A toy cannon uses a spring to project a 5.35-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.35-g soft rubber ball. The spring is originally compressed by 5.04 cm and has a force constant of 8.09 N/m. When the cannon is fired, the ball moves 15.4 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 9 N on the ba (a) With what speed does the projectile leave the barrel of the cannon? 1,40m/s (b) At what point does the ball have maximum speed? 465 cm (from its original position) (c) What is this maximum speed? 1.27 Note that the initial potential energy of the spring is now found in several different forms. Make certain you can list each of them before writing down an energy equation. m/s

Explanation / Answer

Part C

Using energy conservation between starting and max speed point

KEi + PEi + Wf = KEf + PEf

KEi = 0, Since Vi = 0

0.5*k*xi^2 - Ff*d = 0.5*m*Vf^2 + 0.5*k*xf^2

xi = 5.04 cm = 5.04*10^-2

xf = Ff/k = 0.0319/8.09 = 3.94*10^-3

k = 8.09 N/m

m = 5.35 gm = 5.35*10^-3 kg

Ff = 0.0319 N

d = 4.65 cm = 4.65*10^-2 m

Using above values

0.5*8.09*(5.04*10^-2)^2 - 0.0319*4.65*10^-2 - 0.5*8.09*(3.94*10^-3)^2 = 0.5*5.35*10^-3*Vf^2

0.5*5.35*10^-3*Vf^2 = 8.7288*10^-3

Vf = sqrt (8.7288*10^-3/(0.5*5.35*10^-3))

Vf = 1.81 m/sec

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