Mickey, a daredevil mouse of mass 0.0191 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...

Question

Mickey, a daredevil mouse of mass 0.0191 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 93.7 N/m and is initially compressed a distance of 0.149 m from its relaxed position.

If Mickey has a constant horizontal speed of 2.09 m/s while he is flying through the air, how high ℎ above his initial location in the gun does Mickey soar? Assume 𝑔=9.81.

Answer 1

The easiest way to work this problem is by using Conservation of Energy:

Initial Total Energy = Final Total Energy

PE + KE = Gravitational PE + Final KE

1/2 k x^2 +1/2 m v^2 = mgh + 1/2 m v^2

1/2(93.7 N/m)(0.149m)^2 + 0 = (.0191kg)(9.81 m/sec^2)h + 1/2(.0191kg)(2.09 m/sec)^2

1.040 joules = (0.18737 Newtons)h + 0.041715 joules

Solving for h yields h = 5.3285 meters above Mickey's initial height in the gun