remains motionless? A projectile of mass m r is travelling st a constant velocit
ID: 2063997 • Letter: R
Question
remains motionless? A projectile of mass m r is travelling st a constant velocity v rightarrow 0 toward a stationary disk of mass M and radius R that is free to rotate its axis(Figure 10-54). Before impact, the projectile is traveling along a line displaced a distance b below the axis. The projectile strikes the disk and strikes the disk and sticks to point B, Model the projectile as a point mass. (a) Before impact, what is the total angular momentum L 0 of the disk-projectile system about the axis? Answer the following questions in terms of the symbols given at the start of this problem (b) What is the angular speed on of the disk-projectile system just after the impact? (c) What is the kinetic energy of the disk-projectile system after impact? (d) How much mechanical energy is lost in this collision? FIGURE 10-54Explanation / Answer
a)
L = rmv sin = mp b v0
b)
= L/I
= L / (MR2/2 + mR2)
= mp b v0 / (MR2/2 + mR2)
c)
K = 0.5 I 2
= 0.5 * (mp b v0)2 / (MR2/2 + mR2)
d)
E = 0.5 mp v02 - 0.5 * (mp b v0)2 / (MR2/2 + mR2)
= 0.5 mp v02 (1 - 0.5 * (mp b2)/ (MR2/2 + mR2))
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