Calculating Work Done by Spring Constant k

AI Thread Summary
To calculate the work done by the spring, the spring constant k is determined using the formula k = F/x, where F is the force applied and x is the displacement. Given a force of 460 N at a displacement of 5.0 cm, k is calculated to be 920 N/m. The work done by the spring can then be computed using the equation W_s = 0.5*k*x_i^2 - 0.5*k*x_f^2 for various initial and final positions. The discussion focuses on finding the work done as the block moves through specified displacements. Understanding these calculations is essential for solving the homework problem effectively.
bewger
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Homework Statement



When the block is pulled out to x = +5.0 cm, we must apply a force of magnitude 460 N to hold it there. We pull the block to x = +12.0 cm and then release it.

The 3 figures can be described by this.

(a) A spring in its relaxed state. The origin of an x-axis has been placed at the end of the spring that is attached to a block.

(b) The block is displaced by dvec, and the spring is stretched by a positive amount x. Note the restoring force Fvecs exerted by the spring.

(c) The spring is compressed by a negative amount x. Again, note the restoring force.

For each of the following, find how much work the spring does on the block when the block moves from the first point given to the second point given
(a) xi = 6.0 cm to x = 4.5 cm
(b) xi = 6.0 cm to x = -4.5 cm
(c) xi = 6.0 cm to x = -6.0 cm
(d) xi = 6.0 cm to x = -12.0 cm






Homework Equations


F_s = -kd
F_x = -kx

W_s = .5*k*x_i^2 - 0.5*k*x_f^2

The Attempt at a Solution



How do i get k from what's given?

Is it something like F_x/x = k?

So 460/.05 = 920?
 
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