What is the work done against the spring force in joules?

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SUMMARY

The total work done against the spring force when a 75 g mass is suspended from a vertical spring is calculated using the spring constant (k) of 24.5 N/m and the total displacement (x) of 0.13 m. The correct formula applied is W = 1/2 k x^2, leading to a work output of 0.21 J. The initial stretch of the spring from 4.0 cm to 7.0 cm, along with an additional pull of 10 cm, confirms the displacement used in the calculation.

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  • Understanding of Hooke's Law (F = kx)
  • Knowledge of work-energy principles in physics
  • Ability to convert units (grams to kilograms, centimeters to meters)
  • Familiarity with the formula for elastic potential energy (W = 1/2 k x^2)
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Students studying physics, particularly those focusing on mechanics and energy, as well as educators seeking to clarify concepts related to spring forces and work done against elastic forces.

smile97
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so i have tried this problem fifty million times and i can't get the right answer. hopefully someone can help. when a 75 g mass is suspended from a vertical spring, the spring is stretched from a length of 4.0 cm to a length of 7.0 cm. If the mass is then pulled downward an additional 10 cm, what is the total work done against the spring force in joules? i converted grams to kilograms and cm to m and used the equation f=kx and then plugged those numbers into w=1/2kx^2. i can't get the correct answer of 0.21 J. please help
 
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unfortunately, i get 0.1962 J; a wrong one .
 
i get the correct answer of 0.21J

k=24.5
x=0.13

plug them in and out pops the answer
 

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