Hooke's Law:

1.) If it takes 10 N to compress a spring 20cm, how much energy will be stored in the spring when it is stretched 50cm.

***Also, for ex: If I am doing work against a restoring force, say, doing work against gravity, what kind of force is the elastic force of a spring?

F = kx

solve for k
PE = 1/2 kx^2

Doesn't really have a name. Call it a spring force :)

To calculate the energy stored in a spring, we can use Hooke's Law, which states that the force required to compress or stretch a spring is directly proportional to the displacement.

In this case, we need to determine the force required to stretch the spring by 50cm. Hooke's Law equation is given as:

F = k * x

Where:
F is the force,
k is the spring constant, and
x is the displacement.

We know that the force required to compress the spring by 20cm is 10N. So, we can use this information to calculate the spring constant.

10N = k * 20cm

First, let's convert the displacement to meters:
20cm = 0.2m

Now we can solve for the spring constant (k):
k = 10N / 0.2m
k = 50N/m

Now that we have the spring constant, we can calculate the force required to stretch the spring by 50cm:
F = k * x
F = 50N/m * 0.5m
F = 25N

The force required to stretch the spring by 50cm is 25N.

To calculate the energy stored in the spring, we can use the formula for elastic potential energy:

Elastic Potential Energy = (1/2) * k * x^2

We know the spring constant (k) is 50N/m, and the displacement (x) is 0.5m.

Elastic Potential Energy = (1/2) * 50N/m * (0.5m)^2
Elastic Potential Energy = 6.25 Joules

Therefore, the energy stored in the spring when it is stretched 50cm is 6.25 Joules.

Regarding your second question, the elastic force of a spring is a restoring force. It is called a restoring force because it acts in the opposite direction to the displacement, trying to return the spring to its original position. In the case of gravity, when you do work against it, the elastic force of a spring would be a force that opposes that work, trying to bring the spring back to its equilibrium position.