Spring constant with given mass, find Work

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SUMMARY

The discussion focuses on calculating the work done by a spring force when a block of mass 1.50 kg is attached to a spring with a stiffness constant of 2000 N/m. The work is calculated for two scenarios: (a) stretching the spring by 10.0 cm from the equilibrium position and (b) compressing the spring by 3.00 cm from the stretched position. The correct formula for work done by the spring is derived using the integral of the spring force, leading to the conclusion that the work done in both scenarios can be computed using the equation Work = (1/2) * k * Δx².

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of integral calculus for calculating work
  • Familiarity with the concept of equilibrium position in spring systems
  • Basic physics concepts related to mass and force
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  • Study the application of Hooke's Law in different spring systems
  • Learn about the principles of work and energy in physics
  • Explore integration techniques for calculating work done by variable forces
  • Investigate the effects of friction on work done in spring systems
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of work done by springs in practical applications.

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Homework Statement



A block of mass 1.50 kg is attached to one end of a horizontal spring, the other end of which is fixed to a vertical wall. The spring has a stifffness constant of 2000 N/m. The block slides without friction on a horizontal table, set close to the wall. Find the work done by the spring force if the block moves (a) from the equilibrium position till the spring is stretched by 10.0 cm, (b) from this last position till the sring is compressed by 3.00 cm.

Homework Equations



Work = Integral from initial position to final position of the Force of the spring?

The Attempt at a Solution



Im not really sure where to begin with this one, we just started the chapter on Work!
 
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F of spring = -k\Deltax?

So -2000 * 10cm?

And then integrate from 0 to 10cm of the product?
 
A) (1/2)*(2000)*(-.1m)^2 ?
 

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