according to Hooke's law F=-kx how do we calculate the force if we have weight and length/stretch?

Question

and how do we calculate k the force constant, and is k the same for the same spring?

Answer 1

the force is the weight of the object and k is the same for the same spring, hope this helps

Answer 2

Hang a known weight W from the end of the spring and let the spring stretch x distance from that weight. Measure that stretch x.

Then we have W - F = f = Ma = 0; where M is the mass of the weight and spring system and a is the acceleration of that system. a = 0 because neither the weight nor the spring is moving; they are in equilibrium.

Therefore, we have W = mg = kx = F; where g = 9.81 m/sec^2 on Earth's surface and m is the mass of the weight. In which case k = mg/x = W/x, which is the answer you are looking for.

k is not the same for all springs. k is a function of the physical characteristics of the spring: size, material used, strength, etc. You can prove this to yourself with a bit of a thought experiment.

Put that weight W on your car. W pulled the test spring a distance x, but how far did that weight compress the shock absorbers of your car? It didn't did it? In which case k = W/x = W/0 and k ---> infinity.

In fact, this is a bogus trial because x probably did compress the shocks a very little bit, but so small you could not observe it. However, this does point out that different springs (like the shocks) have different k's.

Answer 3

Say you have a weight W and it stretches the spring a distance l when hung vertically. Then:

W - kl = 0 since the weight doesn't move so W = kl = Force of the spring = weight

If you know W and measure l, then k = W/l