An obnoxious brat assigns his 0.0209-kilogram pet mouse Mickey the role of stunt
ID: 2120495 • Letter: A
Question
An obnoxious brat assigns his 0.0209-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 87.5 N/m and is initially compressed 0.141 m. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.43 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
mass of the mouse = m = 20.9 g
spring constant = k = 87.5 N/m
compression = x = 14.1 cm
acceleration due to gravity = g = 9.81 ms-2
total initial energy = 1/2 k x2 = 87.5*0.1412/2 = 0.86979375 = 0.87J
total final energy = mgh+1/2mv2 = 20.9*9.81*h/1000 + 1/2(20.9*2.432)/1000
= 0.205029 h+0.061706205
Equating the energies, we obtain 0.205029h=0.87-0.0617
=> h =3.942369128269659 m