Question

One type of bb gun uses a spring-driven plunger to blow the bb from its barrel.

(a) Calculate the force constant of its spring if you must compress it 0.135 m to drive the 0.0775 kg plunger to a top speed of 26.0 m/s.
a) 450 N/m
b) 550 N/m
c) 650N/m
d) 750 N/m

Answer 1

To calculate the force constant of the spring, use the equation F = k * x. Given the mass and speed of the plunger, calculate the force. Plug the force and compression distance into the equation for k.

Step-by-step explanation:

To calculate the force constant of the spring, we can use the equation:

F = k * x

Where F is the force, k is the force constant, and x is the compression distance. Rearranging the equation, we can solve for k:

k = F / x

Given that the mass of the plunger is 0.0775 kg and its top speed is 26.0 m/s, we can calculate the force using the equation:

F = 0.5 * m * v^2

Using the given values, we find that the force is 67.045 N. Plugging this value and the compression distance (0.135 m) into the equation for k, we get:

k = 67.045 N / 0.135 m = 496.63 N/m

Therefore, the correct answer is 550 N/m.