Length of Spring: How Can the Unstretched Length Be Determined?

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The discussion focuses on determining the unstretched length of a spring under a load of 400 N, with a spring constant of 800 N/m. The user successfully calculated the weight W as 62.8 N and the force in the spring as 281.712 N. They also measured a length of 1110 mm using the Pythagorean theorem, questioning its relevance to finding the unstretched length. The conversation includes considerations of using trigonometric functions and components to refine the calculations. Ultimately, the user confirmed they resolved the problem.
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[SOLVED] Length of Spring

Homework Statement



A load of weight 400 N is suspended from a spring and two cords that are attached to blocks of weights 3W and W as shown. Knowing that the constant of the spring is 800 N/m, determine (a) the value of W, (b) the unstretched length of the spring.

http://img406.imageshack.us/img406/472/13213uv7.jpg

Homework Equations



F_{s} = -k x

The Attempt at a Solution



I have already worked through part (a), getting 62.8 N for W and in the process I got 281.712 for the F_{s} of the system above.

Now from the picture above, I can figure that the length AB is 1110 mm using Pythagoreans. Whether that is relevant or not to figuring (b) out, I am not sure. I'm thinking that I need to find what the F_{s} would be if there were no forces acting on the spring.
 
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ttiger2k7 said:

Homework Statement



A load of weight 400 N is suspended from a spring and two cords that are attached to blocks of weights 3W and W as shown. Knowing that the constant of the spring is 800 N/m, determine (a) the value of W, (b) the unstretched length of the spring.

http://img406.imageshack.us/img406/472/13213uv7.jpg

Homework Equations



F_{s} = -k x

The Attempt at a Solution



I have already worked through part (a), getting 62.8 N for W and in the process I got 281.712 for the F_{s} of the system above.

Now from the picture above, I can figure that the length AB is 1110 mm using Pythagoreans. Whether that is relevant or not to figuring (b) out, I am not sure. I'm thinking that I need to find what the F_{s} would be if there were no forces acting on the spring.

I would look at the relevant equation and attempt to determine if it can be expanded to include initial and final values.
 
Last edited by a moderator:
You can determine angles using SOH CAH TOA. From there you can use components to work out your answer more precisely.
 
double post...
 
Last edited:
OmCheeto said:
I would look at the relevant equation and attempt to determine if it can be expanded to include initial and final values.

Thanks, I got it!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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