Force exerted by rubberbands.?

Question

I have a lab where the only info given is the distance a rubberband stretches. And I need to find the force (N) that the rubberband exerts. Can someone help me out on the first one? The rubberband stretches 10.4 cm. The professor said I can't use Hookes Law due to the fact it is hard to determine the equilibrium of a rubberband? What is another formula I can use?

I can't use mass as a factor either.

Answer 1

The prof. is right. Hooke's law presumes a constant value for the coefficient k in N = kx, which is OK within limits for springs and things. But, in fact, in rubberbands, k is dependent on x; thus, k(x) is more appropriate. In which case, dN = dk(x) x + k(x) dx is the differential equation and the solution would be the integration over x0 to x1 (the amount of stretch, your 10.4 cm for example).

So first thing you need to do is find out what k(x) equals in terms of x. You can find this by adding weight and measuring the stretch with each weight. Graph total weight vs distance (x) to find the equation k(x) = f(x) = n/x; where f(x) represents the graphed equation (e.g., f(x) = mx + b if the relationship is linear), n is the accumulated weight for each value of x, and m is the slope and b the f(x) intercept if the relationship is in fact linear. [NB: If the relationship is not linear over the entire interval of stretch, you might assume linearity if the curve is not too pronounced. That would at least be a first order approximation to the real solution.]

Answer 2

hang weights from the rubber band

Start small and work your way up.

Once you find the weight that stretches the rubber band about 10.4 cm, you will have the force exerted by the rubber band. Its equal to the weight that you hung from it.

You'll need to take a measurement of the unstretched rubber band and make sure you get 10.4cm of stretch (total stretched length minus original unstretched length), not 10.4cm total length.
.

Answer 3

Well, if you can't use Hooke's Law (and I agree, a rubber band is not an ideal spring) and you can't hang masses from it, you're kind of SOL. Can you attach it to a cart, pull, and measure the acceleration of the cart?

Answer 4

Hang weights of varying masses from it, until you get one that stretches it exactly 10.4 cm. Then calculate the force.

Answer 5

k1= 1pv

rc(1).rc(2)= k1/rc(1)* rc(2)

>~^ ur value* k value
>

(note: rem u will have find the value of k1 and k2 applied on both the ends)

k1*k2/ alpha * k(x1 + x2)= v1

now add v1 to the value u find.....good luck.