An obnoxious brat assigns his 18.5-gram pet mouse Mickey the role of stunt mouse
ID: 1965739 • Letter: A
Question
An obnoxious brat assigns his 18.5-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 53.1 N/m and is initially compressed 12.5 cm. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.35 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.
= _____________________ m
Explanation / Answer
First let's find out how much horizontal kinetic energy the mouse has when shot: K = (1/2)mv^2 = (1/2)(0.0185 kg)(2.35 m/s)^2 = 0.0511 J Now find how much kinetic energy is transferred to the mouse from the compressed spring: U = (1/2)kx^2 = (1/2)(53.1 N/m)(0.125 m)^2 = 0.4148 J Subtract the horizontal kinetic energy from this value to get how much energy is transferred into vertical movement: K = 0.4148 - 0.0511 = 0.3637 J We know that energy is conserved so: K = mgh 0.3637 J = (0.0185 kg)(9.81 m/s^2)h h = 2.004 m