Question

Mickey, a daredevil mouse of mass 0.0227 kg,0.0227 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 51.1 N/m51.1 N/m and is initially compressed a distance of 0.129 m0.129 m from its relaxed position. If Mickey has a constant horizontal speed of 2.27 m/s2.27 m/s while he is flying through the air, how high ℎh above his initial location in the gun does Mickey soar? Assume ????=9.81 m/s2.

Answer 1

Answer:

1.65 m

Explanation:

Energy from spring, $E_{s}$ is given by

$E_{s}=0.5kx^{2}$ where k is spring constant and x is the compression distance

$E_{s}=0.5*51.1*0.129^{2}= 0.425178$

$E_{s}=0.425 J$

Kinetic energy, KE at the highest point is given by

$KE=0.5mv^{2}$ where m is mass and v is velocity

KE=0.5*0.0227*2.27= 0.058485 J

Potential energy, PE of spring is given by

PE=mgh where g is gravitational constant and h is maximum height reached by the mouse

PE=0.0227*9.81= 0.222687h

According to the principle of conservation of energy, the potential energy of the compressed spring is equal to the potential and kinetic energy of the mouse at the maximum high point.

$E_{s}=PE+KE$

0.425=0.222687h+0.058485

h=(0.425-0.058485)/ 0.222687=1.646671 m

h=1.65 m