Mickey the Daredevil Mouse

Question

Mickey, a daredevil mouse of mass 0.0206 kg, is attempting to become the world's first "mouse cannonball." He is loaded into a spring‑powered gun pointing up at some angle and is shot into the air. The gun's spring has a force constant of 67.8 N/m and is initially compressed a distance of 0.142 m from its relaxed position.

If Mickey has a constant horizontal speed of 2.49 m/s while he is flying through the air, how high above his initial location in the gun does Mickey soar? Assume g=9.81 m/s^2

Answer 1

The total potential energy that is provided to the system is the spring potential energy:

E_spring = 1/2kx² = 1/2(67.8)(0.142)² = 0.68356 joules

All that energy is converted into kinetic energy as Mickey leaves the spring. And then at Mickey's maximum height he has horizontal kinetic energy (associated with his horizontal velocity of 2.49 m/s) plus he has gravitational potential energy:

E_spring = 0.68356 joules = E_kinetic + E_{gravitational potential} = 1/2mv² + mgh

So 0.68356 = 1/2(0,0206)(2.49²) + 0.0206(9.81)h

0.68356 = 0.06386 + 0.202086h

0.619699 = 0.202086h

h = 3,07 m