Calculating Spring Constant with Hanging Spring and Mass

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SUMMARY

The discussion centers on calculating the spring constant (k) for a spring with a 0.497 kg block attached, which drops 0.12 m before coming to rest. The relevant formula is F = -kx, where the force of the spring equals the gravitational force acting on the block (mg). The equilibrium condition states that kx = mg, leading to the calculation of the spring constant as k = mg/x. The block's mass and the distance it drops are essential for determining k accurately.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Basic knowledge of gravitational force (F = mg)
  • Familiarity with equilibrium conditions in physics
  • Ability to perform basic algebraic manipulations
NEXT STEPS
  • Calculate the spring constant using k = mg/x
  • Explore the concept of angular frequency in spring systems
  • Review examples of Hooke's Law applications in real-world scenarios
  • Investigate potential errors in experimental setups involving springs
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for practical examples of Hooke's Law and spring dynamics.

dmolson
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I have a problem I cannot figure out. It asks to calculate the spring constant when given a spring hung from the ceiling, a 0.497 kg block attached to the free end of the spring. The block is released from rest, drops 0.12 m before coming momentarily to rest. How do I calculate the spring constant?? Please Help!
 
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What does the force in a spring equal?
 
F = -kx I thought
 
Right. That's one of the forces acting on the block. Which is the other one? What is the relation between these two forces in order for the block to be in equilibrium?
 
Right. That's one of the forces acting on the block. Which is the other one? What is the relation between these two forces in order for the block to be in equilibrium?

The other one would be gravity (mg) acting on the block. I thought the relation was F = kx - mg. But I do not know for sure.
 
dmolson said:
The other one would be gravity (mg) acting on the block. I thought the relation was F = kx - mg. But I do not know for sure.

If there was a non-zero net force F, as you stated, the block wouldn't be at rest. The problem states that the block came to rest, after the spring extended for some amount x. So, if the block is at rest, the net force must equal zero. Hence, kx = mg.
 
I tried that solution and it did not work. Here is the original problem.

A spring is hung from the ceiling. A 0.497-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.12 m before momentarily coming to rest. What is the spring constant?
 
Interesting, it should work, unless I'm missing something enormous here. Do you know the solution?
 
No, it is part of the e-homework I have. The next part says to calculate the angular frequency. I only have limited tries and I have tried the second part.
 
  • #10
*have not tried
 

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