Question

Get two spherical or cylindrical objects of equal mass, such as two bottles of water or soda. Freeze one of them (don't freeze full glass bottles, they will break due to the expansion of the water as it freezes.) Place them on a tilted surface such as a table that you have propped up on one side. Which one wins the race and why? Assuming no slipping, how long does each one take to get to the bottom? Verify this makes sense using calculations from the class. You may need to use a bubble level app on your phone (Rigid provides a free one) to obtain the angle of your surface.

Answer 1

aand see that is a by by the emengo The Aurates Filled bottle rolling down with incline rolling bottle better described by a model ignoring all internal the bottle is approximated motion where material point sliding down an. incline. or isit better described rolling down the incline without skidding, a rigid solid cylinder answer is presented here with emo equation of the moving body freezed water bottle can be treated as a. solid cylinder which mase is taken as m and radius igr. so, inertia, of the cylinder is Is Imre It is considered that it nolls without so its ratio of Lamp m R² MR² me² so acceleration of the rolling cylinder givear g sino slipping mr mp3 2 mm is ivear as sime --gsino itt myz where o is the inclination angle with horizontal h= laino h lahraime by the cylinder to each bottom is given by time taken 20

Putting mechanical Eero idiorg 4 g value of e and a © 0.66g.simo For water bottle cum freezed ) Conservation of down, the incline, having energy for the point sliding velocity gives following relationship between kinetic and potential energies I mus=ogh where m >mace of the material point, V is its speed, his the height of the incline and is free fall acceleration foom equation height of the incline h= lsino From equation ) it can be written that after putting h 1v² = gesimo If a body is moving on a incline without Shipping that its acceleration will remain cornstant and from kimematic equation if f a body, start from rest them it acceleration a la luz from equation 5 and 6 =gsimo

by comparison of equation ☺ and equation & it can be said liquid water bottle will take less time to Each bottom, This is because coupling between the walls and liquid is more important in Sonall diameter containers. The torque of viscous liquid force acting on the liquid is proportional to the area of the side wall of the bottle and its nadius.
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