Simple Harmonic Motion and displacement

AI Thread Summary
A 0.69 kg block stretches a spring, and when a second block is added, the spring's displacement increases by a factor of five. The force exerted by the blocks is equal to the spring constant multiplied by the displacement. The initial calculations involve using the gravitational force and a chosen spring constant, leading to an incorrect mass for the second block. The correct relationship shows that the mass of the second block is four times the mass of the first block. The discussion emphasizes keeping equations in symbolic form for clarity and accuracy.
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1. A 0.69 kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length increases by a factor of 5. What is the mass of the second block?



2. Force= spring constant*displacement of spring from unstrained length



3. First off, I'm horrible at algebra so sorry if I make stupid mistakes in this attempt. The force is gravity so that becomes mg (.69kg*9.8 m/s/s).

mg=kx

If I pick a spring constant of 10 (does it matter what I pick?) then the equation becomes:

(.69kg)(9.8m/s/s)=10 x

Which would give a displacement of .6762 m. Now, when we increase it by a factor of 5, that displacement becomes 3.381 m. Plugging that into a new equations gives:

m (9.8m/s/s) = 10 (3.381m)

When I solve for m I get 3.45 kg, which is wrong. Someone tell me what I did wrong?
 
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m is the total mass of the first and second blocks. Try to leave your work in symbols rather than substitute arbitrary numbers; its neater that way.
 
So if I leave it in the symbol format I get that (.69kg)(9.8m/s/s)=kx and m(9.8m/s/s)=k(5x). Now what?
 
(m1 + m2)g = 5 (kx) = 5 (m1)g
:. m2 = 4 m1
 

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