2. (15 points) A spring-loaded dart gun contains an ideal, massless spring with

Question

2. (15 points) A spring-loaded dart gun contains an ideal, massless spring with spring constant k-100 N/m. a) (5 points) A dart is inserted into the gun, compressing the spring by 0.20 m. How much spring potential energy is now stored in the spring? b) (5 points) The gun is now fired. If the dart has a mass of 0.10 kg, what is the kinetic energy of the dart at the instant the spring returns to its original, uncompressed position? c) (5 points) If the gun is fired straight up, how high will the dart travel (above the end of the uncompressed spring)?

Explanation / Answer

a)

PEi=1/2kxi^2=1/2*100*0.20^2 = 2.0 J

b)

By law f conservation of energy

PEf+KEf=PEi+KEi

1/2kxf^2+KEf=PEi+1/2mvi^2

vi=0m/s, xf=0m,

KEf=PEi=2.0j

c)

KEf=1/2mvf^2

½*0.10*vf^2=2.0

vf=6.32m/s

This is initial velocity for earth mass system

Hence vi=6.32m/s

At max height vf=0m/s

Use kinematic eqn,

vf^2=vi^2-2ghmax

Plugging values,

0^2=6.32^2-2*9.8*hmax

hmax=2.04m

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