
((21.2)(2))/(0.196) = k am I calculating wrong?
0.14^2 = 0.0196 (not 0.196)

U1 = (1/2)k(x1^2)
U2 = (1/2)k(x2^2)
KE1 = (1/2)mv1^2
KE2 = (1/2)mv2^2

KE2 = KE1 + U1 - U2

Is that the right Idea?
Yes, exactly the right idea.
 
  • #7
Thank you so much.
I wrote the equation down wrong.
 

1. What is the formula for calculating kinetic energy at 7cm?

The formula for calculating kinetic energy at 7cm is KE = 0.5 * m * v^2, where m is the mass of the object and v is the velocity at 7cm.

2. How do I determine the mass of the object for the calculation?

The mass of the object can be determined through various methods such as weighing it on a scale or using its known density and volume. It is an essential factor in calculating kinetic energy at 7cm.

3. Do I need to convert the velocity to a specific unit before using it in the formula?

Yes, the velocity used in the formula should be in meters per second (m/s). If the velocity is given in other units, it needs to be converted to m/s before using it in the calculation.

4. Can I use this formula to calculate kinetic energy at any distance?

No, this formula is specifically for calculating kinetic energy at 7cm. If you want to find the kinetic energy at a different distance, you would need to use the formula KE = 0.5 * m * v^2 at that specific distance.

5. How can I use this calculation in real-world applications?

The calculation of kinetic energy at 7cm is essential in understanding the movement of objects and can be applied in various real-world scenarios, such as calculating the energy required for a moving object to overcome friction or determining the force needed to stop a moving object at a specific distance.

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