Question

I really need help on D part of the following problem:

A clever engineer designs a "sprong" that obeys the force law F subscript e = -q(x - x subscript e)^3, where x subscript e is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, x subscript e = 0m . Then F subscript x = -qx^3.

Part A:

What are the units of q? N/m^3 (correct)

Part B:

graph

Part C:

Find an expression for the potential energy of a stretched or compressed sprong. U(x) = 1/4qx^4 (correct)

Part D:

A sprong-loaded toy gun shoots a 24 g plastic ball. What is the launch speed if the sprong constant is 4.3 × 10^4 N/m^3, with the units you found in part A, and the sprong is compressed 11 cm? Assume the barrel is frictionless.

Answer 1

KE=Integral force.dx=1/4q x^4

1/2 m v^2=1/4 4.3E4N/m^4 (.11)^4
solve for v
Put mass in kilogram units.