characterizing vibration-assisted atomic force microscopy (afm)-based nanomachining via perception of acoustic emission phenomen
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The change in internal energy of the system is +30 J
Explanation:
We can solve this problem by using the first law of thermodynamics, which states that the change in internal energy of a system is given by the equation:
where
is the change in internal energy
Q is the heat absorbed by the system (positive if it is absorbed, negative if it is released)
W is the work done by the system (positive if it is done by the system, negative if it is done by the surroundings on the system)
Therefore, in this problem, we have
(heat released by the system)
(work done on the system)
Therefore, the change in internal energy is
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Answer:
A) = 1.44 kg m², B) moment of inertia must increase
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is
I = ½ m R²
A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is
I = + m D²
Let's apply these equations to our case
The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms
=
+ 2
= ½ M R²
The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body
M = 7/8 m total
M = 7/8 64
M = 56 kg
The mass of the arms is
m’= 1/8 m total
m’= 1/8 64
m’= 8 kg
As it has two arms the mass of each arm is half
m = ½ m ’
m = 4 kg
The arms are very thin, we will approximate them as a particle
= M D²
Let's write the equation
= ½ M R² + 2 (m D²)
Let's calculate
= ½ 56 0.20² + 2 4 0.20²
= 1.12 + 0.32
= 1.44 kg m²
b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase