Now consider two springs a and b that are attached to a wall. spring a has a spring constant that is four times that of the spring constant of spring b. if the same amount of energy is required to stretch both springs, what can be said about the distance each spring is stretched

Step-by-step explanation:

The energy required to stretch a spring a distance x is:

E = ½ kx²

where k is the stiffness constant.

If spring B has a constant k and is stretched a distance of b:

E = ½ k b²

If spring A has a constant of 4k and is stretched a distance of a:

E = ½ (4k) a²

E = 2 k a²

If the energies are the same:

½ k b² = 2 k a²

b² = 4 a²

b = 2a

So spring B is stretched twice as far as spring A.