Question

Experiment 2 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

Water Bottles cylindrical objects [Freezed and unfreezed) * Here, the two water bottles of equal mass, can be treated as two cylindrical objects. A rolling water bottle better described by a model ignoring all internal motion where the bottle is approximated by a material point sliding down incine cool is better described by a rigid solid cylinder rolling down without skidding, the answer is presented here with energy equation of the moving body. h * For freezed water bottle:- Here, the water bottle freezed can be treated as a solid cylinder, which has mass'm' and radius 8. I me? => So, Inertia of the cylindex is I ? mer >> So, accelration of rolling cylinder is given as gsino gsino If I 1+1 3 mo 5 a gsino 2 la= agsino 3

Now, the figure shows inclination angle with the horizontal. h= lsino l= h sino Now, time taken by the cylinder to reach bottom is given by ti al a Now substitute land 'a' values in £q , wege t= 2x h ag sino 3 It= - 2x h 10.66g sino * Fox unfreezed water bottle:- Now, conservation of mechanical energy for the point sliding down the incline, having zero initial Velocity, gives following relationship between kinetic energy and potential energy. I mu?= mgh where, m = mass of the material/object V - Speed of the object h = height of the incline. = Free fall accelration. 2

Now, From E90, we know that height, [h= lsino Now, from Eq@, we can write as 1 bhu² nigh ₂ vzgh I v3 glsino 6 [h= lsino] * If a body is moving on an iso incline without skidding, then its accelration with in it will remain as constant and from the kinematic Equation if a body starts from the rest position, then its accelration is al= 1 v² 2 Now, from Equations and ③ and ①, we get a= g sino * By substituting Eq@ in Eq@, we will get time to reach bottom of the incline. to al gsino » [a=gsino

* Now, by comparing sq 3 and Eq , it can be solid liquid water bottle, that it will take less time to reach the bottom. This is because, coupling between the walls and liquids is more important in small diameter containers. The torque of viscous fluid force acting on the liquid is directly proportional to the area of the side wall of the bottle and its radius.
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