Answer: 80J
Explanation:
According to the first principle of thermodynamics:
"Energy is not created, nor destroyed, but it is conserved."
Then this priciple (also called Law) relates the work and the transferred heat exchanged in a system through the internal energy [tex]U[/tex], which is neither created nor destroyed, it is only transformed. So, in this especific case of the compressed gas:
[tex]\Delta U=Q+W[/tex] (1)
Where:
[tex]\Delta U[/tex] is the variation in the internal (thermal) energy of the system (the value we want to find)
[tex]Q=-100J[/tex] is the heat transferred out of the gas (that is why it is negative)
[tex]W[/tex] is the work is done on the gas (as the gas is compressed, the work done on the gas must be considered positive )
On the other hand, the work done on the gas is given by:
[tex]W=-P \Delta V[/tex] (2)
Where:
[tex]P=450kPa=450(10)^{3}Pa[/tex] is the constant pressure of the gas
[tex]\Delta V=V_{f}-V_{i}[/tex] is the variation in volume of the gas
In this case the initial volume is [tex]V_{i}=600{cm}^{3}=600(10)^{-6}m^{3}[/tex] and the final volume is [tex]V_{f}=200{cm}^{3}=200(10)^{-6}m^{3}[/tex].
This means:
[tex]\Delta V=200(10)^{-6}m^{3}-600(10)^{-6}m^{3}=-400(10)^{-6}m^{3}[/tex] (3)
Substituting (3) in (2):
[tex]W=-450(10)^{3}Pa(-400(10)^{-6}m^{3})[/tex] (4)
[tex]W=180J[/tex] (5)
Substituting (5) in (1):
[tex]\Delta U=-100J+180J[/tex] (6)
Finally:
[tex]\Delta U=80J[/tex] This is the change in thermal energy in the compression process.
the loudness of a person's voice depends on the A. force with which air rushes across the vocal folds B. strength of the intrinsic laryngeal muscles C. length of the vocal folds D. thickness of vestibular folds
Answer: A. force with which air rushes across the vocal folds
Explanation:
The human voice is produced in the larynx, whose essential part is the glottis. This is how the air coming from the lungs is forced during expiration through the glottis, making its two pairs of vocal folds to vibrate.
It should be noted that this process can be consciously controlled by the person who speaks (or sings), since the variation in the intensity of the sound of the voice depends on the strength of the breath.
The loudness of a person's voice mainly depends on the force of airflow across their vocal folds. This causes the vocal folds to vibrate and the sound to be produced. The volume of this sound is determined by the amplitude of the resulting sound pressure wave.
Explanation:The loudness of a person's voice is primarily dependent on the force with which air rushes across the vocal folds. Sound is created when air is pushed up from the lungs through the throat, causing the vocal folds to vibrate. When air flow from the lungs increases, the amplitude of the sound pressure wave becomes greater, resulting in a louder voice. Changes in pitch are related to muscle tension on the vocal cords.
Vocal cord vibration and sound pressure wave amplitude are thus key factors in determining the loudness of a person's voice.
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Suppose that 2.5 moles of an ideal gas are in a chamber in equilibrium at temperature 310 K and volume 0.5 m3. 1) What is the pressure in the chamberi?
Answer:
The pressure in the chamber are of p= 0.127 atm.
Explanation:
n= 2.5 moles
T= 310 K
V= 0.5 m³ = 500 L
R= 0.08205746 atm. L /mol . K
p= n*R*T/V
p= 0.127 atm
A)If the rms value of the electric field in an electromagnetic wave is doubled, by what factor does the rms value of the magnetic field change? B)If the rms value of the electric field in an electromagnetic wave is doubled, by what factor does the average intensity of the wave change?
A) The magnetic field doubles as well
The relationship between rms value of the electric field and rms value of the magnetic field for an electromagnetic wave is the following:
[tex]E_{rms}=cB_{rms}[/tex]
where
E_rms is the magnitude of the electric field
c is the speed of light
B_rms is the magnitude of the magnetic field
From the equation, we see that the electric field and the magnetic field are directly proportional: therefore, if the rms value of the electric field is doubled, then the rms value of the magnetic field will double as well.
B) The intensity will quadruple
The intensity of an electromagnetic wave is given by
[tex]I=\frac{1}{2}c\epsilon_0 E_0^2[/tex]
where
c is the speed of light
[tex]\epsilon_0[/tex] is the vacuum permittivity
[tex]E_0[/tex] is the peak intensity of the electric field
The rms value of the electric field is related to the peak value by
[tex]E_{rms}=\frac{E_0}{\sqrt{2}}[/tex]
So we can rewrite the equation for the intensity as
[tex]I=c\epsilon_0 E_{rms}^2[/tex]
we see that the intensity is proportional to the square of the rms value of the electric field: therefore, if the rms value of the electric field is doubled, the average intensity of the wave will quadruple.
When is the total momentum of a system conserved?
Answer:
When the net external force is zero
Explanation:
We can answer to this question by referring to Newton's Second Law, which can be written in the following form
[tex]F=\frac{\Delta p}{\Delta t}[/tex]
where
F is the net external force acting on a system
[tex]\Delta p[/tex] is the change in momentum of the system
[tex]\Delta t[/tex] is the time interval
When the total momentum of a system is conserved (so, it does not change), its variation is zero:
[tex]\Delta p = 0[/tex]
In order to satisfy this condition, we see from the formula that we must also have
F = 0
so the net external force acting on the system must be zero.
The initial velocity of a 4.0kg box is 11m/s due west. After the box slides 4.0m horizontally its speed is 1.5 m/s. Determine the magnitude and the direction of the non conservative force acting on the box as it slides.
Answer:
The magnitude and direction of the non conservative force acting on the box is <F= 59.36 N - DUE EAST DIRECTION>.
Explanation:
m= 4 kg
Vi= 11 m/s
Vf= 1.5 m/s
d= 4m
d= Vi * t - a * t²/2
clearing a:
a= 2*(Vi * t - d)/ t²
Vf= Vi - a * t
replacing "a" and clearing t:
t= 2d/(Vf+Vi)
t= 0.64 s
found now the value of a:
a= Vi - Vf / t
a= 14.84 m/s ²
F= m * a
F= 59.36 N
Two wires are perpendicular to each other and form a coordinate axis. The current in the vertical wire is going up (in the positive y direction) and the current in the horizontal wire is going to the right(in the positive x direction). Where is the net magnetic field equal to zero?
Answer:
Magnetic field shall be zero at exactly in between the wires.
Explanation:
We can find the magnetic field by biot Savart law as follows
[tex]\overrightarrow{dB}=\frac{\mu _{0}I}{4\pi }\int \frac{\overrightarrow{dl}\times \widehat{r}}{r^{2}}[/tex]
For current carrying wire in positive y direction we have
[tex]\overrightarrow{dB_{1}}=\frac{\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{1}}}{r_{1}^{2}}[/tex]
Similarly for wire carrying current in -y direction we have [tex]\overrightarrow{dB_{2}}=\frac{-\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{2}}}{r_{2}^{2}}[/tex]
Thus the net magnetic field at any point in space is given by
[tex]\overrightarrow{dB_{1}}+\overrightarrow{dB_{2}}[/tex]
[tex]\frac{\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{1}}}{r_{1}^{2}}+\frac{-\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{2}}}{r_{2}^{2}}=0\\\\\Rightarrow \overrightarrow{r_{1}}=\overrightarrow{r_{2}}[/tex]
For points with same position vectors from the 2 wires we have a net zero magnetic field. These points are exactly midway between the 2 wires
The acceleration of a baseball pitcher's hand as he delivers a pitch is extreme. For a professional player, this acceleration phase lasts only 50 ms, during which the ball's speed increases from 0 to about 90 mph, or 40 m/s.
What is the force of the pitcher's hand on the 0.145 kg ball during this acceleration phase?
The force by the pitcher's hand on the ball during the acceleration phase is found using Newton's Second Law of Motion and is calculated to be 116 Newton.
Explanation:The force exerted by the pitcher's hand can be found using Newtons Second Law of Motion which states that the force acting on an object is equal to the mass of the object times its acceleration.
it can be expressed as
F = m * a
Here, the mass (m) is 0.145 kg, and the acceleration (a) can be found using the formula a = Δv/Δt, where Δv is the change in velocity (40 m/s) and Δt is the change in time (50 ms or 0.05 s).
So, a = 40/0.05 = 800 m/s², and then the force F = 0.145 * 800 = 116 N. Therefore, the force of the pitcher's hand on the ball during this acceleration phase is 116 Newton.
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The force of the pitcher's hand on the ball can be calculated using Newton's second law of motion.
Explanation:The force of the pitcher's hand on the ball can be calculated using Newton's second law of motion, which states that force equals mass times acceleration. In this case, the mass of the ball is 0.145 kg and the acceleration is the change in velocity divided by the time interval. The change in velocity is 40 m/s (the final velocity) minus 0 m/s (the initial velocity), and the time interval is 50 ms (or 0.05 s). Therefore, the force can be calculated as:
Force = mass × acceleration = 0.145 kg × (40 m/s - 0 m/s) / 0.05 s = 0.116 N.
So, the force of the pitcher's hand on the ball during this acceleration phase is approximately 0.116 Newtons.
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A satellite with a mass of 5.6 E 5 kg is orbiting the Earth in a circular path. Determine the satellite's velocity if it is orbiting at a distance of 6.8 E 5 m above the Earth's surface. Earth's mass = 5.98 E 24 kg; Earth's radius = 6.357 E 6 m.
A) 6,800 m/s
B) 7,200 m/s
C) 7,500 m/s
D) 7,900 m/s
Answer:
C) 7,500 m/s
Explanation:
The satellite's acceleration due to gravity equals its centripetal acceleration.
v² / r = GM / r²
Solving for velocity:
v² = GM / r
v = √(GM / r)
Given:
G = 6.67×10⁻¹¹ m³/kg/s²
M = 5.98×10²⁴ kg
r = 6.357×10⁶ m + 6.8×10⁵ m = 7.037×10⁶ m
Substituting the values:
v = √(6.67×10⁻¹¹ × 5.98×10²⁴ / 7.037×10⁶)
v = √(5.67×10⁷)
v = 7500 m/s
A 6 kg penguin gets onto a Ferris Wheel, with a radius of 5m, and stands on a bathroom scale. The wheel starts rotating with a constant acceleration of .001 rad/s2 for two minutes and then runs at a constant angular velocity. After the wheel is rotating at a constant rate, what is the penguin’s a) angular momentum about the center of the Ferris Wheel, b) tangential velocity c) maximum & minimum readings on the bathroom scale (and where do they occur?)
Answer:
Part a)
[tex]L = 18 kg m^2/s[/tex]
Part b)
[tex]v = 0.6 m/s[/tex]
Part c)
[tex]R_{max} = 6.04 kg[/tex]
[tex]R_{min} = 5.96 kg[/tex]
Explanation:
As we know that Ferris wheel start from rest with angular acceleration
[tex]\alpha = 0.001 rad/s^2[/tex]
time taken = 2 min
so here we have its angular speed after t = 2min given as
[tex]\omega = \alpha t[/tex]
[tex]\omega = (0.001)(2\times 60)[/tex]
[tex]\omega = 0.12 rad/s[/tex]
Part a)
Angular momentum of the Penguine about the center of the wheel is given as
[tex]L = I\omega[/tex]
[tex]L = (6\times 5^2)(0.12)[/tex]
[tex]L = 18 kg m^2/s[/tex]
Part b)
tangential speed is given as
[tex]v = r\omega[/tex]
[tex]v = (5)(0.12)[/tex]
[tex]v = 0.6 m/s[/tex]
Part c)
Maximum reading of the scale at the lowest point is given as
[tex]R_{max} = \frac{m\omega^2 r + mg}{g}[/tex]
[tex]R_{max} = \frac{6(0.12^2)(5) + 6(9.81)}{9.81}[/tex]
[tex]R_{max} = 6.04 kg[/tex]
Minimum reading of the scale at the top point is given as
[tex]R_{min} = \frac{mg - m\omega^2 r}{g}[/tex]
[tex]R_{min} = \frac{6(9.81) - 6(0.12^2)(5)}{9.81}[/tex]
[tex]R_{min} = 5.96 kg[/tex]