a gun shoots pellet of mass 00046kg uses a spring k98 Nm the

Solution

mass of pellet m = 0.0046kg

spring constant k=9.8 N/m

Unstreached length of spring S=0.22meters

Compressed distance S \' = 0.11meters

barrel length L = S = 0.22meter

frictional force f = 0.25 N

The pellet speed in m/s when it exists the gun muzzle v = ?

Potential energy stored in the spring due to compression of the spring U =(1/2) kS\' ²

       U = 0.5 x 9.8 x0.11 ²

          = 0.05929 J

Work done on pellet due to frictional force W = f S \'

                                                                  = 0.25 x 0.11

                                                                  = 0.0275 J

So, from law of conservation of energy ,

kinetic energy of the pellet at end K = U - W

                                     (1/2)mv ² = 0.05929 J - 0.0275 J

                                                   = 0.03179 J

                                              v ² = 2(0.03179) /m

                                                   = 0.06358 /0.0046

                                                   = 13.821

                                                v = 3.717 m/s