Consider the popgun in the figure below. The launching mechanism consists of a t

Question

Consider the popgun in the figure below. The launching mechanism consists of a trigger-released spring. The spring is compressed to a position y_A, and the trigger is fired. The projectile of mass m rises to a position y_C above the position at which it leaves the spring, indicated in the figure as position y_B = 0. Consider a firing of the gun for which m = 40.0 g, y_A = -0.110 m, and y_C = 23.0 m. Suppose, however, there is a friction force of magnitude 2.30 N acting on the projectile as it rubs against the interior of the barrel. The vertical length from point (A) to the end of the barrel is 0.680 m. (a) After the spring is compressed and the popgun fired, to what height does the projectile rise above point (B)? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all Intermediate results to at least four-digit accuracy to minimize roundoff error. (b) Draw four energy bar charts for this situation. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

Given

  
   m = 40 g = 0.040 kg, g= 9.8 m/s2

   frictional force is F = 2.3 N along the barrel of length s = 0.680 m

from the given data as there is no friction force acting the projectile can reach Yc = 23.0 m

because the friction force acting in opposite direction to its displacement so the projectile reaches less than 23 m

work done by the frictional force is = F*s = 2.3*0.680 = 1.564 J

now the height reached by projectile is

       mgh = W ==> h = W/mg = 1.564/(0.040*9.8) m = 3.9898 m less than the actual height that is

H = Yc-h = 23 -3.9898m = 19.0102 m

so the height the projectile can reach is 19 m

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