A marble (radius 1.0 cm and mass 9.5 g) rolls without slipping down a ramp of vertical height 10 cm. What is t?

Thanks, chad, for referring me to Table 7.4, but I don't think I need it. Use conservation of energy. PE_top + KE_top = PE_bottom + KE_bottom PE_top = mgh, where "h" is the ramp's height (the value we want to find).

We aren't given "m", but don't worry about that--hopefully that variable will cancel out in the end. KE_top is a combination of the balls translational KE (=½m(v_top)²), and its rotational KE (=½I(?_top)²). That is: KE_top = ½m(v_top)² + ½I(?_top)² "I" is the ball's moment of inertia, which equals (2/5)mR² (R=ball's radius).

That was probably in that table 7.4 that you wanted me to look at. Again, we don't know "R", but don't fret it right now. Since it's rolling without slipping, "?

_top", the ball's initial angular velocity, is related to its linear velocity like so:? _top = v_top/R So that means the rotational KE is: ½I(?_top)² = ½(2/5)mR²(v_top/R)² = ½(2/5)m(v_top)² (Yay! The "R" cancelled out.) And that means the total KE_top is KE_top = ½m(v_top)² + ½(2/5)m(v_top)² = (7/10)m(v_top)² Now at the bottom, we have: PE_bottom = 0.

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