A spring with an 8-kg mass is kept stretched 0.4 m beyond its natural length by a force of 32 N. The spring starts at its equili
2 answers:
Answer:
x = 1.26 sin 3.16 t
Explanation:
Assume that the general equation of the displacement given as
x = A sinω t
A=Amplitude ,t=time ,ω=natural frequency
We know that speed V
V= A ω cosωt
Maximum velocity
V(max)= Aω
Given that F= 32 N
F = K Δ
K=Spring constant
Δ = 0.4 m
32 =0.4 K
K = 80 N/m
We know that ω²m = K
8 ω² = 80
ω = 3.16 s⁻¹
Given that V(max)= Aω = 4 m/s
3.16 A = 4
A= 1.26 m
Therefore the general equation of displacement
x = 1.26 sin 3.16 t
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<h2>Answer: its temperature must increase.</h2>
Explanation:
In an isobaric process the pressure remains constant, which means the initial pressure and the final pressure will be the same.
In addition, during this thermodynamic process, the volume of the ideal gas expands or contracts in such a way that the variation of pressure is neutralized.
Now, according to the First law of Thermodynamics that establishes the conservation of energy:
(1)
Where:
is the internal energy
is the heat transferred
is the work
Now, for an isobaric process:
(2)
Where:
is the pressure (<u>always positive</u>)
is the volume variation of the gas
<u />
<u>Here we have two possible results:</u>
-If the gas expands (positive ), the work is positive.
-If the gas compresses (negative ), the work is negative.
In this case we are talking about the first result (work is positive).
Then, according to the above, equation (1) can be written as follows:
(3)
Clearing :
(4)
Then, for an ideal gas in an isobaric process, part of the heat () added to the system will be used to do work (positive in this case) and the other part <u>will increase the internal energy</u>, hence <u>the temperature will increase as well.</u>