It takes 3.38 J of work to stretch a Hooke’s-law

spring 5.63 cm from its unstressed length.
How much the extra work is required to
stretch it an additional 4.22 cm?
Answer in units of J

Well, if it takes 3.38 J to stretch a Hooke's-law spring 5.63 cm, then we can calculate the extra work required to stretch it an additional 4.22 cm.

Let's call this "extra work" the ultimate work, because it sounds dramatic.

Now, let's do some math-y magic. If the spring obeys Hooke's law, the force required to stretch the spring is proportional to the displacement. So, we can say:

3.38 J / 5.63 cm = Ultimate Work / 4.22 cm

Now, let's solve for the ultimate work:

Ultimate Work = (3.38 J / 5.63 cm) * 4.22 cm

Calculating this with my mathematical prowess yields the result:

Ultimate Work = 2.54 J

So, the extra work required to stretch the Hooke's-law spring an additional 4.22 cm is 2.54 J. Keep it up, spring! You've got this!

To find the extra work required to stretch the spring an additional 4.22 cm, we can use Hooke's Law equation:

Work = 0.5 * k * x^2

Where:
Work is the work done on the spring
k is the spring constant
x is the displacement from the unstressed length

We already know the work done to stretch the spring 5.63 cm, which is 3.38 J. Now we need to calculate the spring constant (k) to find the extra work required.

We can rearrange the equation to solve for k:

k = (2 * Work) / x^2

Substituting the values:
k = (2 * 3.38 J) / (5.63 cm)^2

Now, we can calculate the extra work needed to stretch the spring an additional 4.22 cm:

Extra Work = 0.5 * k * (extra displacement)^2

Substituting the values:
Extra Work = 0.5 * k * (4.22 cm)^2

Let's calculate the spring constant (k) first:

k = (2 * 3.38 J) / (5.63 cm)^2
k ≈ 0.238 N/cm

Now, let's calculate the extra work:

Extra Work = 0.5 * 0.238 N/cm * (4.22 cm)^2
Extra Work ≈ 2.004 J

Therefore, the extra work required to stretch the spring an additional 4.22 cm is approximately 2.004 J.

To find the additional work required to stretch the spring an extra distance, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law equation:
F = k * x

Where:
F = force applied to the spring
k = spring constant
x = displacement of the spring from its equilibrium position

We can rearrange the equation to solve for the spring constant:
k = F / x

We are given the work done to stretch the spring by 5.63 cm (0.0563 m) as 3.38 J.

The work done is given by:
Work = 1/2 * k * x^2

We can solve for the spring constant using the given information:

k = 2 * Work / x^2
= 2 * 3.38 J / (0.0563 m)^2

Once we have the spring constant, we can find the additional work required to stretch the spring by an extra 4.22 cm (0.0422 m):

Additional work = 1/2 * k * (extra x)^2
= 1/2 * k * (0.0422 m)^2

Now, let's substitute the values and calculate:

k = 2 * 3.38 J / (0.0563 m)^2
= 2425 N/m

Additional work = 1/2 * (2425 N/m) * (0.0422 m)^2
≈ 0.271 J

Therefore, the additional work required to stretch the spring by an additional 4.22 cm is approximately 0.271 J.

To stretch 4.22+5.63 = 9.85 cm, that is

(9.85/5.63) = 1.750 times the initial stretch amount. The energy required is the square of that ratio (3.06 times) higher than before.

Energy required went from 3.38 J to 10.35 J

The extra work is the difference of thse numbers.