Answer:
t = 5π/18 + 2nπ/3 or π/6 + 2nπ/3 where n is a natural number
Explanation:
To solve the problem/ we first write the differential equation governing the motion. So,
[tex]m\frac{d^{2} x}{dt^{2} } = -kx \\ m\frac{d^{2} x}{dt^{2} } + kx = 0\\\frac{d^{2} x}{dt^{2} } + \frac{k}{m} x = 0[/tex]
with m = 1 slug and k = 9 lb/ft, the equation becomes
[tex]\frac{d^{2} x}{dt^{2} } + \frac{9}{1} x = 0\\\frac{d^{2} x}{dt^{2} } + 9 x = 0[/tex]
The characteristic equation is
D² + 9 = 0
D = ±√-9 = ±3i
The general solution of the above equation is thus
x(t) = c₁cos3t + c₂sin3t
Now, our initial conditions are
x(0) = -1 ft and x'(0) = -√3 ft/s
differentiating x(t), we have
x'(t) = -3c₁sin3t + 3c₂cos3t
So,
x(0) = c₁cos(3 × 0) + c₂sin(3 × 0)
x(0) = c₁cos(0) + c₂sin(0)
x(0) = c₁ × (1) + c₂ × 0
x(0) = c₁ + 0
x(0) = c₁ = -1
Also,
x'(0) = -3c₁sin(3 × 0) + 3c₂cos(3 × 0)
x'(0) = -3c₁sin(0) + 3c₂cos(0)
x'(0) = -3c₁ × 0 + 3c₂ × 1
x'(0) = 0 + 3c₂
x'(0) = 3c₂ = -√3
c₂ = -√3/3
So,
x(t) = -cos3t - (√3/3)sin3t
Now, we convert x(t) into the form x(t) = Asin(ωt + Φ)
where A = √c₁² + c₂² = √[(-1)² + (-√3/3)²] = √(1 + 1/3) = √4/3 = 2/√3 = 2√3/3 and Ф = tan⁻¹(c₁/c₂) = tan⁻¹(-1/-√3/3) = tan⁻¹(3/√3) = tan⁻¹(√3) = π/3.
Since tanФ > 0, Ф is in the third quadrant. So, Ф = π/3 + π = 4π/3
x(t) = (2√3/3)sin(3t + 4π/3)
So, the velocity v(t) = x'(t) = (2√3)cos(3t + 4π/3)
We now find the times when v(t) = 3 ft/s
So (2√3)cos(3t + 4π/3) = 3
cos(3t + 4π/3) = 3/2√3
cos(3t + 4π/3) = √3/2
(3t + 4π/3) = cos⁻¹(√3/2)
3t + 4π/3 = ±π/6 + 2kπ where k is an integer
3t = ±π/6 + 2kπ - 4π/3
t = ±π/18 + 2kπ/3 - 4π/9
t = π/18 + 2kπ/3 - 4π/9 or -π/18 + 2kπ/3 - 4π/9
t = π/18 - 4π/9 + 2kπ/3 or -π/18 - 4π/9 + 2kπ/3
t = -7π/18 + 2kπ/3 or -π/2 + 2kπ/3
Since t is not less than 0, the values of k ≤ 0 are not included
So when k = 1,
t = 5π/18 and π/6. So,
t = 5π/18 + 2nπ/3 or π/6 + 2nπ/3 where n is a natural number
The time interval at which the mass will head downward at the velocity of 3 ft/s is t = 5π/18 + 2nπ/3.
Given data:
The mass suspended from spring is, m = 1 slug.
The spring constant is, k = 9 lb/ft.
The magnitude of upward velocity is, v = 3 ft/s.
The magnitude of downward velocity is, v' = 3 ft/s.
The given problem can be resolved by framing a differential equation that governs the motion of spring. The differential equation governing the motion of spring is,
[tex]m \dfrac{d^{2}x}{dt^{2}}=-kx\\\\\\\dfrac{d^{2}x}{dt^{2}}+\dfrac{k}{m}x=0[/tex]
With m = 1 slug and k = 9 lb/ft, the equation becomes
[tex]\dfrac{d^{2}x}{dt^{2}}+\dfrac{9}{1}x=0\\\\\\\dfrac{d^{2}x}{dt^{2}}+9x=0[/tex]
Now, the characteristic equation is,
D² + 9 = 0
D = ±√-9 = ±3i
And the general solution of the above equation is,
x(t) = c₁cos3t + c₂sin3t
Now, our initial conditions are
x(0) = -1 ft and x'(0) = -√3 ft/s
differentiating x(t), we have
x'(t) = -3c₁sin3t + 3c₂cos3t
So,
x(0) = c₁cos(3 × 0) + c₂sin(3 × 0)
x(0) = c₁cos(0) + c₂sin(0)
x(0) = c₁ × (1) + c₂ × 0
x(0) = c₁ + 0
x(0) = c₁ = -1
Also,
x'(0) = -3c₁sin(3 × 0) + 3c₂cos(3 × 0)
x'(0) = -3c₁sin(0) + 3c₂cos(0)
x'(0) = -3c₁ × 0 + 3c₂ × 1
x'(0) = 0 + 3c₂
x'(0) = 3c₂ = -√3
c₂ = -√3/3
So,
x(t) = -cos3t - (√3/3)sin3t
Now, we convert x(t) into the form x(t) = Asin(ωt + Φ)
where A = √c₁² + c₂²
= √[(-1)² + (-√3/3)²]
= √(1 + 1/3) = √4/3 = 2/√3 = 2√3/3
and Ф = tan⁻¹(c₁/c₂) = tan⁻¹(-1/-√3/3) = tan⁻¹(3/√3) = tan⁻¹(√3) = π/3.
Since tanФ > 0, Ф is in the third quadrant. So, Ф = π/3 + π = 4π/3
x(t) = (2√3/3)sin(3t + 4π/3)
So, the velocity v(t) = x'(t) = (2√3)cos(3t + 4π/3)
We now find the times when v(t) = 3 ft/s
So (2√3)cos(3t + 4π/3) = 3
cos(3t + 4π/3) = 3/2√3
cos(3t + 4π/3) = √3/2
(3t + 4π/3) = cos⁻¹(√3/2)
3t + 4π/3 = ±π/6 + 2kπ
where k is an integer
3t = ±π/6 + 2kπ - 4π/3
t = ±π/18 + 2kπ/3 - 4π/9
t = π/18 + 2kπ/3 - 4π/9 or -π/18 + 2kπ/3 - 4π/9
t = π/18 - 4π/9 + 2kπ/3 or -π/18 - 4π/9 + 2kπ/3
t = -7π/18 + 2kπ/3 or -π/2 + 2kπ/3
Since t is not less than 0, the values of k ≤ 0 are not included
So when k = 1,
t = 5π/18 and π/6.
t = 5π/18 + 2nπ/3
here, n is a natural number.
Thus, we can conclude that the time interval at which the mass will head downward at the velocity of 3 ft/s is t = 5π/18 + 2nπ/3.
Learn more about the differential equation here:
https://brainly.com/question/14620493
an object experiences buoyant force of 15.9 n when immersed in a fluid of density 917 kg/m^3. what is the volume of the object?
Answer:
0.00176
Explanation:
Credit to the person above.
A 150 g egg is dropped from 3.0 meters. The egg is moving at 4.4 m/s right before it hits the ground. The egg comes to a stop in 0.072 seconds.
What is the magnitude of force that the ground exerted on the egg?
0.66 N
9.2 N
13 N
180 N
Answer is 9.2 N
Answer: Magnitude of the force exerted on the egg by the ground is 9.2N
Explanation:
Given the following :
Mass of egg (m) = 150g = 0.15kg
Height(h) from which egg is dropped = 3m
velocity of egg before hitting the ground (u) = 4.4m/s
Final velocity of egg (V) = 0
Time taken (t) = 0.072s
Magnitude of the force exerted on the egg by the ground can be found by applying Newton's 2nd law:
Momentum = mass × velocity
From Newton's second law:
Force = mass × change in Velocity with time ;
That is
F = m * ΔV / t
Inputting our values
F = 0.15 * (4.4 - 0) / 0.072
F = 0.15 × (4.4 / 0.072)
F = 0.15 × 61.11
F = 9.16N
F = 9.2N
Answer:
9.2 N
Explanation:
Just took practice quiz
Find vertical and horizontal displacement. Please help. 10 points. Thank you.
Explanation:
horizontal velocity = 30 x Cos45 = 19.48m/s
to find horizontal displacement
horizontal displacement = horizontal velocity x timehorizontal displacement = 19.48 x 2 = 38.96mvertical velocity = 30 x Cos45 = 22.81m/s
vertical displacement = vertical velocity x time
vertical displacement = 22.81 x 2 = 45.62m
Answer:
Displacement after two seconds
= <Dx,Dy> = <42.426, 1.593> m to three decimal places
Explanation:
Given:
arrow shot at 30m/s and 45 degrees with horizontal.
Hit bull's eye after 2 seconds.
Find horizontal and vertical displacements.
Vx = 30cos(30) m/seconds constant velocity
therefore
Dx = Vx*t = 30cos(30) m/s * 2 s = 60 cos (45) = 42.426 m
Vy = 30 sin(45) m/s
Dy = Vy*t + a(t^2) /2
= 30*sin(45) -9.81(2^2)/2 (g is accelerating downwards, so negative)
= 1.593 m
The net displacement after 2 seconds is
D = <Dx,Dy> = <42.426, 1.593> m to three decimal places
help fast I want the correct answer please does spectral diffusion cause light to scatter
Answer: No
Explanation:
Whenever light travelling on a straight line encounters obstruction, it diffracts and scatter.
Scattering of light occurs when light passes through a rough path or a diffused surface.
But in case of spectral diffusion, which is the fluctuation in spectroscopy as a result of time dependent frequency shifts.
Spectral diffusion occurs in particular molecules initiated by excessive excitation energy.
Fluctuation in frequency does not mean diffraction of light or particles
Therefore, spectral diffusion does not cause light to scatter.
A 0.675 kg mass is attached to a
spring of spring constant 42.4 N/m,
pulled, and released. What is the
frequency of the resulting
oscillation?
(Unit = Hz)
Answer:
1.26
Explanation:
f=1/(2pi) square root k/m
f=1/(2pi) square root 42.4/.675
f=1.26 I just did this question and found this right
A machine is 40 % efficient. The total energy supplied to the machine is 4 kJ. Calculate how much useful energy can be transferred.
Answer:
1.6 kJ
Explanation:
0.40 (4 kJ) = 1.6 kJ
What are some of the major differences between the ancient Olympics and modern-day Olympics? List and describe at least two differences.
Answer:
-Women are now allowed to participate in the Olympics unlike before when it was only men allowed.
-Modern Olympic Games include many more events. There are more than 20 different sports and almost 300 events in the modern games, while the first Olympics only had running.
-The Olympics are held every two years. While the ancient Olympics were originally held every four years.
-Athletes from countries around the world participate in the modern Olympics unlike in the ancient Olympics where only athletes from ancient Greece competed.
Explanation:
Edmentum Plato answer (i already reworded most of it so you don't have to) <33
If I were to fill a water bottle full of air and go up in elevation, would the water bottle expand or shrink? If I were to fill a water bottle full of air and go down in elevation, would the water bottle expand or shrink? I am at elevation 20000 I think.
Answer:
a. It would shrink
b. It would expand
Explanation:
a. Since the water bottle is filled with air at atmospheric pressure at 20000 ft, and since atmospheric pressure decreases with altitude, when we go up in elevation.
The pressure exerted by the molecules of air in the water bottle seek to balance out the atmospheric pressure as we go higher. Since the atmospheric pressure exerted by the molecules of air in the atmosphere are greater than that exerted by the molecules of air in the water bottle, this causes the volume of the water bottle to decrease and thus shrinks the water bottle until the pressure balances out
b. Since the water bottle is filled with air at atmospheric pressure at 20000 ft, and since atmospheric pressure increases with decreasing altitude, when we go down in elevation.
The pressure exerted by the molecules of air in the water bottle seek to balance out the atmospheric pressure as we go lower. The water bottle expands until the atmospheric pressure outside equals the pressure inside the water bottle.this causes the volume of the water bottle to increase and thus expands the water bottle until the pressure balances out
Which of the following statements are true (mark all that apply) primordial nucleosynthesis produced all of the elements heavier than helium chemical composition of our solar system matches the chemical composition of the Milky Way some of the stars in the Milky Way may be older than the Milky Way your body contains a lot of helium nearly all atoms of elements heavier then helium were produced through nuclear fusion in stellar interiors and through reactions that occur during explosions that massive stars undergo at the ends of their lives or during mergers of stellar remnants called neutron stars some of the oldest galaxies are about 13.2 billion years old nucleosynthesis is a process through which the atoms of various elements are produced you're mainly made of hydrogen
Answer:
The correct options are;
1) The chemical composition of our solar system matches the chemical composition of the Milky Way
2) Nearly all atoms of elements heavier than helium were produced through nuclear fusion in stellar interiors and through reactions that occur during explosions that massive stars undergo at the ends of their lives or during mergers of stellar remnants called neutron stars
3) Some of the oldest galaxies are about 13.2 billion years old
4) Nucleosynthesis is a process through which the atoms of various elements are produced
5) You re mainly made of hydrogen
Explanation:
1) There are dependencies between chemical composition of stars and planets and the same distribution of chemicals we have in our Solar system have been observed to be present in varying resemblance through out the Milky Way
2) The formation of heavier elements are believed to have been formed by astrophysical fusion processes
3) The oldest known object (and hence the galaxy where the star resides), is from a distant star known as GRB 090423 which is about 13 billion years old
4) New atomic nuclear are created by the process of protons and neutrons by the process of nucleosynthesis
5) 62%of the atoms in the body are hydrogen atoms.
When Emma pushes a bag with a force of 27 newtons, the coefficient of kinetic friction between the bag and the floor is 0.23. What is the normal force acting on the bag by the floor? A. 0.085 newtons B. 27 newtons C. 2.7 × 102 newtons D. 1.2 × 102 newtons
Answer:
D. 1.2 × 102 newtons
Explanation:
The computation of the normal force acting on the bag is shown below:
It could find out by applying the following formula
Normal force = Force ÷ coefficient of kinetic friction
where,
Force is 27 newtons
And, the coefficient of kinetic friction is 0.23
Now placing these values to the above formula
So, the normal force is
= 27 newtons ÷ 0.23
= 117.39 N
Therefore the correct option is D.
a force of 50 n acts on abody of mass 5 kg .calculate the acceleration produced
Answer:
a = 10 m/s²
Explanation:
Given:
Force = F = 50 N
Mass = m = 5 kg
Required:
Acceleration = a = ?
Formula:
F = ma
Solution:
Rearranging the formula for a
=> a = F/m
=> a = 50/5
=> a = 10 m/s²
The vibrations of a string fixed at both ends are represented by y=16sin(πx/15 )cos(96πt). Where x and y are in cm and t in seconds. Then the phase difference between the points at x=13cm and x=16 in radian
Answer:
Explanation:
y = 16 sinπx/15 cos(96πt)
When t = 0
y = 16 sinπx/15
here πx/15 is phase of the point at x
if x = 13
Phase = 13π/15
if x = 16
Phase = 16π/15
Phase difference
= 16π/15 - 13π/15
= 3π/15
= π/5 radian .
Who found Uranus? Name?
Answer:William Herschel found the seventh planet now known as uranus
<!> Brainliest is appreciated! <!>
Explanation:
Answer:
William Herschel
Explanation:
how does gravitational pull affect planets with the same mass but different distance from the sun?
Answer:
it just pulls them at the same time
Explanation:
An electron moving with a velocity of 5 × 104 m s -1 enters into a uniform electric field and acquires a uniform acceleration of 104 m s -2 in the direction of its initial motion. (i) Calculate the time in which the electron would acquire a velocity double of its initial velocity. (ii) How much distance the electron would cover in this tim
Answer:
(i) t = 5s
(ii) x = 3.75*10^5 m
Explanation:
(i) To calculate the time that the electron takes to reach twice the value of its initial velocity, you use the following formula:
[tex]v=v_o+at[/tex] (1)
vo: initial velocity of the electron = 5*10^4 m/s
v: final velocity of the electron = 2vo = 1*10^5 m/s
a: acceleration of the electron = 1*10^4 m/s^2
You solve the equation (1) for t, and replace the values of the parameters:
[tex]t=\frac{v-v_o}{a}=\frac{1*10^5m/s-5*10^4m/s}{1*10^4m/s^2}=5s[/tex]
The electron takes 5s to reach twice its initial velocity.
(ii) The distance traveled by the electron in such a time is:
[tex]x=v_ot+\frac{1}{2}at^2[/tex] (2)
you replace the values of the parameters in the equation (2):
[tex]x=(5*10^4m/s)(5s)+\frac{1}{2}(1*10^4m/s^2)(5s)^2\\\\x=3.75*10^5m[/tex]
The distance traveled by the electron is 3.75*10^3m/s
A 500 kg satellite experiences a gravitational force of 3000 N, while moving in a circular orbit around the earth. Determine the speed of the satellite.
Answer:
Speed of the satellite V = 6.991 × 10³ m/s
Explanation:
Given:
Force F = 3,000N
Mass of satellite m = 500 kg
Mass of earth M = 5.97 × 10²⁴
Gravitational force G = 6.67 × 10⁻¹¹
Find:
Speed of the satellite.
Computation:
Radius r = √[GMm / F]
Radius r = √[(6.67 × 10⁻¹¹ )(5.97 × 10²⁴)(500) / (3,000)
Radius r = 8.146 × 10⁶ m
Speed of the satellite V = √rF / m
Speed of the satellite V = √(8.146 × 10⁶)(3,000) / 500
Speed of the satellite V = 6.991 × 10³ m/s
difference between uniform velocity and variable velocity .
Answer:
If a body covers equal displacement in equal interval of time,however small may be the body is said to have uniform velocity. If a body covers in equal displacement in equal interval of time is called variable velocity.
I will give Brainliest to whoever can answer!!!!
If the phase of the vibrating sources was changed so that they were vibrating completely out of phase, what effect would this have on the interference pattern?
Answer:
The nodes and anti nodes would reverse roles.
Explanation:
I believe it has to do with the path differences. If waves are in phase, then the path differences are such that the waves reach the screen with crests superimposing crests and troughs superimposing troughs. This happens when the periods of each wave are equal or the paths themselves differ by a whole number multiple of the wavelength (λ, 2λ, 3λ, ...).
Now make these waves out of phase. Then half of the waves will travel half a wavelength farther than the rest. So the path difference will be 0.5λ, 1.5λ, 2.5λ, ....
A train moves at a constant velocity of 50 km/hHow far will it move in 0.5 h?
A. 10 km
B. 45 km
C.25 km
D. 20 km
Answer:
C
Explanation:
[tex]\dfrac{50km}{h}\cdot 0.5h= \\\\\\50km\cdot 0.5=25km[/tex]
Therefore, the correct answer is choice C. Hope this helps!
The correct answer is C.
It is C because .5 h is equal to 30 minutes. So half of 50 km is 25 km(Divided by 2)
During the warm-up and your scheduled physical activity, what was the weather like? Did the
temperature or conditions affect how much water you drank? How?
Answer: I did these exercises outdoors. The weather was hot and humid, so I drank about two cups of water during the workout. I also drank a cup of water about an hour before I started. Yes, the weather most definitely affected how much I drank.
Explanation: Edmentum
what is acceleration???
Answer:
The rate at which velocity changes.
Explanation:
Acceleration is when motion changes, it is the rate at which velocity changes.
Answer:
Acceleration is defined as change in velocity per unit time.The increase in velocity per unit time is called acceleration.
Hope this is helpful for you.
As a motorcycle takes a sharp turn, the type of motion that occurs is called _______________ motion.
Answer:
circular motion
Explanation:
As a motorcycle takes a sharp turn, the type of motion that occurs is called circular motion.
Circular motion is a movement of an object along a circular path. As this motorcycle makes the sharp turn, it is acted upon by a centripetal force which directs the motorcycle towards the center.
Therefore, circular motion is the correct answer to the question.
Answer:
Circular Motion
A cars start from rest . after 10 seconds its acceleration become 2 meter per second find its final velocity
Answer:
[tex] \boxed{\sf Final \ velocity = 20 \ m/s} [/tex]
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 2 m/s²
Time taken (t) = 10 seconds
To Find:
Final velocity (v)
Explanation:
[tex]\sf From \ equation \ of \ motion: \\ \sf v = u + at \\ \\ \sf v = 0 + 2(10) \\ \\ \sf v = 2 \times 10 \\ \\ \sf v = 20 \ m/s[/tex]
Dominic made the table below to organize his notes about mixtures.
Properties of Mixtures
has no set composition
must have more than one state of matter
must have more than one substance
What mistake did Dominic make?
The title should read "Properties of Solutions" because some mixtures do not have all of the properties listed.
There is a definite recipe to make each mixture, so the composition of a mixture is set.
Although it is possible to have more than one state, it is also possible to have only one state.
A single substance can be used to make a mixture if the substance is composed of more than one element.
Answer:
Althought it us possible to have more then one state, it's also possible to have only one state of matter
Explanation:
You can make solutions of only one state if matter, for example , it two liquids can be mixed to form a solution they are called miscible.
Answer:
The correct answer is C.) Although it is possible to have more than one state, it is also possible to have only one state.
Explanation:
I just did the test on edge and got it right
What will happen to the astronaut when the jets produce these four forces: 10N, 10N, 9N, 9N?
1-D Kinematics
A car starts at a position of -153 m
and undergoes a displacement of
512 m. What is its final position?
(Unit = m)
Answer:
hope it helps you...........
write examples of adaptation in mangrove .?
what are the adaptation of rainforest.?
Answer:
example of adaptation in mangrove
Mangroves are salt-tolerant trees, also called halophytes, and are adapted to life in harsh coastal conditions. They contain a complex salt filtration system and complex root system to cope with salt water immersion and wave action. They are adapted to the low oxygen conditions of waterlogged mud.
adaptation of rainforest
Many animals have adapted to the unique conditions of the tropical rainforests.
hope this can help you
what are laws of newton
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:
Answer:
Newton's Law of Motion
1- Every object persists in its state of rest or uniform motion - in a straight line unless it is compelled to change that state by forces impressed on it.
2- Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration.
3- For every action, there is an equal and opposite reaction.
Which object has the most gravitational potential energy?
O A. A 5 kg book at a height of 2 m
B. An 5 kg book at a height of 3 m
C. An 8 kg book at a height of 3 m
O D. A 8 kg book at a height of 2 m
SUBARU
Answer:
D
Explanation:
its the heaviest so i would assume its D
A garrafa térmica (também conhecida como "vaso de Dewar") é um dispositivo extremamente útil para conservar, no seu interior, corpos (essencialmente líquidos) em altas temperaturas, minimizando trocas de energia com o ambiente, geralmente mais frio. Uma garrafa térmica contém água a 60 o C. O conjunto garrafa térmica + água possui capacidade térmica C=80 cal/o C. O sistema é colocado sobre uma mesa e, após um intervalo considerável de tempo, a sua temperatura diminui para 55 o C. Nesse caso, conclui-se que o sistema formado pela garrafa térmica e pela água no seu interior: a) perdeu 400 cal. B) ganhou 404cal. C) perdeu 4 850 cal. D) ganhou 4 850 cal. E) não trocou calor com o meio externo.
Answer:
A opção A está correta.
O sistema formado pela garrafa térmica e a água perde 400 cal de calor para o meio ambiente.
Option A is correct.
The system formed by the thermos and the water loses 400 cal of heat to the environment.
Explanation:
Quando a temperatura de um sistema reduz, fica claro que o sistema perdeu calor ou energia térmica. Como a temperatura é um dos indicadores mais claros disso, esta conclusão é hermética e correta.
Mas, para saber a quantidade de calor perdida para o meio ambiente, agora fazemos alguns cálculos de energia térmica.
Transferência de calor de ou para o sistema de água e garrafa térmica = c × ΔT
c = capacidade térmica do sistema de água e garrafa térmica = 80 cal /°C
ΔT = Alteração da temperatura do sistema de água e garrafa térmica = (temperatura final) - (temperatura inicial) = 55 - 60 = -5°C
Calor transferido = 80 × -5 = -400 cal.
O sinal de menos mostra que o calor é transferido para fora do sistema, ou seja, o calor é perdido no sistema.
Espero que isto ajude!!!
English Translation
The thermos (also known as "Dewar vase") is an extremely useful device to conserve bodies (essentially liquid) at high temperatures, minimizing energy exchanges with the environment, which is generally colder. A thermos contains water at 60 o C. The thermos + water set has a thermal capacity of C = 80 cal / o C. The system is placed on a table and, after a considerable period of time, its temperature decreases to 55 o C. In this case, it is concluded that the system formed by the thermos and the water inside:
a) lost 400 cal. B) gained 404cal. C) lost 4 850 cal. D) gained 4 850 cal. E) did not exchange heat with the external environment.
Solution
When a system's temperature reduces, it is clear to conclude that the system has lost heat or thermal energy. Since temperature is one of clearest indicators of this, this conclusion is airtight and correct.
But, to know the amount of heat lost to the environment, we now do some thermal energy calculations.
Heat transferrred from or to the water and thermos system = c × ΔT
c = heat capacity of the water and thermos system = 80 cal/°C
ΔT = Change in temperature of the water and thermos system = (final temperature) - (initial temperature)
= 55 - 60 = -5°C
Heat transferred = 80 × -5 = -400 cal.
The minus sign shows that the heat is transferred out of the system, that is, the heat is lost from the system.
Hope this Helps!!!