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Plase show all steps and explain. Thank you! A thick steel bar of mass M is pinn

ID: 1454692 • Letter: P

Question

Plase show all steps and explain. Thank you!

A thick steel bar of mass M is pinned at its center so that it is free to rotate without friction about its center of mass, but cannot have translational motion, as shown. If the half-length of the bar is R, then the moment of inertia about the center of mass is I = MR2/3. A small steel sphere of mass m with speed v0 strikes the end of the rod a distance R from the center of the bar and rebounds in the opposite direction at vf, as shown. Kinetic energy is not conserved in this collision. Find the angular velocity w of the rod after the collision and the velocity of the ball. m=Mass of ball (250g) M=mass of bar (4kg) Vb= Velocity of the bar (7m/s) W= angular velocity V0= Initial velocity of ball (20m/s) Vf= final velocity of ball.

Explanation / Answer

conserving linear momentum

0.25 x20 = 0.25vf + 4x7

Vf = -92 m/sec

conserving angular momentum about CM

0.25x20 R = -0.25x92R + 4/3 w R^2

w = 21/R rad/sec