The lights on and in your vehicle can be as important to your and your passengers' safety as seatbelts, and as visually appealing as great rims or an unusual paint color.
Why headlight consumes much more power than interior dome light ?Automobiles have been around for nearly a decade, almost as long as mass-marketable light bulbs. The first light bulbs were incandescent, which simply passed any current, AC or DC, through a high-impedance filament, which heated up, glowed, and emitted light.
Although their efficiency is low (as low as 10%), they emit light in all directions and are inexpensive. Under the heat required to generate light, the filament material (typically tungsten) evaporates and tends to collect on the inside of the glass bulb, darkening it over time.
Consumers are looking beyond incandescent lights to high intensity discharge headlights and other 12v LED lighting solutions as the automotive industry grows, but there are even more options and modifications available. While there are amazing new technologies available, not all of them are true advancements or even road-legal. Let us shed some light on the situation.
To learn more about Automotive Lighting Technologies refer to:https://brainly.com/question/25397646
#SPJ1
Hello, I needed help with a few assignment questions. Thank you. It's about Newton's second law of motion.
We will have the following:
2) We can determine that the ratio is constant due to the fact that the acceleration of the gravity on Earth remains constant on the planet. And the mass of the planet is constant.
3) What causes the objects accelerate is the mass of the body that supports them and the mass of the very object. In clasical mechanics the acceleration is due to the influence that a body imparts on another. In relativistic mechanics the acceleration is due to the warping of the space that makes the bodies towards the one with a bigger sphere of influence.
It can also be interpreted as the relationship of the force that is imparted on a body by another and the mass of the smaller object.
A rocket accelerates at 65 m/s² with the force of 54,080 N. What is the mass of the rocket?
Answer:
832 kgExplanation:
The mass of the rocket given it's acceleration and force can be found by using the formula
[tex]mass = \frac{f}{a} \\ [/tex]
where
f is the force in N
a is the acceleration in m/s²
From the question
f = 54,080 N
a = 65 m/s²
We have
[tex]mass = \frac{54080}{65} = 832 \\ [/tex]
We have the final answer as
832 kghope this helps you
Help me please!!!!!!!
lab report shows water changing state of matter is an endothermic process with changing temperature this is an example of physical change.
When some of a material's properties change but the identity of the material does not, there is a physical change to the substance. Reversible and irreversible physical changes are further separated into two types. Since the melted ice cube can be refrozen, melting is a physically reversible process.
For instance, when water is heated, the temperature and energy of the water molecules rise, causing the liquid water to vaporize into water. When this occurs, some sort of alteration has occurred, but the water's molecular makeup remains unchanged. A bodily transformation like this is an example.
For more information on physical change kindly visit to
https://brainly.com/question/28742279
#SPJ1
A hover board is moving at 6 m/s . If it slows down at a rate of -3 m/s per second, how long is the board in the air before coming to rest? Round to 4 decimal places if necessary
Explanation
a uniformly accelerated motion is the one in which the acceleration of the particle throughout the motion is uniform,to fidn the time take we can use the formula:
[tex]\begin{gathered} t=\frac{v_f-v_1}{a} \\ where \\ v_f\text{ is the final velocity} \\ v_{i\text{ }}\text{ is the initail velocity} \\ a\text{ is the acceleration, so} \end{gathered}[/tex]Step 1
a)Let
[tex]\begin{gathered} v_i=6\text{ }\frac{m}{s} \\ v_f=0(\text{ rest\rparen} \\ a=-3\frac{m}{s^2} \end{gathered}[/tex]b) now, replace
[tex]\begin{gathered} t=\frac{v_{f}-v_{1}}{a} \\ t=\frac{0-(-6\frac{m}{s})}{3\frac{m}{s}} \\ t=2\text{ seconds} \end{gathered}[/tex]therefore, the answer is 2 seconds
I
A 50 kg ball traveling at 20 m/s would haveA50 kg ball traveling at 5 m/s would haveA 50 kg person falling at 10 m/s would havekinetic energy✓ kinetic energykinetic energythe same2 times more2 times less4 times more4 times lessDoneIntro5 of 9
We have the next formula to calculate the kinetic energy
[tex]KE=\frac{1}{2}mv^2[/tex]where m is the mass and v is the velocity
For the kinetic energy of ball 50 kg traveling at 10 m/s
[tex]KE=\frac{1}{2}(50)(10)^2=2500\text{ joules}[/tex]For the kinetic energy of ball 50 kg traveling at 20 m/s
[tex]KE=\frac{1}{2}(50)(20)^2=10000\text{ joules}[/tex]A 50 kg ball traveling at 20 m/s would have 4 times kinetic energy.
For kinetic energy of the ball 50 kg at 5m/s
[tex]KE=\frac{1}{2}\mleft(50\mright)\mleft(5\mright)^2=625\text{ joules}[/tex]A 50 kg ball traveling at 5 m/s would have 4 times less kinetic energy
For the person 50kg falling 10 m/s
[tex]KE=\frac{1}{2}\mleft(50\mright)\mleft(10\mright)^2=2500joules[/tex]A 50 kg person falling at 10 m/s would have the same kineticenergy}.
The solution is
A 50 kg ball traveling at 20 m/s would have 4 times more kinetic energy.
A 50 kg ball traveling at 5 m/s would have 4 times less kinetic energy.
A 50 kg person falling at 10 m/s would have the same kinetic energy.
need help asappppppp
Visible light, x-rays, and radio waves are forms of electromagnetic waves that can travel through vacuum and mater.
1. While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is theautomobile's acceleration? (Remember that a negative value indicates a slowing down.)
Given data
*The initial speed of the driver is u = 24 m/s
*The final speed of the driver is v = 15 m/s
*The given time is t = 12 s
The formula for the automobile's acceleration is given as
[tex]a=\frac{v-u}{t}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} a=\frac{15-24}{12} \\ =-0.75m/s^2 \end{gathered}[/tex]A pitching machine throws a 0.148kg baseball to the left at 26m/s. A batter then hits the baseball directly back at 39m/s. What is the change in momentum of this baseball
Let us assume that the initial direction of the ball, i.e., from the pitching machine to the batter as the negative direction, and the final direction of the ball is the positive direction.
Given,
The mass of the baseball, m=0.148 kg
The initial velocity of the baseball, u=-26 m/s
The final velocity of the baseball, v=39 m/s
The momentum of the ball before the batter hits it is given by,
[tex]p_1=mu[/tex]On substituting the known values,
[tex]\begin{gathered} p_1=0.148\times-26 \\ =-3.848\text{ kg}\cdot\text{m/s} \end{gathered}[/tex]The momentum of the ball after the batter hits it is given by,
[tex]p_2=mv[/tex]On substituting the known values,
[tex]\begin{gathered} p_2=0.148\times39 \\ =5.772\text{ kg}\cdot\text{m/s} \end{gathered}[/tex]The change in the momentum is given by,
[tex]\Delta p=p_2-p_1[/tex]On substituting the known values,
[tex]\begin{gathered} \Delta p=5.772-(-3.848) \\ =9.62\text{ kg}\cdot\text{m/s} \end{gathered}[/tex]Thus the change in the momentum of baseball is 9.62 kg·m/s
a load of 41 n attached to a spring hanging vertically stretches the spring 3.1 cm. the spring is now placed horizontally on a table and stretched 11 cm. what force is required to stretch it by this amount? answer in units of n.
A load of 41 n attached to a spring hanging vertically stretches the spring 3.1 cm. the spring is now placed horizontally on a table and stretched 11 cm. 145.42 N force is required to stretch it by this amount
k = spring constant
x = displacement
force1 = - k x1
41 = - k (3.1)
k = 13.22 N/cm
force2 = -k x2
= - 13.22 * 11 = 145.42 N
145.42 N force is required to stretch it by this amount
To learn more about spring constant here :
https://brainly.com/question/14670501
#SPJ4
Tariah is riding on her bike at 4m/s (North). If she accelerates at a rate of 1.5 m/s^2 for 2 s, what is her final velocity?
ANSWER:
7 m/s
STEP-BY-STEP EXPLANATION:
Given:
Initial velocity (u) = 4 m/s
Acceleration (a) = 1.5 m/s^2
Time (t) = 2 s
We can calculate the final velocity using the following formula:
[tex]v=u+a\cdot t[/tex]We replace and calculate the value of the final velocity:
[tex]\begin{gathered} v=4+2\cdot1.5 \\ v=4+3 \\ v=7\text{ m/s} \end{gathered}[/tex]The final velocity is equal to 7 m/s.
The final products of photosynthesis are oxygen and ______
A. Sunlight
B. Water
C. Sugar
D. Carbon dioxide
Answer:
gulcose=sugar
Explanation:
the syringe used in the boyle's law experiment leaks, giving you a low pressure. will the calculated constant be too high, too low or unchanged?
The syringe used in the Boyle's law experiment leaks, giving a low pressure,hence, the calculated constant will be too low.
What is the statement of Boyle's law of gases?Boyle's law of gases states that the pressure of a given volume of gas is inversely proportional to the volume of the gas provided that the temperature is kept constant.
This implies that as pressure increases, the volume will decrease at a constant temperature.
On the other hand, if the volume increases, the pressure decreases at a constant temperature.
Learn more about Boyle's law of gases at: https://brainly.com/question/1696010
#SPJ1
Two waves with the same wavelength interact. One has an amplitude of +0.42 m and the
other wave has an amplitude of -0.18 m. When the two waves exactly overlap, what is the
resultant amplitude?
The resultant amplitude of the waves when the two waves overlap is +0.24 m.
What is amplitude of a wave?
The amplitude of a wave is the maximum vertical displacement of the wave or the highest upward displacement of a wave.
The resultant amplitude of the waves when the two waves overlap is calculated as follows;
resultant amplitude = amplitude of the first wave + amplitude of the second wave
resultant amplitude = 0.42 m - 0.18 m
resultant amplitude = 0.24 m
The resultant amplitude of the waves when the two waves overlap depends on the initial amplitude of each wave as shown above.
Learn more about resultant amplitude here: https://brainly.com/question/1704101
#SPJ1
According to newton's 3rd law, the force on the (smaller) moon due to the (larger) earth is.
Bigger in magnitude and pointing away from the force the moon exerts on the earth.
Explain about the Newton's 3rd law?According to Newton's third law, there is an equal and opposite reaction to every force (action) in nature.
Understanding which forces are external to a system is possible with the aid of Newton's third law. Recall that while creating a problem, identifying external forces is crucial since they must be combined together to determine the net force.
Newton's third law states that the force the ball exerts on the bat when it is struck by the bat will be similar in magnitude but directed in the opposite direction. You won't typically feel the bat "recoiling" when you strike the ball forward because your arms are usually rigid.
To learn more about Newton's 3rd law refer to:
https://brainly.com/question/25998091
#SPJ1
A ball is thrown horizontally from the top of a building 53.5 m high. the ball strikes the ground at a point 49.7 m from the base of the building. the acceleration of gravity is 9.8 m/s 2 . find the time the ball is in motion.
Answer: who ever thrown that ball, got an arm.
Explanation:
angle. what is the angle between the colors when they emerge? (b) how far would they have to travel to be separated by 1.00 mm?
A rainbow often has the following hues: red, orange, yellow, green, blue, and violet. Indigo is occasionally included as well. These hues are related to various light wavelengths.
What three sorts of light beams are there?Three types of light beams are possible. Both convergent and divergent, they are parallel.
What different kinds of beams are there?5 Various Light Bulb Types
Incandescent Light Bulbs:
3- Compact Fluorescent Lamps: 2- Fluorescent Lamps (CFL)
4. Halogen lighting
Light-emitting diode No. 5 (LED)
What names do beams have?Following the depth of section, beams are designated according to their respective shortened.
To know more about angle between the colors visit:-
https://brainly.com/question/27965686
#SPJ4
Friction Virtual Lab
Coefficients of Friction.
Run the same simulation above. Use 50 kg mass and set the friction again to halfway. Apply the push, observe and record the maximum value of static friction.
1. Find the coefficient of static friction μs by using the equation (2)
2. Now apply the push so that the object moves with constant speed.
3. Find the coefficient of kinetic friction μk by using the equation (1)
4. According to your notes μs >μk, is this consistent with your results from questions 1 & 3? (If not, repeat the experiment)
4. Now add another 50 kg mass and repeat the experiment to find μk.
5. What is μk now?
6. Are your results in questions 3 and 5 different?
7. According to your notes, the coefficient of friction is constant. Is that consistent with your answer to question 7?
1 ) The coefficient of static friction μs by using the equation (2) = 0.26
3 ) The coefficient of kinetic friction μk by using the equation (1) = 0.19
1 ) The coefficient of static friction
μ[tex]_{s}[/tex] = [tex]f_{s} _{max}[/tex] / F[tex]_{n}[/tex]
μ[tex]_{s}[/tex] = 125 / 50 * 9.8
μ[tex]_{s}[/tex] = 0.26
3 ) The coefficient of kinetic friction
μ[tex]_{k}[/tex] = [tex]f_{k}[/tex] / F[tex]_{n}[/tex]
μ[tex]_{k}[/tex] = 94 / 50 * 9.8
μ[tex]_{k}[/tex] = 0.19
4 ) Yes, from ( 1 ) and ( 3 ),
μ[tex]_{s}[/tex] > μ[tex]_{k}[/tex]
5 ) μ[tex]_{k}[/tex] = [tex]f_{k}[/tex] / F[tex]_{n}[/tex]
μ[tex]_{k}[/tex] = 188 / 100 * 9.8
μ[tex]_{k}[/tex] = 0.19
6 ) No the μ[tex]_{k}[/tex] from ( 3 ) and ( 5 ) are exactly the same.
7 ) Since μ[tex]_{k}[/tex] from ( 3 ) and ( 5 ) are exactly the same, coefficient of friction is constant.
To know more about coefficients of friction
https://brainly.com/question/13754413
#SPJ1
Two unequal masses m and 2m are attached to a thin bar of negligible mass that rotates about an axis perpendicular to the bar. When m is a distance 2d from the axis and 2m is a distance d from the axis, the moment of inertia of this combination is i.
The moment of inertia for this combination is I when m is 2d from the axis and 2m is 2d from the axis, therefore I = mr2.
Explain the moment of inertia.Moment of inertia is a word used to describe a physical property that measures how resistant a body is to having the speed of its rotation along an axis modified by the application of a torque (turning force). Axis options include internal, external, stationary, and moving.
What does it mean to be in an inertial moment?The moment of inertia is recognized as such and not as a moment of force because it opposes circular motion.
To know more about Inertia visit:-
https://brainly.com/question/3268780
#SPJ4
Three vectors are shown in this figure. Their respective moduli are F = 40N T = 75 N and N = 25.6NCalculate the vector a so that F + N + T = 2.00A
First, separate each vector into its vertical and horizontal components. Then, add all the vertical components together, as well as the horizontal components, to find the components of the vectpr F+T+N. Set each component of the vector F+T+N to be equal to the corresponding component of 2.00A to find the components of A. Use the components of A to find the magnitude and direction of the vector A.
The vertical and horizontal components of T are given by:
[tex]\begin{gathered} T_y=T\sin (10.0º) \\ =75N\cdot0.1736\ldots \\ =13.02N \end{gathered}[/tex][tex]\begin{gathered} T_x=T\cos (10.0) \\ =75N\cdot0.9848\ldots \\ =73.86N \end{gathered}[/tex]The vertical and horizontal components of N are:
[tex]\begin{gathered} N_y=N \\ =25.6N \end{gathered}[/tex][tex]N_x=0[/tex]The vertical and horizontal components of F are:
[tex]\begin{gathered} F_y=-F\cdot\cos (15) \\ =-40N\cdot0.9659\ldots \\ =-38.637N \end{gathered}[/tex][tex]\begin{gathered} F_x=-F\cdot\sin (15) \\ =-40N\cdot0.2588\ldots \\ =-10.353N \end{gathered}[/tex]The vertical component of F+N+T is given by:
[tex]\begin{gathered} (F+N+T)_y=F_y+N_y+T_y \\ =-38.637N+25.6N+13.02N \\ =-0.017N \\ \approx0.0N \end{gathered}[/tex]The horizontal component of F+N+T is given by:
[tex]\begin{gathered} (F+N+T)_x=F_x+N_x+T_x \\ =-10.353N+73.86N \\ =63.51N \end{gathered}[/tex]Since F+N+T=2.00A, then this is true for each component:
[tex]\begin{gathered} (F+N+T)_y=(2.00A)_y=2.00\cdot A_y \\ (F+N+T)_x=(2.00A)_x=2.00\cdot A_x \end{gathered}[/tex]Substitute the values for the components of F+N+T to find the values of the components of A:
[tex]\begin{gathered} 2.00A_y=0.00N \\ \Rightarrow A_y=\frac{0.0N}{2.00}=0.0N \end{gathered}[/tex][tex]\begin{gathered} 2.00A_x=63.51N \\ \Rightarrow A_x=\frac{63.51N}{2.00}=31.75N \end{gathered}[/tex]Since the vertical component of A is 0, then the vector A has a magnitude of 31.75N directed toward the positive X axis.
Therefeore, the answer is:
[tex]A=31.75N\text{ toward the positive direction of X.}[/tex]Help me please????????
Answer:it should be A
Explanation:
A satellite is orbiting Earth at a distance of 42.0 kilometers. The satellite has a mass of 900kilograms. What is the force between the planet and the satellite? Hint: Recall Earth's mass aradius from earlier problems.
Answer:
8716.97 N
Explanation:
The force between the planet and the satellite can be calculated using the following equation
[tex]F=G\frac{m_1m_2}{d^2}[/tex]Where G = 6.67 x 10^(-11) N m²/kg², m1 is the mass of the satellite, m2 is the mass of the Earth and d is the distance from the center of the Earth to the satellite
Since the radius of the Earth is 6,371 km, we get
d = 42 km + 6,371 km = 6413 km
Then, to convert to m, we need to multiply by 1000
d = 6413 km x 1000 m/km = 6.413 x 10^6 m
Finally, replacing m1 = 900 kg, m2 = 5.972 x 10^24 kg, and d = 6.413 x 10^6 m, we get:
[tex]\begin{gathered} F=6.67\times10^{-11}\frac{(900)(5.972\times10^{24})}{(6.413\times10^6)^2} \\ F=8716.97\text{ N} \end{gathered}[/tex]Therefore, the force between the planet and the satellite is 8716.97 N
By what factor does the gravitational force between two objects increase if one object doubles in mass and the distance between them decreases by half?
The factor is that since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.
What is gravitational force?Gravitational force is described as the universal force of attraction, which is acting between objects. This force causes mutual attraction between all things with mass or energy.
The newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Learn more about gravitational force at: https://brainly.com/question/27943482
#SPJ1
Please, explain step by step.A car that’s initially traveling at 10 m/s accelerates uniformly for 4 seconds at a rate of 2 m/s2, in a straight line. How far does the car travel during this time?
To understand this first, analyze the conditions of the car
[tex]\begin{gathered} v_0=\frac{10m}{s} \\ t=4s \\ a=\frac{2m}{s} \\ \\ d=\text{?} \end{gathered}[/tex]Whit this data we have to find the distance traveled by the car in these 4 seconds
[tex]\begin{gathered} d=v_0\cdot t+\frac{a\cdot t^2}{2} \\ d=10\cdot4+\frac{2\cdot4^2}{2} \\ d=40+16=56m \end{gathered}[/tex]Please help me with this I’m stuck!
Answer:
C. Similar to both Iron and Oxygen.
Explanation:
For iron to react with oxygen, it must be heated beforehand. Iron burns with a dazzling flame, scattering sparks – incandescent particles of iron cinder Fe₃O₄. The same reaction of iron and oxygen also takes place in air, when during mechanical processing, steel heats up drastically from friction.
Answer: I believe that (C) the oxidation is similar to iron and oxygen.
Explanation: The law of conservation of matter states that matter can't be created nor destroyed. So oxidation would be both iron and oxygen. It will only be changed, but will contain some of oxygen, and some of iron. so I believe the answer is (C)
what seems to happen to the one electron in the outer layer of sodium when it combines with chlorine to form sodium chloride?
A jet of water squirts out horizontally froma hole on the side of the tank as shown below. If the hole has a diameter of 3.62 mm, whatis the height of the water above the hole inthe tank?Answer in units of cm.
The jet of water emerges with a speed v horizontally. Then, it falls a vertical distance of 1.58, and during the time of its fall until it hits the ground, it travels a distance of 0.586 meters.
Since the water moves according to the Projectile Motion formulas, the horizontal motion is uniform and the vertical motion is uniformly accelerated from rest.
Then, we can use the vertical distance to find the time that it takes for the water to reach the ground. Then, divide the horizontal distance traveled by the water by the time it took for the water to fall to find the horizontal speed of the water.
Finally, use Torricelli's Theorem to relate the height of the water above the hole in the pipe to the horizontal speed. Find the height of the hole by isolating it and replacing the value of the known variables.
Step 1: Time
Since the water falls from rest a distance of 1.58m, and the time it takes for an object to fall a distance d in free fall from rest is given by:
[tex]t=\sqrt[]{\frac{2d}{g}}[/tex]Then, replace d=1.58m and the value of the acceleration of gravity g=9.81m/s^2 to find the time it takes for the water to fall:
[tex]t=\sqrt[]{\frac{2(1.58m)}{9.81\frac{m}{s^2}}}=0.5675564161\ldots s[/tex]Step 2: Speed
Since the water travels a horizontal distance of 0.586m during that time, then, the speed of the water jet as it emerges from the hole, is:
[tex]v=\frac{x}{t}=\frac{0.586m}{0.5675564161\ldots s}=1.032496477\ldots\frac{m}{s}[/tex]Step 3: Height (Torricelli's Theorem)
According to Torricelli's Theorem, the speed of a liquid jet emerging from a hole located a distance h below the level of water of a large container, is:
[tex]v=\sqrt[]{2gh}[/tex]Isolate h from the equation:
[tex]h=\frac{v^2}{2g}[/tex]Replace v=1.032496477...m/s and g=9.81m/s^2 to find the height of the water above the hole in the tank:
[tex]h=\frac{(1.032406477\ldots\frac{m}{s})^2}{2(9.81\frac{m}{s^2})}=0.05433481013\ldots m\approx5.43\times10^{-2\text{ }}m[/tex]Write the answer in cm:
[tex]h=5.43cm[/tex]Therefore, the height of the water above the hole in the tank is 5.43 centimeters.
what do we mean by inflation? what do we mean by inflation? the expansion of universe starting with the instant after the big bang the rapid expansion of the universe, driven by white dwarf supernova, that we still observe today the sudden release of photons when particles and antiparticles annihilate each other a sudden expansion of the universe driven by the energy released when the strong and electroweak forces froze out from the gut force the photons released when electrons and protons first combined, forming the cosmic microwave background radiation
a car has a mass of 2,000 kg. there are two passengers in the car, each with a mass of 55 kg. if the coefficient of kinetic friction is .02, what is the force of friction experienced by the car? what is the acceleration of the car if the car is applying a force of 1060 n?
f = μ N
N = m g
f = Frictional force
μ = Co-efficient of friction
N = Normal force
m = Mass
g = Acceleration due to gravity
m = 2000 + 55 + 55
m = 2110 kg
g = 9.8 m / s²
μ = 0.02
f = 0.02 * 2110
f = 42.2 N
According to Newton's second law of motion,
F = m a
F = Force
a = Acceleration
F = 1060 N
a = F / m
a = 1060 / 2110
a = 0.5 m / s²
Therefore,
The force of friction experienced by the car is 42.2 NThe acceleration of the car if the car is applying a force of 1060 N is 0.5 m / s²To know more about Newton's second law of motion
https://brainly.com/question/13447525
#SPJ4
CAN SOMEONE CONFIRM ME PLEASW URGENT
Answer:
Sun has enough mass to attract the planets is the correct answer
Answer:
sun has enough mass to attract the plante
A 0.0500-kg ice cube at −30.0ºC is placed in 0.400 kg of 35.0ºC water in a very well-insulated container. What is the final temperature?
The amount of heat that is gained by water is equal to the amount of heat loss by the ice. Therefore, we have the following relationship:
[tex]-Q_w=Q_i[/tex]Where "Qw" is the heat of water and "Qi" is the heat of ice. The heat of water is given by:
[tex]Q_w=m_wC_w(T_f-T_{0w})[/tex]The amount of heat of ice must be calculated for the two states, solid and liquid. For the solid-state the temperature will be from -30 degrees to 0 degrees, therefore, we have:
[tex]Q_i=m_iC_i(T_f-T_{0i})[/tex]Where Ci is the specific heat of ice in solid-state and is equal to:
[tex]C_i=2090\frac{kJ}{\operatorname{kg}}[/tex]Replacing the values:
[tex]Q_i=(0.05\operatorname{kg})(2090\frac{kJ}{\operatorname{kg}K})(0-(-30C))[/tex]Solving the operations we get:
[tex]Q_i=3135J[/tex]Now we need to determine the amount of heat that needs the ice to convert into liquid. This is given by:
[tex]Q_{i-l}=m_iL_f[/tex]Lf is the latent heat of ice and is equal to:
[tex]L_f=334\frac{kJ}{\operatorname{kg}}[/tex]Replacing the values we get:
[tex]Q_{i-l}=(0.05\operatorname{kg})(334\frac{kJ}{\operatorname{kg}})[/tex]Solving the operations:
[tex]Q_{i-l}=16.7kJ=16700J[/tex]Now we need the amount of heat of liquid ice to its final temperature, this is given by:
[tex]Q_l=m_iC_l(T_f-0)[/tex]Applying the relationship:
[tex]-m_wC_w(T_f-T_{0w})=m_iC_i(T_f-T_{0i})+m_iL_f+m_iC_w(T_f-0)[/tex]Cw is the specific heat of water and is equal to:
[tex]C_w=4184\frac{J}{\operatorname{kg}K}[/tex]And the specific heat of ice is:
[tex]C_i=4184\frac{J}{\operatorname{kg}K}[/tex]Replacing the values. The first two terms on the right side we already calculated and the final temperature is the same for both:
[tex]-(0.4\operatorname{kg})(4184\frac{kJ}{\operatorname{kg}K})(T_f-35)=3135J+16700J+(0.05)(4184\frac{kJ}{\operatorname{kg}K})(T_f)[/tex]Solving operations:
[tex]-1673.6\frac{kJ}{K}(T_f-35)=19835J+209.2\frac{kJ}{K}T_f[/tex]Now we solve for the final temperature:
[tex]-1673.6T_f+58576=19835+209.2T_f[/tex]Subtracting 19835 to both sideS:
[tex]\begin{gathered} -1673.6T_f+58576-19835=209.2T_f \\ -1673.6T_f+38741=209.2T_f \end{gathered}[/tex]Now we add 1673Tf to both sides:
[tex]\begin{gathered} 38741=209.2T_f+1673.6T_f \\ 38741=1882.8T_f \end{gathered}[/tex]Now we divide both sides by 1882.2
[tex]\frac{38741}{1882.8}=T_f[/tex][tex]20.57=T_f[/tex]Therefore, the final temperature is 20.57 °C. This value can be converted into Kelvin using the following relationship:
[tex]T_K=T_C+273.15[/tex]Replacing the temperature:
[tex]T_K=20.57+273.15=293.72[/tex]Therefore, the final temperature is 293.72 K.