Kaplan 45 Physics discrete

[lamborghiniMD]

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Okay so in my book the question says:
A spring is 64cm long unstretched, and is 8% longer when a .5kg mass hangs from it. How long will it be when a .4kg hangs from it?
a) 66cm
b) 68cm
c) 70cm
d) 74cm

Here's how I solved it:
1. mg = kx
2. (.5kg)(9.8 m/ss) = k(.6912m) because 64cm +8% = 64cm +5.12cm = .6912m ,

so k = (.5)(9.8) / (.6912)..... and I know how to solve the rest from there.

my problem is that the book says k = (.5)(9.8) / (.0512) (implying that you just want 8% of 64 for x)

but is the book right? When the question said the spring was "8% LONGER" i assumed it meant 64cm + 8% (thus 69.12cm IS 8% LONGER than 64cm) ?

Can anyone help shed light on this? Thanks!

 

[cloak25]

According to wiki.. x is the displacement of the spring's end from its equilibrium position. In this case, the spring started at 64cm (equilib) and ended up being 69.12 cm so it was displaced 5.12m from its initial (equilibrium) position. I think you only consider the change in spring length. Is the answer B by the way?

 

[lamborghiniMD]

Yes it is B. Okay, so I guess that makes sense. Thank you!

 

[sciencebooks]

Okay so in my book the question says:
A spring is 64cm long unstretched, and is 8% longer when a .5kg mass hangs from it. How long will it be when a .4kg hangs from it?
a) 66cm
b) 68cm
c) 70cm
d) 74cm

Here's how I solved it:
1. mg = kx
2. (.5kg)(9.8 m/ss) = k(.6912m) because 64cm +8% = 64cm +5.12cm = .6912m ,

so k = (.5)(9.8) / (.6912)..... and I know how to solve the rest from there.

my problem is that the book says k = (.5)(9.8) / (.0512) (implying that you just want 8% of 64 for x)

but is the book right? When the question said the spring was "8% LONGER" i assumed it meant 64cm + 8% (thus 69.12cm IS 8% LONGER than 64cm) ?

Can anyone help shed light on this? Thanks!

I got B, but a completely different way... Basically, you know it's going to be 69 m with the bigger mass, so you can eliminate C and D since the smaller mass will stretch it less.

The stretch factor should go down by a factor of will only be 4/5 (or 6.4%) with the new mass (because the mass is only 4/5).

Then I solved from there, lol. No idea why I went about it that way, but it's exactly the same answer.