The train accelerates four times during its journey, and the examples provided illustrate concepts of acceleration and uniform circular motion as they apply to trains, buses, and rides like the carousel.
The train described in the question undergoes acceleration several times throughout its journey:
When it speeds up from a standstill to 5 m/s.When it increases its speed from 5 m/s to 10 m/s on a straightaway.When it slows down from 10 m/s to 5 m/s after a bend.When it comes to a stop at the station.Overall, the train accelerates a total of four times. On the other hand, uniform circular motion, such as that of a carousel horse moving around the center, involves an object traveling in a circular path at a constant speed. Despite the speed being constant, because the direction is changing, the object is still experiencing a centripetal acceleration towards the center of the circle.
For example 10.2.3 regarding the slow acceleration of trains, we can calculate the train's movement and wheel's angular velocity after 200 revolutions given the wheel radius and angular acceleration. To find out how far the train has moved down the track, we can use the formula for the circumference of a circle (C = 2πr) multiplied by the number of revolutions. To find the final angular velocity, we can use the kinematic equation for rotational motion (ω2 = ω02 + 2αθ), where ω0 is the initial angular velocity (zero in this case), α is the angular acceleration, and θ is the angular displacement (total revolutions times 2π).
The train accelerated twice at two different points in its journey. In the first instance, it accelerated from a standstill to 5 meters per second, and in the second instance, it accelerated from 5 meters per second to 10 meters per second.
Does radiation require a heated liquid to transfer energy?
well yes because it will rquerid to have heat
Answer:
Explanation: its false
A worker pushes a large rock to the north while another worker helps by pushing it to the east. If they both exert equal force, in what direction does the rock move?
northeast
east
north
southwest
Answer:
Northeast
Explanation:
Let magnitude of the force acting along north and east be F.
One worker pushes it toward north and another pushes it along east with same magnitude.
According to law of parallelogram the Resultant force has direction along northeast as shown in the figure.
How does mass affect the time it takes an object to hit the ground?
For an ideal condition The Mass does not affect the time taken by an object to hit the ground.
As the ground attracts all object with the same acceleration due to gravity 9.8 m/s². so all objects that drop from a certain height hit the ground at same time .
But in real condition there is air resistance present ,due to which objects of different masses take different time to hit the ground.
If you toss a coin straight upward in train that gains speed while the coin is in the air, the coin will land?
The coin tossed straight upward on a train that is accelerating will land back in your hand, retaining its initial horizontal velocity and moving forward with the train due to Newton's first law of motion and the principle of relative motion.
If you toss a coin straight upward on a train that gains speed while the coin is in the air, the coin will still land back in your hand, provided there is no significant air resistance inside the train and you do not move from your spot. This is because when the coin is tossed, it already has the horizontal velocity of the train. As per Newton's first law of motion, objects in motion stay in motion with the same velocity unless acted upon by an unbalanced force.
Therefore, even though the train is accelerating, the coin retains its initial horizontal velocity and moves forward with the train.
An important concept to take note of here is the principle of relative motion. To an observer inside the train, the coin appears to move straight up and down because both the observer and the coin are sharing the same initial horizontal velocity due to the motion of the train. To an observer outside the train, the coin would appear to be following a projectile motion pathway, because they can see both the vertical and the accelerated horizontal motion of the coin. However, since the internal movement of the coin and the observer are both relative to the moving train, the coin will land back in the hand from which it was tossed, assuming the hand remains in the same position relative to the train.
What were some of newton mathematical and scientific contributions
Which vector should be negative?
any vector whose magnitude is less than 1
a displacement in the direction North
any vector whose magnitude is greater than 1
the velocity of a falling object
Answer: the velocity of a falling object.
As the object is falling down it is experiencing a velocity that is continuously reducing each second and becomes 0 once it reaches the ground. The graph between velocity and time in this case would be a negative slope.
Thus for a object falling down the velocity considered would be negative owing to the reducing speed.
The kind of hazardous waste disposal that most closely resembles recycling is _____.
I believe your answer is Waste Exchange
In the film, 2001: A Space Odyssey, astronauts travel through space and experience artificial gravity created by a spinning, cylindrical space station. In order to generate the same gravitational acceleration felt on Earth's surface, a space station rotates so that an astronaut standing inside its outer rim moves tangentially at 30.9 m/s. What is the diameter of the space station?
Artificial gravity is created by rotating the cylinder
So here we can say that the acceleration is due to centripetal acceleration
So here we know that the formula of centripetal acceleration is given by
[tex]a_c = \frac{v^2}{R}[/tex]
so here we know that
[tex]a_c = 9.8 m/s^2[/tex]
[tex]v = 30.9 m/s[/tex]
now we will plug in all values
[tex]9.8 = \frac{30.9^2}{R}[/tex]
[tex]R = \frac{30.9^2}{9.8}[/tex]
[tex]R = 97.43 m[/tex]
So above is the radius of the cylinder
Now to find the diameter
[tex]d = 2R[/tex]
[tex]d = 2*97.43[/tex]
[tex]d = 194.8 m[/tex]
so its diameter is 194.8 m
In order to generate the same gravitational acceleration felt on Earth's surface, the diameter of a spinning, cylindrical space station, around which an astronaut standing inside its outer rim moves tangentially at 30.9 m/s, should be approximately 194.36 meters.
Explanation:The problem in question concerns the concept of artificial gravity and circular motion in physics. To answer this question, we would use the formula for the centripetal acceleration in circular motion, which is a = v² / r, where v = velocity (30.9 m/s) and r = radius of the circle (the part we are trying to find). We equate this to g, the acceleration due to gravity on earth, which is 9.81 m/s². This gives us the equation 9.81 m/s² = (30.9 m/s)² / r. Solving for r gives us r = (30.9 m/s)² / 9.81 m/s² = 97.18 m. This is the radius. But we need the diameter of the space station, so we multiply the radius by 2, giving us a diameter of approximately 194.36 meters.
Learn more about Artificial Gravity and Circular Motion here:https://brainly.com/question/14977156
#SPJ3
Cardiovascular Activities all have what 4 characteristics
fast moving and long intervals , light but quick movements, usually with light weight
Cardiovascular activities are characterized by significant cardiac output, compliance, volume of the blood, and viscosity of the blood. These activities affect how much blood the heart pumps, and can contribute to overall heart health.
Explanation:Cardiovascular activities are characterized by four primary attributes. First, they involve a significant Cardiac Output, which is the volume of blood the heart pumps per minute. Second, they incorporate varying levels of Compliance, referring to the ability of a vessel to stretch and increase its volume with increasing transmural pressure. The third characteristic is the Volume of the Blood in the body, meaning that cardiovascular activities affect how much blood the heart pumps with each beat. The final characteristic is the Viscosity of the Blood, which refers to the thickness and stickiness of the blood, a factor that can impact blood flow and pressure. Participating in regular cardiovascular activities can help maintain and improve these factors, contributing to overall heart health.
Learn more about Cardiovascular Activities here:https://brainly.com/question/29616656
#SPJ2
What parts of clam are likely to be preserved?
A museum curator moves artifacts into place on many different display surfaces. Consider the following table giving approximate values for coefficients of friction: – schomer – (HHSPhy4F18) 1 Materials μs μk steel on steel 0.74 0.57 aluminum on steel 0.61 0.47 rubber on dry concrete 1.0 0.8 rubber on wet concrete – 0.5 wood on wood 0.4 0.2 glass on glass 0.9 0.4 waxed wood on wet snow 0.14 0.1 waxed wood on dry snow – 0.04 metal on metal (lubricated) 0.15 0.06 ice on ice 0.1 0.03 Teflon on Teflon 0.04 0.04 synovial joints in humans 0.01 0.003 What is Fs,max for moving a 167 kg alu- minum sculpture across a horizontal steel platform? The acceleration of gravity is 9.81 m/s2 . Answer in units of N.
you must give a force for just moving
Fmax=151*0,61*9,81= 904 N <--------------
and
F=151*0.47*9.81= 646 N ... to keep in motion
hope this helps :)
To calculate the maximum static friction (Fs,max) that can be experienced by the 167 kg aluminum sculpture on a steel surface, we first find the normal force by multiplying its mass with acceleration due to gravity. Using the coefficient of static friction for aluminum on steel, we can then calculate Fs,max.
Explanation:The maximum static friction (Fs,max) that can be experienced by the 167 kg aluminum sculpture on a steel surface can be calculated using the formula of friction. Friction's direction is always opposite of the motion and it is usually dependent on the materials in contact and the normal force. The normal force (N) in this case would be equal to the weight of the sculpture which can be calculated by multiplying its mass (m) with the acceleration due to gravity (g). That is, N = mg = (167 kg)(9.81 m/s²).
Once the normal force is known, the next step is to find the maximum static friction (Fs,max) using the equation: Fs,max = μsN. The coefficient of static friction (μs) between aluminum and steel is given as 0.61 from the provided data. Hence, we can substitute the values in the formula to find the desired value.
Learn more about Static Friction here:https://brainly.com/question/13000653
#SPJ2
How will the behavior of the gases in the piston chamber change if heat is applied to the system? Assume the piston moves to keep the pressure constant. A) The gas particles will speed up. B) More gas particles will be produced. C) Fewer gas particles will be produced. D) The kinetic energy will decrease.
Answer: A) The gas particles will speed up.
Explanation: When heat is supplied to the system, the kinetic energy of the molecules increase and thus they start moving randomly and thus the gas molecules will speed up.
Charles law states that volume is directly proportional to the temperature of the gas at constant pressure and number of moles.
[tex]V\propto T[/tex] (At constant pressure and number of moles)
As we know kinetic energy is directly related to temperature, thus as temperature is increased, the kinetic energy of the molecules also increase.
[tex]K.E=\frac{3}{2}RT[/tex]
R = gas constant
T= temperature
The part of an atom that is most empty space is the ?
Mark creates a graphic organizer to review his notes about electrical force.
Which labels belong in the regions marked X and Y?
A) X: Decreasing to half will quadruple force
Y: Doubling will double force
B) X: Doubling will cut force in half
C) X: Doubling will double force
Y: Decreasing to half will quadruple force
D) X: Decreasing to half will double force
Y: Doubling will cut force in half
A) X: Decreasing to half will quadruple force
Y: Doubling will double force
The regions marked X and Y will be given as
X: Decreasing to half will quadruple the force
Y: Doubling will double force
What is electrical force?The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb, hence the name.
Coulomb's law was essential to the development of the theory of electromagnetism, maybe even its starting point,[1] as it made it possible to discuss the quantity of electric charge in a meaningful way.
The law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.
[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]
Hence the regions marked X and Y will be given as
X: Decreasing to half will quadruple the force
Y: Doubling will double force
To know more about electrical force follow
https://brainly.com/question/25923373
A helicopter above the ground is descending at 3.1 m/s it drops a package from rest relative to the helicopter just before it hits the ground the package is falling at a rate of 9.5 m/s relative to the helicopter find the velocity of the package relative to the ground.
12.6 m/s, up
6.4 m/s up
12.6 m/s down
6.4 m/s down
Initial speed of the package will be same as the speed of helicopter as it has been dropped from the helicopter.
So if we find the velocity of package relative to helicopter then it will be zero
so here we can say
[tex]v_i = v_{helicopter} = 3.1 m/s[/tex]
Now here relative velocity of the of the package will increase due to free fall in gravity and then just before if hit the ground the speed of the package will be 9.5 m/s relative to the helicopter.
so here we can say
[tex]v_{p/H} = v_p - v_H[/tex]
[tex]v_{p/H} = 9.5 m/s[/tex]
[tex]v_H = 3.1 m/s[/tex]
so here the net velocity with respect to ground will be
[tex]v_p = V_{p/H} + v_H[/tex]
[tex]v_p = 3.1 + 9.5 = 12.6 m/s[/tex]
so package will hit with speed 12.6 m/s downwards
A 1400 kg van is traveling at 24m/s when the driver takes her foot off the gas pedal. The car eventually rolls to a stop after 225 meters. Find the force of friction acting on the van.
We can use the kinematics equation
v1^2-v0^2=2as
where v1=final velocity = 0 m/s
v0=initial velocity = 24 m/s
a=acceleration = to be determined
S=distance travelled during acceleration = 225 m
=>
a=(v1^2-v0^2)/(2S)
=(0^2-24^2)/(2*225)
=-576/450
=-1.28 m/s^2
So van is decelerating at 1.28 m/s^2
The frictional force is therefore
F = ma = 1400 kg * 1.28 m/s^2 = 1792 N
The force of friction acting on the 1400 kg van, which comes to a stop after 225 meters, is calculated using the work-energy principle and is found to be 1792 Newtons.
Finding the Force of Friction Acting on the Van
To determine the force of friction acting on a van that rolls to a stop after the driver takes her foot off the gas pedal, we need to apply the principles of kinetic energy and work done. The work done by friction is equal to the change in kinetic energy of the van as it comes to a stop. Since the van starts at a speed (v) of 24 m/s and ends at 0 m/s, the initial kinetic energy ([tex]KE_i[/tex]) is
[tex]KE_i = 1/2 mv^2[/tex]
where m is the mass of the van (1400 kg). The work done by friction (W) equals the force of friction (f) multiplied by the distance (d) over which it acts, hence W = fd. Work done by friction is also equal to the change in kinetic energy:
[tex]W = KE_i - KE_f[/tex]
Because the van stops, [tex]KE_f[/tex] (final kinetic energy) is 0, and the work done by friction will equal the initial kinetic energy. We can calculate the force of friction now that we know the work done and the distance:
f = [tex]KE_i[/tex] / d
Using the given values:
[tex]KE_i[/tex] = 1/2 (1400 kg)(24 m/s)² = 403200 J
So the force of friction (f) can be calculated as:
f = 403200 J / 225 m = 1792 N
The force of friction acting on the van is therefore 1792 N.
Modern atomic theory states that the atom is a diffuse cloud surrounding a small, dense nucleus. Identify which particle is in the nucleus. A) ion b) proton c) electron d) free radical
b) proton
the proton is the only one of these that are in the nucleus. if you think the electron is, its not; the electrons are all outside the nucleus in the electron cloud. :)
What energy is being transformed an electric blanket warms a bed on a chilly night
Final answer:
Electrical energy is transformed into thermal energy by an electric blanket to warm a bed. The electric current passes through a heating element in the blanket, where the resistance generates heat to provide warmth.
Explanation:
When an electric blanket warms a bed on a chilly night, electrical energy is being transformed into thermal energy. This process involves the conversion of electricity into heat through the use of a heating element within the blanket. As electricity flows through the heating element, the resistance of the material converts electric energy into heat, which then warms up the bed. This is an example of energy transformation where the desired output is the warming effect, even though some energy may be lost to the environment as part of this process.
Electric blankets are designed to be energy efficient, ensuring that the majority of electric power is converted into heat to keep users warm. This functionality is similar to other devices that transform energy into heat, such as space heaters or waterbed heaters. However, it's worth noting that no process is 100% efficient, and some energy will be lost in the form of waste heat.
Soils refers to natural material from the earth, but not artificial material (like AstroTurf or asphalt). True False
Answer:
It is true that Soil refers to natural material from the earth, but not artificial material (like AstroTurf or asphalt).
Artificial materials are the materials that are made by human like AstroTurf or asphalt while Soil is one of the natural materials giving to us by God. Soil is a material composed of five ingredients which are minerals, soil organic matter, living organisms, gas, and water.
An electric force exists between which pair of objects? Check all that apply.
A) a neutral object and a negative object
two negative objects
B) a neutral object and a positive object
C) two positive objects
D) a negative object and a positive object
E) two neutral objects
An electric force exists between the following:
-Two negative objects
-Two positive objects
-A negative object and a positive object
Electric forces exist between charged objects. Therefore, two negative objects, two positive objects, and a positive and a negative object all experience electric force. However, under certain conditions, a neutral object and a charged object may also experience electric force.
Explanation:An electric force exists between objects with charge. So, the correct pairs from your options that will experience electric force are: two negative objects (since like charges repel), two positive objects (as these also repel each other) and a negative object and a positive object (because opposite charges attract each other).
A neutral object and a positive object, as well as a neutral object and a negative object, may also experience electric force due to induced charges under certain conditions. However, two neutral objects will not experience electric force as they do not have charge.
Learn more about Electric Force here:https://brainly.com/question/20935307
#SPJ3
What is the speed of a truck that travels 10 i’m in 10 minutes ?
10km/10min is a legitimate speed. So is meters/sec, km/hour (kph), etc.
Kph is very common for vehicles:
10 km/10 min (60 min/hr) = 60 kph
Charlie throws a ball up into the air. While the ball is airborne, which is the greatest force acting on the ball to slow it down? A. applied force B. friction force C. gravitational force D. normal force
Answer:
it is gravitational force
Explanation:
i did the test is the pretest of force and motion trust me its right
Two identical balls are dropped from a tall building, one a few seconds later after the other. Air resistance is not negligible. As the balls fall, the distance between the balls will
a. decrease
b. increase
c. increase then remain constant
d. remain constant
why do lunar and solar eclipses not happen every month?
Eclipses only occur during full and new moons.
Earth rotates around its axis faster than the moon.
The moon and Earth only travel through the penumbras.
The moon’s axis does not always align with Earth’s shadow.
Answer:
The moon’s axis does not always align with Earth’s shadow.
Explanation:
The lunar eclipse happens when the Earth comes between the moon and the Sun, blocking the light falling on the moon. It occurs on a full moon. On the other hand, a solar eclipse occurs when the moon comes between the Earth and the Sun, blocking the sunlight falling on Earth. It occurs on new moon day. For each to occur, the three bodies must be aligned in straight line. As the orbital plane of the moon is not exactly aligned to that of the Earth, the eclipses do not occur every month.
The reason why lunar and solar eclipses do not happen every month is because: D. The moon’s axis does not always align with Earth’s shadow.
An eclipse is simply an astronomical phenomenon (event) that usually takes place when a celestial body such as a Moon in space moves in between the Sun and another celestial body such as planet Earth, usually causing the total or partial blockage or obscuration of light to the celestial body.
Based on space exploration and science, there are two (2) main types of eclipse;
I. Lunar eclipse: it is an astronomical phenomenon (event) that occurs when planet Earth gets between the Moon and the Sun, thereby causing it to cover or obscure the Moon with its shadow.
II. Solar eclipse: this is an astronomical phenomenon (event) that typically occurs when the Sun is obscured or blocked by the Moon, thereby engulfing a portion of planet Earth.
However, these astronomical phenomenon (lunar and solar eclipses) do not happen every month because the axis of the Moon is tilted five (5) degrees and as such doesn't always align with Earth’s shadow.
In conclusion, without this tilt of the Moon from Earth's orbit around the Sun, lunar and solar eclipses would happen every month.
Read more: https://brainly.com/question/21828533
generally you must stir a can of paint before you use it.. is paint miscible or immiscible? explain
Paint is immiscible because the layer that forms on top of settled paint is a substance which cannot dissolve with the rest of the paint. Stirring the paint is only temporarily in effort to form an even and thoroughly mixed solution by physically mixing the separate molecules of the solution. However, for it to be miscible, it the solution has to be evenly distributed (chemically) on a molecular level as to not separate when left for a lengthy period of time.
A .25 kg ball initially at rest is hit with a 460 N impact. What is the time of impact for this event if the ball ends up moving 40 m/s
Time of impact: [tex]\(0.0217\)[/tex] seconds, calculated using impulse-momentum theorem with force [tex]\(460 \, \text{N}\) and mass \(0.25 \, \text{kg}\)[/tex].
To find the time of impact, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in momentum of the object. Mathematically, it can be expressed as:
[tex]\[ J = \Delta p \][/tex]
Where:
- [tex]\( J \)[/tex] is the impulse
- [tex]\( \Delta p \)[/tex] is the change in momentum
The impulse [tex](\( J \))[/tex] can be calculated using the force [tex](\( F \))[/tex] and time [tex](\( \Delta t \))[/tex] of impact:
[tex]\[ J = F \cdot \Delta t \][/tex]
Given that the force [tex](\( F \))[/tex] is 460 N, we can rearrange the equation to solve for the time ([tex]\( \Delta t \)[/tex]):
[tex]\[ \Delta t = \frac{J}{F} \][/tex]
The change in momentum ([tex]\( \Delta p \)[/tex]) can be calculated using the mass [tex](\( m \))[/tex] and the final velocity (\( v_f \)) of the ball:
[tex]\[ \Delta p = m \cdot v_f \][/tex]
Given that the mass [tex](\( m \))[/tex] is 0.25 kg and the final velocity [tex](\( v_f \))[/tex] is 40 m/s, we can substitute these values into the equation to find the change in momentum.
Once we have both the impulse [tex](\( J \))[/tex] and the change in momentum [tex](\( \Delta p \))[/tex], we can solve for the time of impact [tex](\( \Delta t \))[/tex].
Let's calculate:
[tex]\[ \Delta p = m \cdot v_f = 0.25 \, \text{kg} \times 40 \, \text{m/s} = 10 \, \text{kg} \cdot \text{m/s} \][/tex]
[tex]\[ \Delta t = \frac{J}{F} = \frac{10 \, \text{kg} \cdot \text{m/s}}{460 \, \text{N}} \][/tex]
[tex]\[ \Delta t = \frac{10}{460} \, \text{s} \][/tex]
[tex]\[ \Delta t[/tex] ≈ [tex]0.0217 \, \text{s}[/tex]
So, the time of impact for this event is approximately [tex]\( 0.0217 \)[/tex] seconds.
what are chemical properties
Answer:
It is a characteristic of matter that describes its ability to change into a different substance.
Explanation:
In a hydraulic jack, the pipe below the load has an area of 5 m2, and the pipe through which the input force transmits has an area of 0.1 m2. If the input force is 200 N, what is the output force in kN?
A. 10 kN
B. 20 kN
C. 15 kN
D. 13 kN
As per Pascal's law
Pressure must be equally transmitted to all points of fluids
So here we can say
[tex]P_{in} = P_{out}[/tex]
As we know that pressure is the ratio of force and area so we can say
[tex]\frac{F_{in}}{A_{in}} = \frac{F_{out}}{A_{out}}[/tex]
Given that
[tex]F_{in} = 200 N[/tex]
[tex]A_{in} = 0.1 m^2[/tex]
[tex]A_{out} = 5 m^2[/tex]
[tex]\frac{200}{0.1} = \frac{F_{out}}{5}[/tex]
[tex]F_{out} = 5 * 2000 = 10000[/tex]
so output force will be 10 kN
so A option is correct
Answer:
The answer is A 10 kN
Explanation:
I got it right on the test.
Objects in free fall accelerate due to ______
A. Gravity
B. Momentum
C. Energy
D. Velocity
Answer:
The correct answer is A.
Objects in free fall accelerate due to gravity.
Explanation:
Momentum can help an object to keep its state of motion at a constant velocity when no external force is applied. It can never accelerate the object.
According to the laws of motion, we know that acceleration is produced in a body only when a Force is applied in the direction of motion of body.
During a free fall, only the force of gravity is acting on an object and that too in the direction of its motion. Hence, the acceleration produced in a free falling object is due to gravity.
Answer:
gravity
Explanation:
What is the maximum height achieved if a 0.600 kg mass is thrown straight upward with an initial speed of 75.0 m·sâ1? ignore the effect of air resistance?
A 0.600 kg mass thrown upward with an initial speed of 75.0 m/s will reach a maximum height of approximately 287.76 meters, ignoring the effects of air resistance. This is determined using the physics formula v² = u² + 2gH (a kinematic equation for motion under gravity).
Explanation:This problem can be solved using the physics concept of motion under gravity. The object is thrown with an initial velocity to reach a maximum height where its velocity becomes zero. In order to find out the maximum height (H) achieved, we can use the kinematic equation: v² = u² + 2gH, where 'v' is the final velocity, 'u' is the initial velocity, and 'g' is the acceleration due to gravity.
Given in the problem, u = 75 m/s (upward direction implies positive value), v = 0 m/s (at maximum height, the final velocity is zero), and g = -9.8 m²/s (downward direction implies negative value).
By substituting these values into the equation, we get 0 = (75 m/s)² + 2(-9.8 m²/s)(H), which yields H = (75 m/s)² / 2(9.8 m²/s) or approximately 287.76 meters.
This means that, ignoring air resistance, an object with a mass of 0.600 kg thrown upward with an initial speed of 75.0 m/s will reach a maximum height of approximately 287.76 meters.
Learn more about Physics of Motion here:https://brainly.com/question/13966796
#SPJ12