The caber toss is a traditional Scottish sport that involves hurling a caber, which is essentially a large piece of a tree: a caber is a 6 m long, 80 kg tree trunk. Large strong people hurl these and the goal is to get the caber to land as far away as possible and rotate in the air, so what was the highest part of the trunk initially is actually the part that hits the gound first. See this clip to understand how the caber rotates.
It's HARD to do this. To see how hard, consider a perfectly vertical caber with one end on the ground. You then launch the caber vertically with some speed v0 and give it a rotation. What is the minimum kinetic energy in Joules you need to give the caber so that when it lands the caber is perfectly vertical again, but the OTHER end of the caber hits the ground?
2133
238J
To determine the minimum kinetic energy needed to achieve the desired outcome in the caber toss scenario, we can consider the conservation of angular momentum.
The angular momentum of an object is given by the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In this case, we have a caber being launched vertically with an initial speed v0 and given a rotation. The moment of inertia (I) for a long thin rod rotating about one end is given by the equation I = (1/3)ML^2, where M is the mass of the caber and L is its length.
Let's assume that the caber lands perfectly vertical with its other end hitting the ground. This means that the final angular velocity (ω) would need to be zero.
Considering the conservation of angular momentum, we can equate the initial angular momentum (L0) to the final angular momentum (Lf). Since the caber starts from rest at the vertical position, its initial angular momentum is zero, i.e., L0 = 0.
The final angular momentum can be calculated as Lf = Iω. Given that ω = 0, Lf will also be zero.
Setting L0 equal to Lf, we have:
0 = Iω
Substituting the expression for the moment of inertia (I) and rearranging the equation, we get:
0 = (1/3)ML^2 * 0
This equation implies that the minimum kinetic energy required to achieve the desired outcome is zero. In other words, there is no need for any initial kinetic energy in order to land the caber with the other end hitting the ground.
However, it's important to note that in the real world, there will always be some friction and air resistance acting on the caber, which will affect its motion and require some initial kinetic energy to overcome those dissipative forces.