Question 11, chap 8, sect 7. part 1 of 3 10 points A uniform rod, supported and

Question

Question 11, chap 8, sect 7. part 1 of 3 10 points A uniform rod, supported and pivoted at its midpoint, but initially at rest, has a mass of 86 g and a length 6 cm. A piece of clay with mass 50 g and velocity 1.8 m/s hits the very top of the rod, gets stuck and causes the rod- clay system to spin about the pivot point O at the center of the rod in a horizontal plane. viewed from above the scheme is 1.8 m/s 50 g (a) 86 g (b) (c) Figure: The piece of clay and rod: (a) before they collide, (b) at the time of the collision, and (c) after they collide. After the collisions the rod and clay system has an angular velocity w about the pivot.

Explanation / Answer

initial angular momentum of the system is Li = m*v*r = 50*10^-3*1.8*(0.06/2) = 27*10^-4 kg-m^2/sec

final moment of inertia is If = (1/12)*M*L^2 + m*r^2 = ((1/12)*80*10^-3*0.06^2)+(50*10^-3*(0.06/2)^2) = 6.9*10^-5 Kg-m^2

Using law of conservation of angular momentum

Li = Lf

27*10^-4 = If*wf

27*10^-4 = 6.9*10^-5*wf

wf = 39.13 rad/sec

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