An archer pulls her bowstring back 0.488 m by extending a force that increases uniformly from zero to 251 N.
What is the equivalent spring constant of the bow?
Answer in units of N/m.
k = 251N./0.488m = 514 N/m.
To find the equivalent spring constant of the bow, 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 can be written as:
F = -kx
where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
In this case, the force exerted by the archer is increasing uniformly from zero to 251 N, and the displacement of the bowstring is 0.488 m. We can assume that at the equilibrium position, there is no force applied to the bowstring.
To find the spring constant, we need to rearrange Hooke's Law to solve for k:
k = -F / x
Substituting the given values into the equation:
k = -251 N / 0.488 m
Now, we can calculate the spring constant:
k ≈ -514.34 N/m
The negative sign indicates that the force exerted by the archer is in the opposite direction of the displacement. However, since we are only interested in the magnitude of the spring constant, we can ignore the negative sign.
Therefore, the equivalent spring constant of the bow is approximately 514.34 N/m.