Canisters Rolling Down a Half Pipe

In summary, the problem involves calculating the velocity of a canister of nerve gas that is rolled towards Bond at the bottom of a curved trench. The canister has a mass of 16 kg, a radius of 0.8 m, and a rotational inertia of 10 kg*m2. The trench has a radius of 3.5 m. Using conservation of energy and the equation for calculating rotational kinetic energy, the final velocity of the canister is found to be sqrt((2*m*g*R3) / (m*R2 + I)). However, there may be an error in the calculations as the computer is showing the answer as incorrect.
  • #1
onegreatweb
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Homework Statement


Oddjob rolls a canister of nerve gas twoards Bond, who is at the bottom of a curved trench. The canister has a mass of 16 kg, a radius of r = 0.8 m, and a rotational inertia of 10 kg*m2. It starts with no velocity. If the trench has a radius of R = 3.5 m, how fast is the canister moving when it reaches Bond?

Homework Equations



Conservation of Energy: Ei = Ef


The Attempt at a Solution



PEi = KEf + KErotation
mgR = (1/2)m*vf2 + (1/2)I*ω2
mgR = (1/2)m*vf2 + (1/2)I*(vf/R)2
mgR = vf2 (m/2 +I/(2R2))
vf2 = (2*m*g*R3) / (m*R2 + I)
vf = sqrt((2*m*g*R3) / (m*R2 + I))

I plugged in all the numbers but the computer says this is incorrect. Where did I go wrong?

Edit: I posted the wrong question initally. Oops. This is the correct one with the correct image.
 

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  • #2
Is Bond at the bottom of the trench? Or on the opposite side?
 

1. How does the size of the canister affect its rolling speed down a half pipe?

The size of the canister does not have a significant impact on its rolling speed down a half pipe. As long as the canister is round and has a smooth surface, it will roll down the half pipe at a consistent speed regardless of its size.

2. What is the role of gravity in the motion of a canister down a half pipe?

Gravity is the main force that causes the canister to roll down the half pipe. As the canister moves down the slope of the half pipe, gravity pulls it towards the bottom, causing it to accelerate and increase in speed.

3. Can the shape of the half pipe affect the rolling motion of the canister?

Yes, the shape of the half pipe can affect the rolling motion of the canister. A half pipe with a steeper slope will cause the canister to roll at a faster speed, while a shallower slope will result in a slower rolling speed. Additionally, a half pipe with a rough or uneven surface may cause the canister to roll at an irregular or slower speed.

4. Does the mass of the canister affect its rolling motion down a half pipe?

The mass of the canister does not directly affect its rolling motion down a half pipe. However, a heavier canister may have more momentum and may require more force to stop or change direction once it is rolling down the half pipe.

5. What other factors besides gravity can affect the rolling motion of the canister down a half pipe?

The rolling motion of the canister down a half pipe can also be affected by the surface of the half pipe, the shape of the canister, and any external forces acting on the canister, such as friction or air resistance. Additionally, any imperfections or irregularities in the half pipe or canister can also impact the rolling motion.

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