Solve Spring Constant: 40g Mass, 20N/m

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To determine how much the spring is stretched, first calculate the weight of the 40g mass using the formula F = mg, where g is the acceleration due to gravity (approximately 9.81 m/s²). This results in a force of approximately 0.392 N. Since the spring constant k is 20 N/m, apply Hooke's Law (F = -kx) to find the stretch of the spring. Rearranging the formula gives x = F/k, leading to a stretch of about 0.0196 meters or 19.6 mm. The discussion emphasizes understanding the relationship between mass, weight, and spring force to solve the problem effectively.
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Homework Statement


A mass of 40.0 grams is attached to a vertical spring with a spring constant k = 20.0 N/m and lowered slowly until the spring stops stretching. How much is the spring stretched?


The Attempt at a Solution


I assume I have to use F = -kx? But I don't know the force so how would I figure this out? I am really stuck. Please help.
 
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Hint: How much does the mass weigh?
 
40.0 grams, but how is that a hint? F = ma and I don't know acceleration, so how does the mass help?
 
Given a mass 'm', how do you figure out its weight? What gravitational force acts on it?
 
Would it be F = mg? It said the spring was lowered slowly so I assumed the acceleration was slower than gravity.
 
ajmCane22 said:
Would it be F = mg?
Yes!
It said the spring was lowered slowly so I assumed the acceleration was slower than gravity.
mg gives the weight of an object regardless of its acceleration. (If the object were dropped, so that the only force acting was gravity, then its acceleration would be g.)
 
Thanks! :)
 

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