Explanation:
To express each vector in the figure using unit vector notation, we can use the following equations:
⃗ =
⃗ =
where is the x-component of the vector and is the y-component of the vector.
For vector :
x = 24.5cos(33.5) = 20.8
y = 24.5sin(33.5) = 14.2
So
⃗ =
For vector :
x = -46.9cos(57.5) = -31.8
y = -46.9sin(57.5) = -38.4
So
⃗ =
Note that the negative sign on the x-component of vector is due to the fact that it is in the third quadrant.
It is important to take into account that the angle provided on the question is in degrees, and in this case trigonometric functions are used to calculate the x and y component of the vector.
The top of the mercury thread in a mercury glass thermometer reached point X at 0 Celsius and point Z at 100 Celsius..
The top of the mercury thread in a mercury glass thermometer reached point X at 0 Celsius and point Z at 100 Celsius- Point Y.so, option (b) is correct.
What is thermometer ?
An instrument used to gauge how hot or cold something is is called a thermometer. Thermometers can be used to check your temperature or determine whether you have a fever. The definition of a thermometer, which is made up of the words thermo (heat) and meter (measuring tool), is rather simple.
What is mercury ?
A variety of industries employ mercury. It is used to make caustic soda and chlorine gas, as well as in thermometers, barometers, batteries, and electrical switches.: a heavy silver-white toxic metallic element that is liquid at normal temperatures and is utilized particularly in scientific instruments. the quicksilver symbol for the element mercury.
Therefore, top of the mercury thread in a mercury glass thermometer reached point X at 0 Celsius and point Z at 100 Celsius- Point Y.so, option (b) is correct.
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What goes up must come down"-if you throw a baseball in the air, it will go upwards and then descend in a _____ curve.
Answer:
it will come down in a parabola curve
a small metal ball is given a negative charge, then brought near (i.e., within a few millimeters) to end a of the rod. what happens to end a of the rod when the ball approaches it closely this first time? select the expected behavior.
Weak attraction between the sphere and the rod is caused by end A of the rod inducing a positive charge (and correspondingly, end B acquires a negative induced charge).
This suggests that a charge may have moved from A to B. In an insulator, charge flow is restricted, hence the induced charges are frequently insignificant. because a pliable metal ball is charged negatively. Charged matter experiences a force when exposed to an electromagnetic field because of the physical nature of electric charge. Electrical charges can be positive or negative (commonly carried by protons and electrons respectively). Matter experiences a force when retained in an electromagnetic field due to the physical property of electric charge.
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when light encounters a medium, the interference between the incident light and the light scattered by the medium leads to a wavefront that moves slower than the speed of light, c. the speed of light in the medium is given by v
The molecules and particles in a medium scatter light when it comes into contact with them, and as a result, the wavefront moves more slowly in a media than it would in a vacuum. v = c/n.
where c is the speed of light in a vacuum and n is the index of refraction of the medium, calculates the speed of light in a particular medium. The index of refraction is a measurement of how much light travels slower through a medium than it does in a vacuum. Light travels through a medium at a slower speed the higher the index of refraction. The wavefront is impacted by refraction, reflection, and other phenomena as it travels through the medium.
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Vacillate the change in the. Kinetic energy KE of the bottle when the mass is increased use the formula KE=1/2 mv2 where m is the mass and v is the speed
When the mass is 0.125 kg, the kinetic energy is 1 J
When the mass is 0.250 kg, the kinetic energy is 2 J.
When the mass is 0.375 kg, the kinetic energy is 3 J.
When the mass is 0.500 kg, the kinetic energy is 4 J.
What is the kinetic energy of the bottle?
The kinetic energy of the bottle is the energy possessed by the bottle due to its mass and motion.
K.E = ¹/₂mv²
where;
m is the mass of the bottlev is the speed of the bottleWhen the mass is 0.125 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.125 kg x ( 4 m/s )²
K.E = 1 J
When the mass is 0.250 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.25 kg x ( 4 m/s )²
K.E = 2 J
When the mass is 0.375 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.375 kg x ( 4 m/s )²
K.E = 3 J
When the mass is 0.500 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.5 kg x ( 4 m/s )²
K.E = 4 J
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the 50-kg passenger in a car moving at 10 m/s crashes into a tree and stops in 0.2 seconds. the average force exerted on the passenger to bring her to a stop is
The average force exerted on the passenger to bring her to a stop is 2500 Newton.
To calculate the average force exerted on the passenger, we can use the equation: force = mass x acceleration. The acceleration in this case is the deceleration experienced by the passenger, which can be calculated by dividing the change in velocity by the change in time.
In this case, the passenger's velocity changes from 10 m/s to 0 m/s in 0.2 seconds, so the deceleration is:
deceleration = (change in velocity) / (change in time)
deceleration = (0 m/s - 10 m/s) / 0.2 seconds
deceleration = -50 m/s²
Note that the negative sign indicates that the acceleration is in the opposite direction of the velocity. In this case, the passenger's velocity is initially positive (moving forward), but the deceleration is negative, indicating that the force is acting in the opposite direction, slowing the passenger down.
Therefore, the force exerted on the passenger is:
force = mass x acceleration
force = 50 x -50 = 2500 N.
force = 2500 Newton
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work and Tes...
Three plates may be charged positively or negatively or be
electrically neutral. In the drawing shown, plate A is attracted by
both plates B and C. What occurs if plates B and C are brought
close together?
A
↑
B
A
C
OB and C would attract one another.
OB and C would repel one another.
B and C would exert no force on each other.
There is too little information given to make a conclusion.
a scientist describes an electrically neutral atom with a model that consists of a nucleus that is a point particle with a positive charge
According to Thomson's atomic model, an atom is made up of a positively charged sphere into which negatively charged electrons are implanted.
Define neutral atom ?
When an atom has an equal number of electrons and protons, it has an equal number of negative (the electrons) and positive electric charges (the protons). As a result, the atom's total electric charge is zero, and it is said to be neutral.Heavier atoms tend to have more neutrons than protons, but the number of electrons in an atom is always equal to the number of protons. So an atom as a whole is electrically neutral.The number of protons (positively charged) and electrons (negatively charged) are equal in an atom. Therefore the opposite charges are balanced and thus there is no net charge on the atom. Moreover, neutrons present in the atom have no charge. Hence an atom is electrically neutral.To learn more about neutral atom refers to:
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) find the amplitude, period, and horizontal shift. (assume the absolute value of the horizontal shift is less than the period.)
By applying trigonometry function graph theory, it can be concluded that the amplitude is 2, the period is π, the horizontal shift is 0, and the equation that represents the graph is y = 2 cos (2x)
A trigonometry function is a function whose graph repeats continuously over a certain period. The trigonometry function graph consists of hills and valleys that repeat continuously over a certain period.
There are some terms regarding a trigonometry function graph:
Amplitude is the farthest deviation of a point on a trigonometric function graph from its horizontal line (eg the x-axis).Period is the distance the trigonometric function graph repeats from the initial reference point to the first repetition point.Horizontal shift is a shift to the left or right of the sin graph so that it is the same as the cosine graph and vice versa.Now we look at our trigonometric function graph.
Since the farthest deviation of the graph is in points (0,2), (π/2,-2), and (π,2), thus the amplitude of the graph is 2. We denote it as a = 2.
The graph repeats from the initial reference point to the first repetition point after π, thus the period of the graph is π.
The value of k can be obtained from this:
2π/k = period
k = 2π/period
= 2π/π
= 2
The horizontal shift is 0, which means there's no shifting on the cosine graph.
Now we input the value of a, k and b into the equation:
y = a cos (k (x - b))
= 2 cos (2 (x - 0))
= 2 cos (2x)
Thus the amplitude is 2, the period is π, the horizontal shift is 0, and the equation that represents the graph is y = 2 cos (2x)
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a car travels along stright line at constant speed of 20 m/s for a distance d and then another distance in the same direction at constant speed of 30 km/hr. what is averege speed of the entire trip?
A car traveling at a constant speed of 20 m/s has travelled 3 minutes × 60 seconds/minute * 20 m/s = 3600 meters after 3 minutes.
What is speed?The rate at which an object's position changes in any direction is referred to as its speed. The ratio of distance travelled to travel time is used to determine speed. Velocity and speed are two terms used to describe how quickly an object moves along a path. That is to say, velocity is a vector and speed is a scalar value.
Speed is defined as the rate at which a distance changes over time. The base units of distance and time are combined to form the SI unit of speed. Distance multiplied by speed Time is equal to one metre per second. The SI unit for speed is the m/s.
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which of the following is an example of kinetic energy? view available hint(s)for part a which of the following is an example of kinetic energy? the energy held in bonds between atoms wind rotating a turbine a book on the top shelf of a closet a rock on top of a hill
A windmill turning An illustration of kinetic energy is the following.
What exactly is an energy in science?The ability to "achieve work," or the capability to exert a force strong enough to move an item, is how energy is defined. Despite the ambiguity in the definition, the idea is actually pretty simple: electricity simply refers to the force that propels objects. The two different categories of energy are potential and kinetic.
Simple energy definitionThe most basic definition of energy is the capacity for work. Energy causes things to move and change. It's everywhere and comes in a variety of shapes. Energy is needed while cooking food.
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The density of a solid object is defined as the ratio of the mass of the object to its volume. The dimension of density isa) ([M][L]b)[M] /[L]C) [M][L] ^-3D) [L]^3 / [M]
The dimensional formula of density is calculated from the formula of density to be ρ = [M] [L]⁻³ which is option (C).
There are only seven fundamental physical quantities. We may determine the dimension of any other physical quantity using these fundamental quantities. With the help of the dimensions of mass and length, we must determine the density dimension in this situation. Volume is a measure of length. Any dimensional formula is usually written in the form of mass [M], length [L] and time [T].
If an object has mass M and volume V then the density of the object is given by,
ρ = M/V
[ρ] = [M]/[V] = [M]/[L]³ = [M] [L]⁻³
Thus, the dimensional formula of density is [M] [L]⁻³.
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A racecar starting from rest acclerates uniformly at a rate of 4.9 meters per second2.What is the car's speed after it has traveled 200 meters
The speed of the car after 200 meters is v = 44.3 m/s (3 sf).
What is speed?The rate at which an object's position changes in any direction is referred to as speed. The ratio of distance travelled to travel time is used to calculate speed. Speed and Velocity both refer to how quickly something moves along a path. Speed measures how quickly something moves along a path.
In other words, velocity is a vector and speed is a scalar value. The rate at which a distance changes over time is referred to as speed. The base unit of distance plus the base unit of time are combined to form the SI unit of speed. Distance times speed metre second equals time. m/s is the SI unit for speed.
u = 0
a = 4.9
s = 200
v² = 0²+2*4.9*200
v = √(2*4.9*200)
v = √1960
v = 44.3 m/s (3 sf)
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A small fly of mass 0.30 g is caught in a spider's web. The web vibrates predominately with a frequency of 3.4 Hz.
-what is the value of the effective spring stiffness constant "k" for the web, in N/m?
-At what frequency would you expect the web to vibrate if an insect of mass 0.60g were trapped, in Hz?
I tried using the equation f=1/2pi*sqrt(k/m) but am not getting it right. Help greatly appreciated!!!!
The effective spring stiffness constant "k" for the web will be 0.139 N/m and frequency will be 2.83 Hz.
Frequency is defined as the rate of changes in current direction per second. It is given in hertz (Hz), an internationally recognised unit of measurement. One cycle per second is equal to one hertz. Cycles per second are represented by the unit hertz (Hz). A cycle is the technical term for a whole alternating current or voltage pulse.
(a) m = 0.30 g = 0.30 x 10^-3 kg
f = 3.4 Hz
Spring frequency can be calculated using the formula below
f = [tex]\frac{1}{2pi} \sqrt{\frac{k}{m} }[/tex]
so solving,
Where, k be the spring constant
k = 0.139 N/m
(b)
k = 0.139 N/m
Let the frequency be f.
f = [tex]\frac{1}{2pi} \sqrt{\frac{k}{m} }[/tex]
f = 2.83 Hz
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find the distance that the earth travels in three days in its path around the sun. assume that a year has 365 days and that the path of the earth around the sun is a circle of radius 93 million miles. [note: the path of the earth around the sun is actually an ellipse with the sun at one focus (see section 11.2). this ellipse, however, has very small eccentricity, so it is nearly circular.] (round your answer to one decimal place.)
To find the distance that the Earth travels in three days in its path around the sun, we first need to find the circumference of the Earth's orbit. We can use the formula for the circumference of a circle, C = 2πr, where C is the circumference, π is approximately equal to 3.14, and r is the radius of the circle (93 million miles).
C = 2πr = 2 * 3.14 * 93 million miles = 584 million miles
Now that we know the circumference of the Earth's orbit, we can find the distance the Earth travels in three days by multiplying the circumference by the proportion of the orbit that the Earth travels in three days.
Three days is 3/365 of a year, so we can use the following formula:
Distance = (3/365) * C = (3/365) * 584 million miles = 40,931 miles
Therefore, the distance that the Earth travels in three days in its path around the sun is approximately 40,931 miles
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suppose you receive a traffic ticket for speeding and want to contest it in court. come up with two arguments, one using systematic error and the other using random error, that you could use to challenge the the speed given by either your speedometer or the radar gun.
Systematic error:
You could use systematic error to challenge the speed indicated by your speedometer or radar gun.
A systematic error is one that occurs as a result of a consistent and repeatable cause, such as a malfunctioning instrument or a calibration problem.
You could, for example, argue that the officer's radar gun was not properly calibrated, resulting in a consistently higher measurement of your speed.
Random error:
Another argument you could use to challenge the speed given by your speedometer or radar gun is that the measurement was influenced by random error.
Random error is a type of error that occurs as a result of uncontrollable factors such as wind or temperature changes.
You could, for example, argue that the wind was blowing hard on the day you received the ticket, affecting the accuracy of the radar gun's measurement.
It's important to note that these are just some of the possible arguments for fighting a traffic ticket. When determining whether an error occurred and whether it is significant enough to contest the ticket, the court will consider a number of factors.
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an object in a fluid experiences a buoyant force from the fluid. if the object is completely immersed, which of the following does the magnitude of this force depend on? select all that apply.
The fluid exerts a buoyant pull on an object when it is submerged in it. if the item is fully submerged. The amount of buoyancy an object experiences depends on both the fluid's density and objects volume. Hence, option B is correct.
As the density of the fluid grows, the buoyant force becomes stronger. Similar to this, as an object's volume increases, so does the buoyant force. The buoyant force's strength can also be influenced by the air pressure, which can alter how much force an item perceives to be exerted at its greatest intensity. The buoyant force will have a greater impact on the object the deeper it is buried in the fluid. As a result, if the object is completely submerged, the buoyant force's strength will depend on the object's volume and the density of the fluid.
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The complete question is:
A fluid exerts a buoyant force on an object when it is submerged in it. Which of the following determines how strong this force will be if the object is fully submerged? select all that apply.
A) The body's mass, fluid density
B) Density of the fluid and body volume
C) The body's weight
D) Shape of the body
if the 1.5-m-long cord ab can withstand a maximum force of 3500 n, determine the force in cord bc and the distance y so that the 200-kg crate can be supported. fbc
3500 N is the same amount of force in cord BC as it is in cord AB. The equation of equilibrium Fy=Fabsin(theta)=Fbccos(theta), where theta is the angle between the two cords, may be used to compute the distance y.
The idea of force equilibrium can be used. To balance the weight of the crate (200 kg * 9.8 m/s2 = 1960 N), the force in cord BC (F bc) must be equal to the force in cord AB (3500 N). The idea of mechanical advantage may also be used to determine the distance y, which in this example equals the weight-to-force ratio of the BC cord. As a result, y = (200 kg * 9.8 m/s2) / 3500 N = 0.564 m if we assume that y is the distance from the point of suspension to the container. As a result, the distance y is 0.564 m and the force in cord BC is 3500 N.
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a rocket is to be launched from deep space where there is no gravitational field. 81% of the initial mass of the rocket is fuel and this fuel is injected with a relative velocity of 2300 m/s.
The rocket's initial upthrust when it first starts traveling upwards is 2300 N.
What is force?A force is an effect in physics that may modify the velocity of an item. A force can cause a mass item to change its velocity, or accelerate. Intuitively, force may be characterized as a push or a pull. A force is a vector quantity since it has both magnitude and direction. The term "force" has a specific meaning in science. At this level, it is quite acceptable to refer to a force as a push or a pull. A force is not something that an item possesses or possesses. Another item applies a force to another. The concept of a force is not restricted to living or nonliving entities.
Here,
It ejects fuel vapours at the rate of 1 kg/sec. this fuel is injected with a relative velocity of 2300 m/s.
F=dm/dt*v
=1*2300
=2300 N
The initial upthrust on the rocket when it just starts moving upwards is 2300 N.
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a 67-kg base runner begins his slide into second base when he is moving at a speed of 3.3 m/s. the coefficient of friction between his clothes and earth is 0.70. he slides so that his speed is zero just as he reaches the base.
The runner moves 0.80 metres before stopping at second base. To resolve this issue, we can make use of the ideas of labour and energy.
The friction force on the runner's work can be computed as follows:
W_friction = -f_friction * d, where
f_friction = friction force = μ_k * N
N = normal force = m * g
d = distance traveled by the runner
The initial kinetic energy of the runner is given by:
K_initial = (1/2) * m * v^2
The runner's final kinetic energy is zero. According to the work-energy theorem, an object's kinetic energy changes when work is done to it. As a result, the initial kinetic energy of the runner and the work produced by friction are equal:
W_friction = ΔK = K_initial
When we substitute the values, we obtain:
W_friction = - μ_k * m * g * d = (1/2) * m * v^2
μ_k * m * g * d = (1/2) * m * v
^2
d = (1/2) * v^2 / (μ_k * g)
By substituting the values, we get:
d = (1/2) * (3.3^2) / (0.7 * 9.8) = 0.80 m
As a result, the runner moves 0.80 metres before stopping at second base.
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for the charge distribution provided, indicate the region (a to e) along the horizontal axis where a point exists at which the net electric field is zero. (figure 2)
At point C along the horizontal axis, the net electric field is zero.
Electrically charged particles are surrounded by a physical phenomenon termed an electric field that either attracts or repels all other adjacent charged particles. The physical field surrounding a system of charged particles can also be referred to. Electric charges and time-varying electric currents make up electric fields.Both electric and magnetic fields are manifestations of the electromagnetic field, one of the four fundamental interactions (sometimes known as forces) of nature.
1. In the region B along the horizontal axis , a point exists at which the net electric field is zero.
2. Nowhere in any region along the horizontal axis the net electric field is zero.
3. In the region A along the horizontal axis , a point exists at which the net electric field is zero.
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1. What is the work done created when a vehicle is pushed by a force of 106N producing a distance of 10.5m?
2. What is the friction force if the coefficient of friction of a box in a ground is 0.3 and its mass is 101kg, and the gravitational acceleration is 9.81 m/s2?
3. What is the net work done if the change in kinetic energy 200 J
4. What is the net work done if an object of mass 50 kg initially moving at 2m/s increases its velocity to 6 m/s?
5. What is the final velocity of an object with a mass of 5.2kg if the initial velocity was 2 m/s and the net work done is 50 J.
6. If the mass of the object (M) is 2kg.
The force (F) of 58 N displaces the object M by 3 m. The coefficient of friction is 0.3 and the gravitational acceleration is 9.81 m/s2. Find the net work done.
HELP ASAP
The net work done is the sum of the work done by the force (F) and the work done by friction.
What is the net work done if the change in kinetic energy 200 J?The work done by force (F) is calculated as Force × Distance (F × d), which in this case is 58 N × 3 m = 174 Nm.The work done by friction is calculated as Force × Distance (μ × m × g × d), in this case 0.3 × 2 kg × 9.81 m/s2 × 3 m = 58.2 Nm.Therefore, the net work done is 174 Nm + 58.2 Nm = 232.2 Nm. This is the amount of work done when the object of mass 2 kg is displaced by a force of 58 N over a distance of 3 m, with a coefficient of friction of 0.3 and a gravitational acceleration of 9.81 m/s2.The net work done in this example is the sum of the work done by the force of 58 N and the work done by the frictional force.The work done by the force of 58 N is given by W = F x d = 58 N x 3 m = 174 J.The work done by the frictional force is given by W = Ff x d = Ff x d = 0.3 x 9.81 x 2 kg x 3 m = 29.22 J.Therefore, the net work done is the sum of both work, which is W = 174 J + 29.22 J = 203.22 J.This type of net work is known as the work of non-conservative forces, since the frictional force opposes the motion of the object and reduces the total energy of the system.To learn more about the work of non-conservative forces refer to:
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A person measures his or her heart rate by counting the number of beats in 30 s. If 33 ± 1 beats are counted in 30.0 ± 0.5 s, what is
the uncertainty in the heart rate in beats per minute?
The uncertainty in the heart rate in beats per minute is 2 minute by using the rules for propagation of uncertainty.
How to calculate uncertainty in the heart rate in beats per minute?
To find the heart rate in beats per minute, we need to divide the number of beats by the time in minutes. So, we have (33 ± 1 beats) / (0.5 min). To find the uncertainty in the heart rate, we need to find the propagation of uncertainty for this division.
Using the rules for propagation of uncertainty, we have:
(heart rate) = (33 ± 1 beats) / (0.5 min)
(heart rate) = 66 ± (1/0.5) beats/min
(heart rate) = 66 ± 2 beats/min
So the uncertainty in the heart rate is 2 beats per minute.
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dan koshland suggested the induced-fit mechanism for enzymes. which of the following cartoons illustrates the induced-fit hypothesis of enzyme-substrate interaction?
According to the induced fit theory by Daniel Koshland, binding of substrate to the enzyme brings a conformational change in the enzyme to either enhance or inhibit its activity.
which of the following cartoons illustrates the induced-fit hypothesis of enzyme-substrate interaction?
The induced-fit model states a substrate binds to an active site and both change shape slightly, creating an ideal fit for catalysis. Enzymes promote chemical reactions by bringing substrates together in an optimal orientation, thus creating an ideal chemical environment for the reaction to occur.The induced fit hypothesis states that while an enzyme is in the unbound state (i.e., not binding to the substrate), the active site is not structurally optimal for substrate binding.The Fischer's lock and key hypothesis and Koshland's induced fit hypothesis are two hypotheses suggested to explain catalyses and specificity of enzymes. The lock and key hypothesis us where the fit between the substrate and active site is very specific like that of a lock and key.To learn more about enzymes refers to:
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The figure below shows the trajectory of a particle with mass m bound to (orbiting) an object of mass M by the Newtonian gravitational force. At which location(s) does the equation Fnet = m|v⃗|^2/|r⃗| apply?
The figure below shows the trajectory of a particle with mass m bound to (orbiting) an object of mass M by the Newtonian gravitational force therefore the location which equation Fnet = mv²/r applies is at B.
What is Centripetal force?This is referred to as any force which causes a change in direction of velocity toward the center of the circular motion and the formula is mv²/r .
For an object moving in a circular path, the centripetal force acts on it towards the centre of the path and in this scenario, location B is closest to the centre and the force which makes it remain on that same path which is why it was chosen as the correct choice.
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part a compare the energy of a 1-megaton hydrogen bomb to the energy released by a major earthquake.
The energy of a 1-megaton hydrogen bomb will be 5 times to the energy released by a major earthquake.
A weapon with a 1 megaton yield would be as powerful as 1 million tonnes of TNT. In terms of joules, a megaton is equal to 4.18 1015. A 1-megaton hydrogen bomb will have a 5 times greater energy output than a large earthquake. An earthquake emits energy at a variety of frequencies, so all of the shaking frequencies during the entire event must be taken into account in order to get an appropriate figure. The observed amplitude increases tenfold with each whole number rise in size, while the energy released is 32 times greater.
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How do measured values of weather and climate differ?
Measured values of weather and climate differ from one another because the weather is a short-term change in the atmosphere whereas climate is the environmental condition over a long period in a specific area.
How do measure values of weather and climate differ?The part of weather and climate are those quantities or properties that are steady regularly. The six main elements are weather and climate: temperatures, atmospheric pressure, wind, humidity, drizzle, and cloudiness. Different land can have different climates.
Weather is called the day-to-day information of atmospheric changes in a specific area at a specific time. Climate is the statistical details on the average weather condition of a specific land for more than 30 years. 2. The weather of a place involves the short-term atmospheric condition.
So we can conclude that The difference allying weather and climate is a measure of time.
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pls answer this hard question
thanks :)
The temperature at which the two metals will touch each other is 505 ⁰C.
What is the temperature at which the two metals touch each other?The temperature at which the metals touch each other is calculated as follows;
L = ΔL / αΔθ
where;
ΔL is change in lengthL is the original lengthSince both metals have equal length, our new equation becomes;
ΔL₁ / α₁Δθ = ΔL₂ / α₂Δθ
where;
α₁ is linear expansivity of ironα₂ is linear expansivity of copperΔL₁ is extension of iron,ΔL₂ is extension of copperΔL₁ / α₁ = ΔL₂ / α₂
ΔL₁ / ΔL₂ = α₁ / α₂
ΔL₁ / ΔL₂ = ( 12 x 10⁻⁶ ) / ( 19 x 10⁻⁶ )
ΔL₁ / ΔL₂ = 0.63
ΔL₁ = 0.63ΔL₂
The expansion of the two metals will be equal to 1.55 cm gap.
ΔL₁ + ΔL₂ = 1.55 cm
0.63ΔL₂ + ΔL₂ = 1.55
1.63ΔL₂ = 1.55
ΔL₂ = 1.55 / 1.63
ΔL₂ = 0.95 cm
The change in temperature is calculated as follows;
Δθ = ΔL₂ / (L₂α₂)
Δθ = ( 0.95 ) / ( 100 x 19 x 10⁻⁶ )
Δθ = 500 ⁰C
The temperature at which the two metals will touch each other is calculated as follows;
T - T₀ = Δθ
T = Δθ + T₀
T = 500 ⁰C + 5 ⁰C
T = 505 ⁰C
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suppose that you drive the 9.7 km from your university to home in 25.5 min. (note: average speed is distance traveled divided by time of travel.) your average speed in km/h is
The average speed of the travel from university to home is calculated to be 22.82 km/hr.
Average speed is known to be described as the total distance travelled by an object in particular time interval.
Given that,
Distance travelled = 9.7 km
Time taken for travel = 25.5 min
We know, 1 hour = 60 min
Converting minutes to hours, we have, 25.5/60 = 0.425 hr
The relation between distance, speed and time is known to be, distance = speed × time
Making speed as subject, we have,
Speed = Distance/time = 9.7/0.425 = 22.82 km/hr
The required average speed of the travel from university to home is calculated to be 22.82 km/hr.
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calculate the second and third viraial coefficients( b and c) for a gas obeying the van der waals equation
The van der Waals equation is a modified version of the ideal gas equation that accounts for the finite size of gas molecules and the attractive forces between them. The equation is given by:
[tex](P+a/V^{2})(V-b) = RT[/tex]
The virial coefficients (b and c) are used to describe the behaviour of a gas in terms of the interactions between its molecules.
To calculate the second virial coefficient (b), we can integrate the van der Waals equation over the volume:
[tex]b = (\frac{2\pi }{3})^{2} *a^{\frac{3}{2} } m(-\frac{1}{2} )[/tex]
Where m is the molar mass of the gas.
To calculate the third virial coefficient (c), we need more information, such as the polarizability of the gas molecules and the interactions between them.
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