Move over Jeff Bezos, this invention is about to make you the richest person in the world. You have just invented the OyOy. It is the very latest in home safety and is so easy to use! (Attatched Figure) If your building is on fire, simply reach out and grab the cord on the OyOy and you will be lowered safely toward the ground at a low velocity. The OyOy has a total mass of M = 93.5 kg and is shaped like a cylinder of radius R = 0.950 meters. The secret to the operation of the OyOy is its patented shaft whose radius is only r = 0.0840 meters. The cord is wound around the small shaft and this is the secret to your low velocity. Rotation-OyOy-Energy (Figure) We will use the approximation that the shaft is of negligible mass compared to the total. This means that you can treat the entire OyOy as though it is a solid cylinder with mass M and radius R. Imagine that a customer of mass m = 72.0 kg is using the OyOy and begins his decent from an initial height of y0 = 13.70 meters. Determine all the following: The FORMULA for the moment of Inertia: I = ? The FORMULA for the relationship between w and v: w = ? The velocity of the customer at the ground: v = ? m/s NOTE: Be very careful because there are TWO radii in the problem: R and r The first two parts of this problem want formulas, not numerical values.
Move over Jeff Bezos, this invention is about to make you the richest person in the world. You have just invented the OyOy. It is the very latest in home safety and is so easy to use!
(Attatched Figure) If your building is on fire, simply reach out and grab the cord on the OyOy and you will be lowered safely toward the ground at a low velocity. The OyOy has a total mass of M = 93.5 kg and is shaped like a cylinder of radius R = 0.950 meters. The secret to the operation of the OyOy is its patented shaft whose radius is only r = 0.0840 meters. The cord is wound around the small shaft and this is the secret to your low velocity.
Rotation-OyOy-Energy (Figure)
We will use the approximation that the shaft is of negligible mass compared to the total. This means that you can treat the entire OyOy as though it is a solid cylinder with mass M and radius R. Imagine that a customer of mass m = 72.0 kg is using the OyOy and begins his decent from an initial height of y0 = 13.70 meters.
Determine all the following:
The FORMULA for the moment of Inertia: I = ?
The FORMULA for the relationship between w and v: w = ?
The velocity of the customer at the ground: v = ? m/s
NOTE:
Be very careful because there are TWO radii in the problem: R and r
The first two parts of this problem want formulas, not numerical values.
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