The gas is undergoing an isothermal process, which is a process in which temperature remains constant. This process involves the gas expanding from a compressed state to a more expanded state.
What is gas?
Gas is a form of energy that is produced through the burning of fossil fuels, such as coal, oil, and natural gas. It is used to power many of the everyday things we use, including our cars, stoves, and furnaces. Gas is also used to generate electricity, as well as provide heat for homes and businesses. When burned, gas creates a number of pollutants, such as carbon dioxide, carbon monoxide, sulfur dioxide, and nitrogen oxides, which can have a negative effect on the environment. To reduce its environmental impact, gas should be used as efficiently as possible. This means using appliances with higher energy ratings and making sure that any maintenance needed is kept up to date. In addition, using renewable energy sources, such as solar and wind power, can help reduce the use of gas.
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Consider the following isobaric process for air, modelled as a Calorically Perfect Ideal Gas
(CPIG), from state 1 to state 2. P1 = 200 kPa, T1 = 500 K, T2 = 600 K. Show that the
condition satisfies the second law of thermodynamics. (Show all relevant steps involved).
These given conditions satisfy the second law of thermodynamics.
As the process is isobaric
So there will be a straight line of P= 200kPa in P-v and P-T planes
P1 = P2 = 100kPa
For perfect ideal gas, v-T plane:
[tex]v = (\frac{R}{P}) T[/tex]
[tex]v_{1} = (\frac{R}{P_{1} }) T_{1}[/tex] = 287 × 500/200000 = 0.717 m³/kg
[tex]v_{2} = (\frac{R}{P_{2} }) T_{2}[/tex] = 287 × 600/200000 = 0.861m³/kg
As it is the calorically perfect gas
de = [tex]c_{v}[/tex]dT
Integration on both sides
e2 - e1 = [tex]c_{v}[/tex](T2 - T1)
= ( 716.5J/kg/K) (600-500)
= 71650 J/kg
also,
Tds = de + Pdv
Tds = [tex]c_{v}[/tex]dT +Pdv
For ideal gas
V = RT/P
dv = Rdt/P - RTdp/P²
Tds = [tex]c_{v}[/tex]dT + Rdt - RTdp/P
ds = ([tex]c_{v}[/tex] + R)dT/T - RdP/P
ds = ([tex]c_{v} + c_{p} -c_{v}[/tex])dT/T - RdP/P
ds = [tex]c_{p}[/tex]dT/T - RdP/P
Integration on both sides
s2 - s1 = [tex]c_{p}[/tex]ln (T2/T1) - R ln (P2/P1)
Since P is constant
s₂ - s₁ = [tex]c_{p}[/tex] ln (T2/T1)
= 1003.5 ln (600/500)
= 1003.5 × 0.182
= 182.95 J/kg/K
w = Pdv
[tex]w_{12}[/tex] = P(v₂ - v₁)
= 2,00,000 ( 0.861 - 0.717)
= 28,800 J/kg
de = δq -δw
δq = de + δw
q₁₂ = (e₂ - e₁) + w₁₂
= 71,650 + 28,800 = 1,00,450 J/kg
Now in this process, the gas is heated from 500 K to 600 K. We would expect at a minimum that the surroundings were at 600 K.
Let’s check for second law satisfaction.
s₂ - s₁ ≥ q₁₂ / Tₓ
182.95 ≥ 1,00,450 / 600 K
182.95 J/kg/K ≥ 167.41 J/kg/K
Hence this condition satisfies the second law of thermodynamics
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Light is incident normally on the short face of a 30∘−60∘−90∘ prism (Figure 1). A drop of liquid is placed on the hypotenuse of the prism.
a) If the index of the prism is 1.50, find the maximum index that the liquid may have for the light to be totally reflected.
Express your answer using three significant figures.
1.06 is the maximum refractive index that the liquid may have for the light to be totally reflected.
Only when a light source passes from a denser to a rarer medium can it completely reflect.
When the angle of incidence surpasses a specific critical value, specular reflection occurs in the more highly refractive of the two mediums at their interface, and this reflection is known as total reflection.
sin [tex]i_{c}[/tex] = μ[tex]_{r}[/tex] / μ[tex]_{d[/tex]
From the diagram
Angle of incidence = 60°
sin60° ≥ sin[tex]i_{c}[/tex] = μ[tex]_{r}[/tex]/μ[tex]_{d}[/tex]
μ[tex]_{r}[/tex] ≤ μ[tex]_{d}[/tex] sin60°
μ[tex]_{r}[/tex] ≤ √1.5 × √3/2
= 1.06
Hence, the maximum index that the liquid may have for the light to be totally reflected is 1.06
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Glucose solution is administered to a patient in a hospital. The density of the solution is 1.308 kg/l. If the blood pressure in the vein is 35.7 mmHg, then what is the minimum necessary height of the IV bag above the position of the needle?
The minimum necessary height of the IV bag above the position of the needle, if the density of the solution is 1.308kg/L, and the pressure in the vein is 35.7 mmHg is, 2.78m.
To find the answer, we need to know more about the pressure exerted by a liquid column.
How to find the height of IV bag above the position of needle?Consider a liquid of density ρ contained in a vessel of height h, the pressure exerted by the liquid column at the bottom of the vessel is given by ,[tex]P=[/tex] ρgh
In our question, it is given that,[tex]density=1.308 kg/L\\\\P=35.7 mmHg.\\[/tex]
Thus, the height of the bag h will be,[tex]h=\frac{P}{density*g} =\frac{35.7}{1.308*9.8}\\\\ h=2.78 m[/tex]
Thus, we can conclude that, the height of the Iv bag is 2.78 m above the position of needle.
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If the solution has a density of 1.308 kg/L and the vein pressure is 35.7 mmHg, the minimum height of the IV bag above the needle position is 2.78 m.
We need to learn more about the pressure that a liquid column exerts in order to determine the solution.
How can I determine the height of IV bag above where the needle is?The pressure exerted by the liquid column at the bottom of the vessel is given by for a liquid with density enclosed in a vessel of height h.[tex]P=[/tex] ρgh
In our inquiry, it is assumed that,[tex]Density=1.308kg/L\\P=35.7mmHg[/tex]
As a result, the bag's height will be,[tex]h=\frac{P}{density*g}\\\\ h=2.78m[/tex]
As a result, we may say that the I.V. bag is 2.78 m above the ground.
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Tuning an Instrument. A musician tunes the C-string of her instrumeut to a fundamental frequency of 65.4 Hz. The vibrating portion of the string is 0.600 m long and has a mass of 14.4 g. (a) With what tension must the musician stretch it? (b) What percent increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D?
(a) The tension the musician must stretch it is 147.82 N.
(b) The percent increase in tension is needed to increase the frequency is 26%.
Tension in the stringv = √T/μ
where;
v is speed of the waveT is tensionμ is mass per unit length = 0.0144 kg / 0.6 m = 0.024 kg/mv = Fλ
in fundamental mode, v = F(2L)
v = 2FL
v = 2 x 65.4 x 0.6 = 78.48 m/s
v = √T/μ
v² = T/μ
T = μv²
T = 0.024 x (78.48)²
T = 147.82 N
When the frequency is 73.4 Hz;v = 2FL = 2 x 73.4 x 0.6 = 88.08 m/s
T = μv²
T = (0.02)(88.08)²
T = 186.19 N
Increase in the tension= (186.19 - 147.82)/(147.82)
= 0.26
= 0.26 x 100%
= 26 %
Thus, the tension the musician must stretch it is 147.82 N.
The percent increase in tension is needed to increase the frequency is 26%.
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Calculate the magnitude of the electric field at one corner of a square 1.10 m on a side if the other three corners are occupied by 4.05×10−6 C charges. What is the direction of the electric field?
The direction of magnetic field is south-east and the magnitude is
[tex]23.66[/tex] × [tex]10^{3} N/C[/tex].
Here, the magnitude of CD and BC will be cancelled, as they both are in the opposite direction and equal to each other.
the magnitude, towards the diagonal AC will result in CP, which is the direction of the electric field.
magnitude of electric field can be defined as :- The force per charge on the test charge is a straight forward way to define the size of the electric field.
To find the magnitude of the electric field use the formula
[tex]E = kq/ r^{2}[/tex]
inserting the values,
[tex]E = 9. 10^{9}[/tex] × [tex]4.05[/tex] × [tex]10^{-6} / 1.1 \sqrt{2}[/tex]
[tex]E= 36.45[/tex] × [tex]10^{3}[/tex] / [tex]1.54[/tex]
[tex]E = 23.66[/tex] × [tex]10^{3}[/tex] N/C
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what can you say about the speed of a ball that travelled a distance of 20 m and displacement of 10 m in 5 seconds
The speed of the ball at the given distance and time of motion is 4 m/s.
What is speed?The speed of an object is the rate of change of distance traveled by the object with time.
Speed is a scalar quantity because it has only magnitude and no direction. It is measured in meters per second.
Speed of the ballFor a ball that travelled a distance of 20 m and displacement of 10 m in 5 seconds, the speed of the ball at the given distance and time of motion is calculated as follows;
Speed of the ball = distance traveled by the ball / time of motion
from the question, distance = 20 mtime of motion, t = 5 secondsspeed of the ball = 20 m / 5 s
speed of the ball = 4 m/s
Thus, the speed of the ball at the given distance and time of motion is 4 m/s.
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An air-filled 39.1 μH solenoid has a length 4.0 cm and a cross-sectional area 0.60 cm2. How many turns are in this solenoid?
a.21000
b.144
c.12
d.120
e.1200
No. of turns in the solenoid is an option (b) 144.
The self-inductance of a long solenoid depends only on its physical properties (such as the number of turns of wire per unit length and the volume), and not on the magnetic field or the current.
Self-inductance of solenoid = 39.1 μH
= 39.1 × [tex]10^-^6[/tex] H
Length of the solenoid = 4.0 cm
Cross-sectional area = 0.60 cm²
Expression for the self-inductance of a coil ;
L = µ₀N²A / [tex]l[/tex]
where,
L = Self- Inductance
N = No. of turns.
A = Cross-sectional area
[tex]l=[/tex] Length of the solenoid
L =( 4π × [tex]10^-^7[/tex] × N² × 0.60 ) / 4.0
39.1× 4.0 / 4π × [tex]10^-^7[/tex] × 0.60 = N²
N² = 2.07 × [tex]10^6[/tex]
N = 144
Therefore, the no. of turns of the solenoid is 144.
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Why should you use an iron hammer instead of a wooden
hammer?
Answer:
more durability and easier to pound a hammer with the heavy weight.
Explanation:
One should use an iron hammer instead of the wooden hammer because the force developed with the help of the iron hammer is far greater than the wooden hammer
What is Newton's second law?Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
The mathematical expression for Newton's second law is as follows
F = m*a
where F represents the force applied
m is the mass of the object
a is the acceleration of the object
As we know that force is a product of mass and acceleration, let us assume that both iron and wooden hammers have the same dimension , considering the acceleration applied is the same while hammering ,
As for the same dimension the mass of iron hammer would be greater as result force applied through the iron hammer would be grater
Since the iron hammer's force is so much stronger than the wooden hammer's force, one should use an iron hammer instead of a wooden hammer.
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Two bullets are fired at the same time with the same kinetic energy.
If one bullet has twice the mass of the other, what is the ratio of the speed of the lighter bullet to the speed of the heavier?
Which can do the most work?
The ratio of the speed of the lighter bullet to the speed of the heavier will be four times the heavier bullet.
Both can do same amount of work.
What is kinetic energy?Kinetic energy of a body is the energy due to the motion of the body.
Kinetic energy = mv²/2
where m is mass and v is velocity of the object.
Since both objects have the same kinetic energy but one bullet has twice the mass of the other, the ratio of the speed of the lighter bullet to the speed of the heavier will be four times the heavier bullet.
The kinetic energy of both bullets is the same. Hence, they can do equal amount of work.
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A 550-g squirrel with a surface area of 945 cm2 falls from a 4.0-m tree to the ground. Estimate its terminal velocity. (Use the drag coefficient for a horizontal skydiver. Assume that the squirrel can be approximated as a rectanglar prism with cross-sectional area of width 11.6 cm and length 23.2 cm. Note, the squirrel may not reach terminal velocity by the time it hits the ground. Give the squirrel's terminal velocity, not it's velocity as it hits the ground.)
m/s
What will be the velocity of a 55.0-kg person hitting the ground, assuming no drag contribution in such a short distance?
m/s
The velocity of a 55.0-kg person hitting the ground, is mathematically given as
vt=39.5983m/s
What will be the velocity of a 55.0-kg person hitting the ground, assuming no drag contribution in such a short distance?Generally, the equation for is mathematically given as
mass of squirrel,
[tex]m=550 \mathrm{~g}\\\\Surface area, $A=945 \mathrm{~cm}^{2}=88 \times 10^{-3}$\\\\Height, $h-4 \mathrm{~m}$\\[/tex]
Terminal velocity is given by:
[tex]$v_{i}=\sqrt{\frac{2 m g}{\rho A C}}$[/tex]
where \rho is the density of fluid that is falling and it is given by
[tex]$\rho=\frac{m}{V}$[/tex]
since, volume =area * height
[tex]^{\rho=} \frac{0.55 \mathrm{Kg}}{0.0945 \mathrm{~m}^{2} \times 4.0 \mathrm{~m}}\\\\$\rho=0.1455 \mathrm{Kg} / \mathrm{m}^{3}$[/tex]
A is the surface area of squirrels.
C is the drag coefficient.
The surface area facing the fluid is given by:
[tex]A_{f}=\frac{0.0945 \mathrm{~m}^{2}}{2} \\\\\\ A_{f}=0.04725 \mathrm{~m}^{2}[/tex]
so, terminal velocity is :
[tex]$v_{t}=\sqrt{\frac{2 \times 0.55 \mathrm{Kg} \times 9.8 \mathrm{~m} / \mathrm{s}^{2}}{0.1455 \mathrm{Kg} / \mathrm{m}^{3} \times 0.04725 \mathrm{~m}^{2} \times 1}}$[/tex]
Vt=39.5983
In conclusion, the terminal velocity of the squirrel is 39.5983m/s
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All moving objects have ____________.
A. Force
B. Distance
C. Momentum
D. Time
Answer:
I think it's force
Explanation:
Mark as brainliest if it is right
Answer: A
Explanation:
Force can cause a stationary object to start moving or a moving object to change its speed or direction or both
A proton moving along the positive x-axis enters a uniform magnetic field which is directed along the
positive y-axis. If the magnitude of the field is 0.7 T, and the charge and speed of the proton are 1.5 x10-19 C
and 3.0 x 106 m/s respectively. Calculate the force acting on the proton
Answer: The force acting on the proton of charge 1.5 x10-19 C moving with velocity 1.5 x10-19 C under the influence of a magnetic field of 0.7 T will be 3.15×10^-13 N.
Explanation: To find the answer we need to know more about the Lorentz magnetic force.
What is the Lorentz magnetic force acting on the proton?Consider a proton of charge q moving with a velocity v in a magnetic field, then the Lorentz magnetic force exerted on the proton can be expressed as,F= q (v× B)
[tex]F= qvBsin\alpha[/tex] where, [tex]\alpha[/tex] is the angle between v and B.
In the question, it is given that,[tex]B=0.7 T\\q=1.5*10^{-19}C\\v= 3*10^{6}m/s.\\\alpha =90 degree.\\[/tex] because, from the question it is clear that the proton is moving along x axis and the magnetic field is along the y axis.
Thus, we can find the force acting on the proton as,[tex]F=qvBsin\alpha =1.5*10^{-19}C*3*10^6 m/s*0.7T*sin (90)\\F=3.15*10^{-13}N[/tex]
Thus, we can conclude that the Lorentz force acting on the proton will be 3.15×10^-13 N.
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In response to a magnetic field of 0.7 T, a proton with a charge of 1.5 x 10-19 C travelling at a speed of 1.5 x 10-19 C will experience a force of 3.15 x 10^-13 N.
We need to learn more about the Lorentz magnetic force in order to locate the solution.
What does the proton experience as the Lorentz magnetic force?If you imagine a proton with charge q travelling at speed v in a magnetic field, you can write down the Lorentz magnetic force acting on the proton as,F= Q (v× B)
[tex]F=QvBsin\alpha[/tex]
[tex]\alpha[/tex] the angle between v and B is, where.
It is stated in the query that, the magnetic field is along the y axis and the proton is travelling along the x axis. Thus, the angle will be 90 degrees.As a result, we can identify the proton's driving force as,[tex]F=3.15*10^{-13}N[/tex]
Thus, we can infer that the proton will be subject to a 3.15 10^-13 N Lorentz force.
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Select the correct answer.
Using the statistical definition of entropy, what is the entropy of a system where W = 4?
Using the statistical definition of entropy, The entropy of a system W = 4 is 1.91×10²³.
What is entropy?Entropy is typically referred to as a measurement of a system's randomness or disorder. In 1850, a German physicist named Rudolf Clausius first proposed this idea. Entropy is a thermodynamic property used to characterize a system's behavior in terms of temperature, pressure, entropy, and heat capacity. This thermodynamic explanation took the systems' equilibrium condition into account.
Entropy can be calculated using a mathematical expression.
Entropy = Total change of heat / thermodynamic temperature
S= KblnW
S is the statistical entropy
The value of Boltzmann's constant is 1.38×10⁻²³.
S= 1.38×10⁻²³ ln(4)
S = 1.91×10⁻²³
Using the statistical definition of entropy, The entropy of a system W = 4 is 1.91×10²³.
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Answer: C.
1.91 × 10⁻²³ joules/kelvin
Explanation: edmentum
Object A has the same mass as Object B but Object A is traveling faster. What can we say about the momentum of Object A compared to that of Object B?
Answer:
Object A's momentum is larger
Explanation:
as the formula for momentum goes:
P = M * V
where P is momentum, M is mass, V is velocity.
so where Va (Object A's velocity) is larger than Vb (Object B's velocity) we get:
( i ) Va > Vb
as the masses of both objects are equal, we mark:
( ii) Ma = Mb = M
we multiply both sides of ( i ) by M to get:
( iii ) Va × M > Vb × M
and we finally get:
( iv ) Pa > Pb
Answer: Object A's momentum of larger than compared to that of object B.
Explanation:
A treasure chest full of silver and gold coins is being lifted from a pirate ship to the shore using two ropes as shown in the figure. The mass of the treasure chest is 75.6 kg.
Tension in rope A:
7.42×102 N
Tension in rope B:
7.52×102 N
What is the tension in rope C?
Tension in the rope C is 1.24× 10² N.
To find the answer, we need to know about the horizontal component of tension in the rope B.
What's the angle made by the rope B by horizontal?From the figure of the answer, in the triangle PQR, tan(θ)= PQ/QR = 6/1= 6 θ= tan inverse of 6 = 80.5°What's the horizontal component of the tension in rope B?Horizontal component= tension in rope B × cos80.5°
= 7.52×10² N × cos80.5°
= 1.24×10² N
What's the tension in the rope C?From the figure, we have found that the tension in rope C = horizontal component of the tension in rope BSo, tension in rope C= 1.24×10² NThus, we can conclude that the tension in the rope C is 1.24× 10² N.
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Technetium -99 (half-life = 6.01) is used in the medical imaging. How many half-lives would go by in 44.0h?
The number of half-lives that would go by in 44 h is 7 half-lives
What is half life?This is the time taken for half a substance to decay
How to determine the number of half lifeThe number of half-lives that will elaspe after 44 h can be obtained as illustrated below:
Half-life (t½) = 6.0 hTime (t) = 44 hNumber of half-lives (n) =?n = t / t½
n = 44 / 6.01
n = 7
Thus, 7 half-lives will elaspe after 44 h
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Glucose solution is administered to a patient in a hospital. The density of the solution is 1.308 kg/l. If the blood pressure in the vein is 35.7 mmHg, then what is the minimum necessary height of the IV bag above the position of the needle?
The minimum necessary height of the IV bag above the position of the needle is 0.37 m.
we know that,
P = ρgh
where,
P = 35.7mmHg
= 4759.609 Pa
g = 9.8[tex]\frac{m}{s^{2} }[/tex]
ρ = 1.308 kg / m^3
now, substituting all the values, we get,
4759.609 = 1.308 × 9.8 × h
h = 0.37 m
The minimum necessary height of the IV bag above the position of the needle = 0.37 m.
what is an IV bag ?
A reagent, also called as an analytical reagent, is a substance or compound that is added to a system in chemistry to bring about a chemical reaction or examine to see if one happens. Even though the terms "reagent" and "reactant" are frequently used synonymously, "reactant" refers to a substance that is consumed during a chemical reaction.
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What adaptation of a cactus protects it from predators? a round cactus with many spines Broad leaves Sharp spines Thick stems Yellow flowers
A round cactus with many spines is the adaptation of a cactus that protects it from predators.
A cactus, unlike other plants, has unique adaptations in its roots, leaves, and stems that allow it to flourish in hot and dry surroundings.
The one adaptation that protects the cactus from predators is spines.
A cactus does not have any parts that resemble leaves if you could look at one closely.
Instead, the leaves are transformed into spines, which protrude from the plant's tiny bumps known as areoles.
Herbivores that live in the desert may be enticed to eat the cactus. The spines prevent these predators by modifying leaves into spines.
Other than protection, Spines perform many functions like
1) Since evaporation is a problem in a desert since water is scarce, the spines prevent excessive evaporation.
2) The spines also impede airflow and prevent evaporation by trapping air.
3) Collecting dew from the early-morning fog is another crucial job that the spines do.
The gathered dew turned into liquid water and ran down to the earth below. The plant then absorbs this water.
Hence, the adaptation of a cactus that protects it from predators is round cactus with many spines.
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An action force is 50 N to the left. The reaction force must be:
A. 50 N right
B. 50 N down
C. 50 N left
D. 50 N up
A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ρ0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'f or s' are possible answers in some of the cases.
The new sphere has a density of ρ > ρ0 and a mass of m = m0.
The new sphere has a mass of m > m0 and a radius of r = r0.
The new sphere has a radius of r = r0 and a density of ρ > ρ0.
The correct response for each of the condition given in the questions are,
[tex]d > d_0 , m=m_0[/tex] ⇒ f or s [tex]m > m_0, r=r_0[/tex]⇒ r [tex]r=r_0,d > d_0[/tex] ⇒ rTo find the answer, we have to know about the Archimedes principle.
How to solve the problem for different conditions?The Archimedes principle states that the upthrust F on a body is equal to the weight W of the displaced liquid.The sum of forces must be zero for the sphere to be in equilibrium.[tex]F-W=0\\F=W\\W=mg, where.\\m=density*volume=d*V\\V=\frac{4}{3} \pi r^3[/tex]
Let's apply the idea of density to the body and water now. We are taking d instead of ρ.[tex]d_wVg = d_0(\frac{4}{3}\pi r^3 ) g \\d_wV = d_0(\frac{4}{3}\pi r^3 )[/tex] (1)
Let's examine each example for the initial condition with d₀, m₀, and r₀, where the height of the water is h.Case 1:
The new sphere's mass is m = m₀ .The new sphere's density, d > d₀.Here, the smaller, denser sphere with the same mass, If the sphere floats, the amount of water it displaces will be equal to its mass, which will be the same as the amount of water the original sphere displaces.Consequently, the water level is unchanged.But if the sphere descends, the water displaced is less than the sphere's mass, m = m0, and the level drops, f.Therefore, f or s is the appropriate response.Case 2:
The new sphere's radius, r = r₀, and mass, m > m₀.Consequently, the new sphere is denser than the old one.The right answer is r, because the mass of the water displaced where the sphere floats is m > m0, which is greater than the water displaced for the initial sphere.Case 3:
sphere with the same radius but a higher density.When the right side of equation (1) rises, the left side must also rise in order for the volume to rise and the height to rise as a result (r)Thus, we can conclude that,
[tex]d > d_0 , m=m_0[/tex] ⇒ f or s [tex]m > m_0, r=r_0[/tex]⇒ r [tex]r=r_0,d > d_0[/tex] ⇒ rLearn more about Archimedes principle here:
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A block of mass 2.60 kg is placed against a horizontal spring of constant k = 725 N/m and pushed so the spring compresses by 0.0500 m.
What is the elastic potential energy of the block-spring system (in J)?
_______J
If the block is now released and the surface is frictionless, calculate the block's speed (in m/s) after leaving the spring.
_____s/s
The elastic potential energy of the block-spring system is 0.906 J.
Velocity of the block , v = 0.83 m/s.
What is elastic potential energy?Elastic potential energy is the energy stored in a stretched or compressed elastic material.
Elastic potential energy = Ke²/2The elastic potential energy of the block-spring system = 725 * 0.05²/2 The elastic potential energy of the block-spring system = 0.906 J
The elastic potential energy of the spring is converted to kinetic energy of the block.
1/2 mv² = 0.906 J
where v is velocity
v = √(0.906 * 2)/2.6
v = 0.83 m/s.
In conclusion, elastic potential energy is present in compressed or stretched elastic materials.
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A contestant in a winter games event pulls a 36.0 kg block of ice across a frozen lake with a rope over his shoulder as shown in Figure 4.29(b). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03.
Figure 4.29
(a) Calculate the minimum force F he must exert to get the block moving.
40.873
(b) What is its acceleration once it starts to move, if that force is maintained?
m/s2
(a) The minimum force F he must exert to get the block moving is 38.9 N.
(b) The acceleration of the block is 0.79 m/s².
Minimum force to be applied
The minimum force F he must exert to get the block moving is calculated as follows;
Fcosθ = μ(s)Fₙ
Fcosθ = μ(s)mg
where;
μ(s) is coefficient of static frictionm is mass of the blockg is acceleration due to gravityF = [0.1(36)(9.8)] / [(cos(25)]
F = 38.9 N
Acceleration of the blockF(net) = 38.9 - (0.03 x 36 x 9.8) = 28.32
a = F(net)/m
a = 28.32/36
a = 0.79 m/s²
Thus, the minimum force F he must exert to get the block moving is 38.9 N.
The acceleration of the block is 0.79 m/s².
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A gas is confined to a vertical cylinder by a piston of mass 2 kg and radius 1 cm. When 5J of heat are added, the piston rises by 2.4 cm. Find: (a) the work done by the gas; (b) the change in its internal energy. Atmospheric pressure is 105Pa
The work done by gas is 0.753 J and change in internal energy is 4.247J
So we are given that mass is 2kg , radius 1 cm and the amount of heat is 5 cm
The piston raised by 2.4cm
As we know that Work done is PΔV
Where ΔV is change in volume
Therefore ΔV = πr^2 h = π x (.01)^2 x .024 =7.53×10^(-6)m^3
Here pressure is 10^5 pa
So W = [tex]10^5\times7.53\times10^-(6)[/tex]
Therefore W = 0.753 J
Now coming to change in internal energy
Change in Internal Energy = Heat Added - Energy lost in work
∴ 5J - 0.753 J = 4.247J
Hence the change in internal energy is 4.247 J
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The decibel level of the sound from a certain hair dryer is measured at 60 dB. Find the intensity of the sound.
Based on the calculations, the sound intensity level is equal to 1.0 × 10⁻⁵ W/m².
How to determine intensity of the sound?Mathematically, sound intensity level can be calculated by using this formula:
[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]
Where:
I is the intensity of the sound.
Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² W/m².
Rewriting the formula, we have:
β/10 = logI - logIo
Substituting the parameters into the formula, we have;
60/10 = logI - log(1.0 × 10⁻¹²)
6 = logI + 12
logI = 6 - 12
logI = -6
I = 1.0 × 10⁻⁵ W/m².
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A 40.0 kg beam is attached to a wall with a hi.nge and its far end is supported by a cable. The angle between the beam and the cable is 90°. If the beam is inclined at an angle of θ = 31.0° with respect to horizontal.
The horizontal component of the force exerted by the hi.nge on the beam = 8.662×101 N
What is the magnitude of the force that the beam exerts on the hi.nge?
The magnitude of the force that the beam exerts on the hi.nge will be,261.12N.
To find the answer, we need to know about the tension.
How to find the magnitude of the force that the beam exerts on the hi.nge?Let's draw the free body diagram of the system using the given data.From the diagram, we have to find the magnitude of the force that the beam exerts on the hi.nge.For that, it is given that the horizontal component of force is equal to the 86.62N, which is same as that of the horizontal component of normal reaction that exerts by the beam on the hi.nge.[tex]N_x=86.62N[/tex]
We have to find the vertical component of normal reaction that exerts by the beam on the hi.nge. For this, we have to equate the total force in the vertical direction.[tex]N_y=F_V=mg-Tsin59\\[/tex]
To find Ny, we need to find the tension T.For this, we can equate the net horizontal force.[tex]F_H=N_x=Tcos59\\\\T=\frac{F_H}{cos59} =\frac{86.62}{0.51}= 169.84N[/tex]
Thus, the vertical component of normal reaction that exerts by the beam on the hi.nge become,[tex]N_y= (40*9.8)-(169.8*sin59)=246.4N[/tex]
Thus, the magnitude of the force that the beam exerts on the hi.nge will be,[tex]N=\sqrt{N_x^2+N_y^2} =\sqrt{(86.62)^2+(246.4)^2}=261.12N[/tex]
Thus, we can conclude that, the magnitude of the force that the beam exerts on the hi.nge is 261.12N.
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The hi.nge will be subjected to a force of 261.12N from the beam.
We must understand the tension in order to choose the solution.
How can the amount of force the beam applies on the height be determined?Let's use the provided information to create the system's free body diagram.We need to calculate the force the beam is exerting on the height using the diagram.For this, it is assumed that the horizontal component of force is 86.62N, the same as the horizontal component of the normal reaction that the beam exerts on the height.We need to identify the vertical component of the normal reaction the beam exerts on the height. We must equalize the total force acting in the vertical direction to achieve this.[tex]N_y=F_v=mg-Tsin59[/tex]
Finding the tension T is necessary to determine Ny. Thus, we can use the net horizontal force to equate this.[tex]F_H=N_x=Tcos59\\T=\frac{F_H}{cos59} =169.84N[/tex]
As a result, the normal reaction that the beam has on the height becomes, with a vertical component,[tex]N_y=(40*9.8)-(169.84*sin59)=246.4N[/tex]
As a result, the force the beam applies on the height will be of the order of,[tex]N=\sqrt{N_x^2+N_y^2} =261.12N[/tex]
Thus, we can infer that the force the beam applies to the height is 261.12N in size.
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A baseball player holds a 1.42 N baseball in his hand, a distance of 34.0 cm from the elbow joint as shown in the figure below. The biceps attached at a distance of 2.75 cm from the elbow exerts an upward force of 12.6 N on the forearm. Consider the forearm and hand to be a uniform rod with a mass of 1.20 kg. Calculate the net torque acting on the forearm and hand.
Answer:
90.3N
Explanation:
⊥mg = (0.170 m)(1.20 kg) 9.81 m/s
τ ball = r⊥Wball = (0.340 m)(1.42 N) = − 0.483 N ⋅m
F − 2.001− 0.483 N ⋅m = 0
F = 2.484 N ⋅m
0.0275 m = 90.3 N
The net torque acting on the forearm and hand is 90.3N
What is torque?
Torque is a measure of the pressure that can motivate an object to rotate about an axis. simply as pressure is what causes an object to accelerate in linear kinematics, torque is what reasons an item to collect angular acceleration. Torque is a vector amount.
⇒mg = (0.170 m)(1.20 kg) 9.81 m/s
⇒torque = r⊥weight of the ball
⇒ (0.340 m)(1.42 N) = − 0.483 N ⋅m
⇒F = − 2.001− 0.483 N ⋅m = 0
⇒F = 2.484 N ⋅m
⇒0.0275 m = 90.3 N
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What force causes a bike to move forward?
A. Air resistance
B. Thrust
C. Friction
D. Gravity
The Answer is Option C. Friction.
Explanation:
The friction force acts in the forward direction on the rear wheel and it acts in the backward direction on the front wheel. The magnitude of friction force on the rear wheel can be more, equal or less than that on the front wheel.
State the newton's law of motion and give
application of each law.
Answer:
In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
Explanation:
Planet-X has a mass of 4.74×1024 kg and a radius of 5870 km.
1. What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet?
2. If the period of rotation of the planet is 16.6 hours, then what is the radius of the synchronous orbit of a satellite?
The minimum speed required for a satellite in order to break free permanently from the planet and the radius of the synchronous orbit of a satellite are 7.3 Km/s and 3.1 × 10⁴ km respectively.
To find the answer, we need to know about the escape velocity and time period of revolving satellite.
What's the expression of escape velocity of a satellite?Mathematically, escape velocity= √(2GM/R)G = gravitational constant, M = mass of planet, R= radius of the planetHere, M = 4.74×10²⁴kg, R = 5870 kmEscape velocity= √(6.67×10^(-11)×4.74×10²⁴/5.870×10⁶)= 7.3 Km/s
What's the expression of time period of a circularly orbiting satellite?T= {2π×r^(3/2)}/√(GM)r= (T/2π)⅔× (GM)^(1/3)r is the radius of the orbitWhat's the radius of the circular orbit, if the time period of the satellite is 16.6 hours?T = 16.6 hours = 16.6×3600 second = 59760sr = (59760/2π)^⅔× (6.67×10^(-11)×4.74×10²⁴)^(1/3)= 3.1 × 10⁴ km
Thus, we can conclude that the escape velocity and the radius of the synchronous orbit of a satellite are 7.3 Km/s and 3.1 × 10⁴ km respectively.
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What is the symbol for a variable resistor?
A. Horizontal wire
B. 2 parallel wires
C. Line with a zig zag pattern with a diagonal line drawn across it
D. Circle with an X through it
The symbol for a variable resistor is a line with a zig zag pattern with a diagonal line drawn across it.
What is a variable resistor ?
A resistor whose electric resistance value may be altered is known to as a variable resistor. A variable resistor, which works usually by sliding a contact (wiper) over a variable resistor, is basically an electro-mechanical transducer.
The flow of electrical current is restricted by a resistor. The resistivity of a fixed resistor is steady. By adjusting a slider's position, the resistance of this resistor can be altered. Some volume controls and dimmer switches employ variable resistors.
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