Help challenging problem on energy and projectile motion

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SUMMARY

The discussion revolves around a physics problem involving energy and projectile motion, specifically analyzing the trajectory and behavior of a barrel that falls, slides, rolls, and ultimately lands in water. Key parameters include the mass of the spare lid at 6.8 kg, a height of 14 meters from the road to the shore, and a distance of 5.4 meters from the slope's bottom to the water's edge. The barrel's motion is characterized by a 45-degree launch angle after being nudged by a tree branch, and it bobs in the water every 2.4 seconds. The central question posed is whether the barrel contained whiskey and, if so, how much.

PREREQUISITES
  • Understanding of basic physics concepts such as energy conservation and projectile motion.
  • Familiarity with kinematic equations and their application in real-world scenarios.
  • Knowledge of buoyancy principles and how they affect floating objects.
  • Ability to perform calculations involving mass, height, and distance in a physics context.
NEXT STEPS
  • Study the principles of energy conservation in sliding and rolling motion.
  • Learn how to calculate projectile motion using initial velocity and launch angle.
  • Explore buoyancy calculations to determine the volume of whiskey that could fit in the barrel.
  • Investigate real-world applications of these physics concepts in engineering and design.
USEFUL FOR

Physics students, educators, and anyone interested in applying mechanics to solve practical problems involving motion and buoyancy.

jmb07
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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 2.4 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?
 
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jmb07 said:
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 2.4 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?

What is your approach to the problem?
 

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