An archer, about to shoot an arrow, is applying a force of +260 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?

Question

An archer, about to shoot an arrow, is applying a force of +260 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?

Answer 1

To find the displacement of the bow string, we can use Hooke's Law, which states that the force exerted by an ideal spring is directly proportional to the displacement of the spring.

Hooke's Law: F = -kx

Where:
F = Force exerted by the spring (260 N)
k = Spring constant (510 N/m)
x = Displacement of the spring (unknown)

Rearranging the equation, we have:
x = -F/k

Substituting the given values, we get:
x = -260 N / 510 N/m
x = -0.51 m

However, since the question asks for displacement, we need to take the absolute value of the displacement, as displacement is a scalar quantity. Therefore, the displacement of the bow string is 0.51 m.