An obnoxious brat assigns his 0.0197-kilogram pet mouse Mickey the role of stunt
ID: 1280802 • Letter: A
Question
An obnoxious brat assigns his 0.0197-kilogram pet mouse Mickey the role of stunt mouse by stuffing him into a spring gun and shooting him up into the air at some angle. The gun's spring has a force constant of 67.1 N/m and is initially compressed 0.149 m. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.47 m/s. How high above his initial location in the gun does Mickey soar? (In case you are worried, a miniature parachute opens at this point and Mickey lands safely. The brat is slightly less obnoxious than we thought.) Take g = 9.81 m/s2.
Explanation / Answer
The energy stored in the spring is,
E = (1/2)kx2
= (1/2)(65.5 N/m)(0.133 m)2
= 0.588 J
The kinetic energy of the person is,
KE = (1/2)mv2
= (1/2)(0.0199 kg)(2.47 m/s)2
= 0.0607 J
The potential enrgy is equal to the difference between the energy of
the person and energy stored in the spring.
mgh = 0.588 J - 0.0607 J
Thus, the required height is,
h = [0.588 J - 0.0607 J]/mg
= [0.588 J - 0.0607 J]/(0.0199 kg)(9.8 m/s2)
= 2.70 m