The muzzle velocity of a typical 500 g spud is 25 m/s . The force given by the spud is K/(x+.09) where x is the distance of the barrel in meters. If the length of the barrel is 75 cm, what is the constant K? What is the force on the spud?

Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter6: Motion In Two Dimensions
Section6.3: Relative Velocity
Problem 27PP
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The muzzle velocity of a typical 500 g spud is 25 m/s . The force given by the spud is K/(x+.09) where x is the distance of the barrel in meters. If the length of the barrel is 75 cm, what is the constant K? What is the force on the spud?

Expert Solution
Step 1

Work done on spud = change in kinetic energy

               F.dS =KFinal-KInitial

              Fdxcos0 =12mvFlinal2-12mvInitial2    Here F=Kx+0.09 , VFinal=25 m/s , VInitial=0 , m=500g=0.5 Kg

              00.75Kx+0.09dx=12×0.5×(25)2-0

              Kloge(x+0.09)00.75=156.25

             K(loge(0.75+0.09)-loge(0+0.09))=156.25           

              Using logem-logen=logemn

            Kloge0.840.09=156.25

             K×2.23=156.25

              K= 70.067

 

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