A child assigns his 0.0205-kilogram pet mouse Mickey the role of stunt mouse by

Question

A child assigns his 0.0205-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 86.7 N/m and s initially compressed 0.139 m. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.11 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.) Take g 9.81 m/s2 Number

Explanation / Answer

mass of the mouse = m = 0.0205 kg

spring constant of the spring = k = 86.7 N/m

initial compression of the spring = x = 0.139 m

speed at maximum height = V = 2.11 m/s

here in this problem, we will use Conservation of energy principle

When spring is compressed, Total energy is just the spring potential energy.

so Total energy when spring compressed = spring potential energy = (0.5) k x2                              Eq-1

Lets assume the height at the highest point as ''h''

Then Potential energy at Highest point = mgh

Kinetic energy at highest point = (0.5)mV2

So Total energy at highest point = Kinetic energy + Potential Energy = mgh + (0.5)m V2     Eq-2

Using conservation of energy

Total energy when spring compressed = Total energy at highest point

(0.5) k x2 = mgh + (0.5) m V2

(0.5) (86.7 N/m) (0.139 m)2 = (0.0205 kg) (9.8 m/s2) h + (0.5) (0.0205 kg) (2.11 m/s)2

0.838 J = (0.2009 N) h + 0.0456 J

(0.2009 N) h = 0.838 J - 0.0456 J

(0.2009 N) h = 0.7924 J

h = 0.7924 J / 0.2009 N

h = 3.94 m

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