quiz17_solution - v_x is unaltered in the air and the ball...

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04/04/08 Physics 201 Quiz 17 A ball of radius R, mass m and moment of inertia I rolls down an incline plane of height h and then up a 45 degree ramp of height h/2 from which it is launched into the air. How high in the air y does the ball go? ans: when the ball reaches the top of the upward ramp it has energy mgh/2=mv^2/2+I omega^2/2=(m+I/R^2)v^2/2 so v^2=mgh/(m+I/R^2)=v_x^2+v_y^2.
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Unformatted text preview: v_x is unaltered in the air and the ball continues to spin. Therefore only the y-contribution to the translational kinetic energy is exchanged for potential energy. mgy=1/2m v_y^2=m/2(mgh/(m+I/R^2)/2) Therefore y=h/4(1+I/(mR^2))....
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