Physics question about finding spring constant?

Chung-yin

2014-10-08 5:30 am

One end of a massless spring is attached to a vertical wall and the other end is attached to a block of mass 2.0 Kg on a frictionless horizontal surface. Initially the spring is at its relaxed position and the block is stationary. Then a constant force F pulls the block horizontally to the right.
When the spring is stretched by 1.0 m, the block reaches a maximal kinetic energy of 4.0 J. The block stops when the spring is stretched by 2.0 m.
Please find the spring constant k and the magnitude of the horizontal component of force F.

Am I right for using the following equation?

KEi + Ui = KEf + Uf
1/2mu^2 + 1/2k(xi)^2 = 1/2mv^2 +1/2k(xf)^2
4 + 1/2k(1)^2 = 0 + 1/2k(2)^2
k=8/3 N/m

&

F=k(2)=16/3N

Thank you.

回答 (1)

[匿名]

2014-10-08 5:47 am

Your spring constant answer is ✓ with Conservation of energy principles.

however since the block reaches a maximum k.e when the extension x = 1 m, this => the force F is balanced at this point with the restoring spring force -kx.

for an extension < x = 1 m, F(resultant) is towards the right = F - kx, giving the block an acceleration and increasing its velocity and k.e.

for an extension > x = 1 m, F(resultant) is towards the left = -kx + F, giving the block a deceleration and decreasing its velocity and k.e.

therefore F = k(1) = 8/3 N

hope this helps

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