my teacher gave me this problem as extra credit - but I'm not sure how to approach it. I feel like there's too many extra things going on, and am not sure on what variables to focus on? Any help is appreciated...
Question 1)
One winter break, while visiting Scotland's Loch Ness, you stop to tour the ruins of Urquhart
Castle, which are found on the loch's western shore. A truck carrying barrels passes and, as it does, a
sealed barrel and a spare lid fall from the truck and land by the side of the road. The barrel comes to
rest at the very top of the snowy slope that leads down to the loch's shoreline. A few moments later, the
wind from the next car is just enough to push the barrel over the edge to slide, not roll, down the slick
slope. Once the barrel reaches the bottom, it begins to roll across the level shore. It rolls over exactly 3
times before rolling into a tree branch at the water's edge. Upon hitting the branch, the barrel is
knocked up and into the air, at what appears to be a 45 degree angle. It flies through the air for about 2
seconds before landing in the water. After it is in the water for a few moments, you notice that the
barrel is floating right side up with about half of it above the surface. To your astonishment, a small
aquatic creature, the likes of which you have never seen, begins to play with the barrel. Following one
particularly strong nudge to the barrel, which leaves the barrel bobbing up and down in the water, the
creature is scared away by shouts from other tourists. After recording that the barrel bobs up and down
once every 1.36 seconds you walk along the road to further investigate what you have just witnessed.
Your investigation reveals that the mass of the spare lid is 6.8 kg, the road is 14m above the shore, and
that distance from the bottom of the slope to the water's edge is 5.4m.
Now, you have enough information to answer a very important question, namely, was there any
whiskey in the barrel and, if so, how much?
Note on approximating the rotational inertia of a barrel of low-viscosity liquid:
As with any collection of objects, you can determine the rotational inertia of a barrel by adding
up the rotational inertias of its parts. A barrel can be thought of us a thin hollow cylindrical shell with
two disks for lids. Since the radius of the shell is the same as the radius of the lids, the total rotational
inertia of the barrel is given by I = MS R2 + 2 (½ ML R2 ) = ( MS + ML )R2 where MS is the mass of the
shell and ML is the mass of one lid. You may wonder why I have not taken into account the effect of
any liquid the barrel may be containing. If the viscosity of the liquid is low, as we will assume in this
problem, the liquid will not rotate when the barrel rotates and will thus not contribute to the rotational
inertia.
Question 1)
One winter break, while visiting Scotland's Loch Ness, you stop to tour the ruins of Urquhart
Castle, which are found on the loch's western shore. A truck carrying barrels passes and, as it does, a
sealed barrel and a spare lid fall from the truck and land by the side of the road. The barrel comes to
rest at the very top of the snowy slope that leads down to the loch's shoreline. A few moments later, the
wind from the next car is just enough to push the barrel over the edge to slide, not roll, down the slick
slope. Once the barrel reaches the bottom, it begins to roll across the level shore. It rolls over exactly 3
times before rolling into a tree branch at the water's edge. Upon hitting the branch, the barrel is
knocked up and into the air, at what appears to be a 45 degree angle. It flies through the air for about 2
seconds before landing in the water. After it is in the water for a few moments, you notice that the
barrel is floating right side up with about half of it above the surface. To your astonishment, a small
aquatic creature, the likes of which you have never seen, begins to play with the barrel. Following one
particularly strong nudge to the barrel, which leaves the barrel bobbing up and down in the water, the
creature is scared away by shouts from other tourists. After recording that the barrel bobs up and down
once every 1.36 seconds you walk along the road to further investigate what you have just witnessed.
Your investigation reveals that the mass of the spare lid is 6.8 kg, the road is 14m above the shore, and
that distance from the bottom of the slope to the water's edge is 5.4m.
Now, you have enough information to answer a very important question, namely, was there any
whiskey in the barrel and, if so, how much?
Note on approximating the rotational inertia of a barrel of low-viscosity liquid:
As with any collection of objects, you can determine the rotational inertia of a barrel by adding
up the rotational inertias of its parts. A barrel can be thought of us a thin hollow cylindrical shell with
two disks for lids. Since the radius of the shell is the same as the radius of the lids, the total rotational
inertia of the barrel is given by I = MS R2 + 2 (½ ML R2 ) = ( MS + ML )R2 where MS is the mass of the
shell and ML is the mass of one lid. You may wonder why I have not taken into account the effect of
any liquid the barrel may be containing. If the viscosity of the liquid is low, as we will assume in this
problem, the liquid will not rotate when the barrel rotates and will thus not contribute to the rotational
inertia.