An obnoxious brat assigns his 21.9-gram pet mouse Mickey the role of stunt mouse
ID: 1277880 • Letter: A
Question
An obnoxious brat assigns his 21.9-gram 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 77.5 N/m and is initially compressed 13.7 cm. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.19 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. Assume that the mass of the spring is small enough that the spring's change in potential energy during the spring's expansion is negligible.
Explanation / Answer
We can solve this question by using the conservation of energy.
The spring energy is converted to the kinetic energy and the gravitational energy.
SE = KE + GE
(1/2) k x2 =(1/2) m v2 + mgh.
0.5*54.7*.1332 = 0.5*0.0219*2.132 + 0.0219*9.81*h.
3.64302 = 0.0233454 + 0.214839*h.
h= (3.64302 - 0.0233454) / 0.214839
h = 16.8483124572
h= 16.85m (approx.)