Calculating Work Done by Spring Constant k

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SUMMARY

The discussion centers on calculating the work done by a spring with a spring constant \( k \) based on the force required to hold a block at a specific displacement. When the block is pulled to \( x = +5.0 \) cm, a force of 460 N is applied, allowing the calculation of \( k \) as 920 N/m using the formula \( k = \frac{F_x}{x} \). The work done by the spring when moving the block between various positions is determined using the equation \( W_s = 0.5 \cdot k \cdot x_i^2 - 0.5 \cdot k \cdot x_f^2 \). This provides a clear method for calculating work done in different scenarios.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with work-energy principles in physics
  • Ability to manipulate algebraic equations
  • Knowledge of units for force and displacement (N and cm)
NEXT STEPS
  • Calculate work done by springs in various configurations using \( W_s = 0.5 \cdot k \cdot x_i^2 - 0.5 \cdot k \cdot x_f^2 \)
  • Explore the implications of spring constants in real-world applications
  • Study the relationship between force, displacement, and potential energy in springs
  • Investigate different methods for measuring spring constants experimentally
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and spring dynamics, as well as educators looking for practical examples of work and energy principles.

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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