An obnoxious brat assigns his 0.0199-kilogram pet mouse Mickey the role of stunt

Question

An obnoxious brat assigns his 0.0199-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 65.5 N/m and is initially compressed 0.133 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

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