A toy cannon uses a spring to project a 5.26 g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.26 g soft rubber ball. The spring is originallycompressed by 4.95 cm and has a forceconstant of 8.09 N/m. When the cannon isfired, the ball moves 14.6 cm through thehorizontal barrel of the cannon, and there is a constant frictionalforce of 0.0320 N between the barrel andthe ball. (a) With what speed does the projectile leavethe barrel of the cannon?
(b) At what point does the ball have maximum speed?
(c) What is this maximum speed? I know that I figured out part A. but I cannotfigure out what i am doing wrong for b or c. For be I thought that the max speed would occurat 4.95 cm but that is not right. and for c I thought that i would havekx^2=mv^2. What am I doing worng (a) With what speed does the projectile leavethe barrel of the cannon?
(b) At what point does the ball have maximum speed?
(c) What is this maximum speed? I know that I figured out part A. but I cannotfigure out what i am doing wrong for b or c. For be I thought that the max speed would occurat 4.95 cm but that is not right. and for c I thought that i would havekx^2=mv^2. What am I doing worng

Explanation / Answer

            Given that the masss of the ball is m = 5.26 g = 5.26*10-3 kg             The compressed distance is x = 4.95 cm = 4.95*10-2m               The force constant of the spring is K = 8.09 N/m              Thedistance travelled in the barrel is d = 14.6 cm = 0.146 m              The frictional force is f = 0.0320 N -----------------------------------------------------------------------------     (c) From the conservation ofenergy at the spring is in compressed postion and at the ballreleases is                                    (1/2)Kx2= (1/2)mV2   (  If the gun ishorizontal )                                 (1/2)Kx2 = (1/2)mV2 + mgx        ( if the gun isverticle )                                              V = [ Kx2 / m - 2gx ] 1/2                                                  = ---------- m/s      (b) The maximum velocity of the gun atthe initial position of projection that is x= 0                                                                                                        = ---------- m/s      (b) The maximum velocity of the gun atthe initial position of projection that is x= 0                                                      

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