A pulley is used to lift a heavy mass from the floor to the platform. The IMA of the system is 5 and the AMA is 2.5. What is the
2 answers:
Answer:
efficiency= or 50%
Explanation:
IMA means Ideal Mechanical Advantage, and it indicates the ratio between the input forces and the output forces without taking into consideration the force needed to overcome friction. In pulleys, this is calculated by counting the number of ropes on the system that in this case is 5
IMA = 5
IMA is greater to the AMA because it doesn't take into consideration friction.
AMA is the Actual Mechanical Advantage, and it is the measure of the usefulness of the pulley, and it indicate the ratio between the output force (Fo) and the input force (Fi). The smaller this ratio, the less useful is the pulley, meaning, it does not simplify the job it is designed to ease, for example, a pulley that does not reduce the force needed to lift a load.
AMA=2.5
So from these two definitions, if we have the actual force ratio and the ideal force ratio, we basically have the "what it is" and the "what could be", a very crude representation of efficiency:
efficiency= or 50%
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Here is the full question:
The rotational inertia I of any given body of mass M about any given axis is equal to the rotational inertia of an equivalent hoop about that axis, if the hoop has the same mass M and a radius k given by:
The radius k of the equivalent hoop is called the radius of gyration of the given body. Using this formula, find the radius of gyration of (a) a cylinder of radius 1.20 m, (b) a thin spherical shell of radius 1.20 m, and (c) a solid sphere of radius 1.20 m, all rotating about their central axes.
Answer:
a) 0.85 m
b) 0.98 m
c) 0.76 m
Explanation:
Given that: the radius of gyration
So, moment of rotational inertia (I) of a cylinder about it axis =
k = 0.8455 m
k ≅ 0.85 m
For the spherical shell of radius
(I) =
k = 0.9797 m
k ≅ 0.98 m
For the solid sphere of radius
(I) =
k = 0.7560
k ≅ 0.76 m