An archer, about to shoot an arrow, is applying a force of +250 N to a drawn bow string. The bow behaves like an ideal spring whose spring constant is 510 N/m. What is the displacement of the bow string?

k x = 250 = 510 x

so
x = 250/510

thanks Damon

Well, this is quite a calculating situation! Let's see if I can hit the bullseye with this answer.

To figure out the displacement of the bow string, we can use Hooke's Law, which states that the force applied on a spring is directly proportional to the displacement of the spring.

Now, Hooke's Law equation is F = -kx, where F is the force, k is the spring constant, and x is the displacement. However, notice that the force is provided as +250 N, so to make it work with Hooke's Law, we'll consider it as -250 N (because opposite forces have opposite signs).

Now we can rearrange the equation to solve for x: x = -F / k.

Plugging in the values, we have:
x = -(-250 N) / 510 N/m

Simplifying, we get:
x ≈ 0.49 m

So, the displacement of the bow string is approximately 0.49 meters. That's quite a stretch!

To calculate the displacement of the bowstring, we can use Hooke's Law, which states that the force applied is equal to the spring constant multiplied by the displacement. The formula is given by:

F = k * x

Where:
F = force applied to the bowstring (250 N)
k = spring constant (510 N/m)
x = displacement of the bowstring (unknown)

Rearranging the formula to solve for x:

x = F / k

Substituting the given values:

x = 250 N / 510 N/m

Evaluating this expression:

x = 0.49 m

Therefore, the displacement of the bowstring is 0.49 meters.

To find the displacement of the bowstring, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring.

Hooke's Law can be expressed as F = kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement.

In this case, the force applied by the archer is +250 N, and the spring constant is 510 N/m.

We can rearrange Hooke's Law to solve for the displacement:
x = F / k

Substituting the given values, we have:
x = 250 N / 510 N/m

Dividing the force applied by the spring constant, we get:
x = 0.49 m

Therefore, the displacement of the bowstring is 0.49 meters.