The S.I units of K so that the equation velocity = K × density is dimensionally correct is Kg⁻¹m⁴s⁻¹
How do I determine the S.I units of K?Velocity is defined as follow:
Velocity = displacement / time
Thus, the S.I units of velocity is m/s
Density is defined as mass per unit volume i.e
Density = mass / volume
Thus, the S.I units of density is Kg/m³
With the above information, we can determine the the S.I units of K. Details below:
S.I units of velocity = m/sS.I units of density = Kg/m³S.I units of K =?Velocity = K × density
m/s = K × Kg/m³
Divide both sides by Kg/m³
K = (m/s) / (Kg/m³)
Invert
K = m/s × m³/Kg
K = m⁴/sKg
K = Kg⁻¹m⁴s⁻¹
Thus, we can conclude that the S.I units of K is Kg⁻¹m⁴s⁻¹
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Convert the following to engineering notation: (a) 0.045 W (b) 2000 pJ (c) 0.1 ns (d) 39,212 as (e) 3 \Omega3Ω (f) 18,000 m (g) 2,500,000,000,000 bits (h) 10^{15} \text { atoms } / \mathrm{cm}^{3}10 15atoms /cm 3
The following data can be converted to the engineering notation as the following. (a) 0.045 W is 45 mW. (b) 2000 pJ is 2nJ. (c) 0.1 ns is 100 pS (d) 39,212 as is 39.212 fs (e) 3 \Omega3Ω is 3Ω (f) 18,000 m is 18 km (g) 2,500,000,000,000 bits is 2.5 terabits (h) 0^{15} \text { atoms } / \mathrm{cm}^{3}10 15atoms /cm 3 is [tex]10^{21} \frac{atoms}{m^{3} }[/tex].
Engineering notation is the representation of expressing the numbers that are too big or too small and are represented in the decimal form times 10 raise to the power. It is similar to the scientific notation but in engineering notation, the powers of ten are always multiples of 3.
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 100 is used, it is written in scientific notation.
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a 1000-mw(e) nuclear power plant operates at a thermal efficiency of 33% and at 75% capacity for 1 year. how many kilograms of nuclear fuel are consumed during the year?
The nuclear power plant needs 95.217 kg of nuclear fuel or uranium 235 is used during the whole year to operate.
Here the nuclear power plant produces 1000MW of energy.
So, for one year the total energy that can be produced = 1000× 365× 24 = 8760000 MWh
Since the reactor has a 75% capacity, energy produced = 8760000×75/100 = 6750000 MWh. = 6.75×10⁹ kWh
Converting to joules = 6.75× 10⁹× 3.6× 10⁶ = 2.365×10¹⁶
Thermal efficiency is 33%. So, 2.365×10¹⁶ × 0.33
= 7.80×10¹⁵ J.
To find out the mass, we need to know the number of atoms. So converting the energy to meV.
7.80× 10¹⁵ × 6.242× 10¹² = 4.87 ×10²⁸ meV
From one atom 200 meV is produced.
So, number of atoms = 4.87 ×10²⁸/200 = 2.44×10²⁶ atoms.
No of moles = number of atoms/ Avogadro's number = 2.44×10²⁶/ 6.022 ×10²³ = 405.18 moles.
Mass = Number of moles× molar mass
=405.18 × 235 = 95217.52 g = 95.217 Kg
So the amount of uranium 235 required by the nuclear reactor for an year is 95.217 g.
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The figure shows the electric field lines for two point charges separated by a small distance. Determine the ratio q1/q2.
The figure shows the electric field lines for two point charges separated by a small distance. Determine the ratio is [tex]-\frac{1}{3}[/tex].
The directions that a positive test charge would accelerate if it were placed along the electric field lines are indicated by the lines. Because of this, the lines are pointed in the direction of negatively charged source charges rather than positively charged source charges. Each line must have an arrowhead pointing in the proper direction to convey information about the field's direction. Any number of lines could be present in an electric field line pattern. The number of lines is typically regulated because drawing so many lines tends to make the patterns harder to read. Usually, a few lines around a charge are enough to convey the characteristics of the electric field in the area around the lines.
Field lines emerges from positive charge and go inside negative charge.
[tex]\frac{q_{1} }{q_{2} }[/tex]=[tex]\frac{-6}{18} =-\frac{1}{3}[/tex]
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What are three tips to start a healthy dating relationship mentioned in the article? (Site 1)
Faith, respect, and effective communication are the three tips to start a healthy dating relationship mentioned in the article.
What are three recommendations for beginning a happy relationship?
Trust, respect, effective communication, adaptability, a common interest, time apart, different connections (with family and friends), and appreciation. Each partner needs to have confidence in the other. Never should your partner belittle you, test you, or say anything disparaging about you.
What are good relationships?
Healthy relationships involve open communication, honesty, trust, and respect between partners as well as work and compromise from both parties. There is no imbalance of power. Partners are free to make decisions together, respect each other's independence, and take individual actions without worrying about the consequences.
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a particle travels along a straight line with an acceleration of a=(10−0.2s) m/s2 , where s is measured in meters
The required velocity of a particle travelling in a straight line with the given acceleration function at s = 10 m is calculated to be 15.52 m/s.
At, s = 0, the velocity of the particle is v = 9 m/s.
Now, let us find the particle's velocity at s = 10 m,
Consider the acceleration function, a = (10 − 0.2 s)
Since, a = v dv/ds, so the above equation can be written as,
v dv/ds = (10 − 0.2 s)
Integrate the above function using the variable separable approach,
9 to v ∫ v dv = 0 to 10 ∫ (10 − 0.2 s) ds
9 to v (v²/2) = 0 to 10 (10 s - 0.2 s²)
v²/2 - 9²/2 = 10× 10 - (0.2 × 10²)
v = 15.52 m/s
Thus, the velocity as s = 10 m, is 15.52 m/s.
The given question is incomplete. The complete question is 'Determine the velocity of the particle when s = 10 m if v = 9 m/s, at s = 0.'
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what tool of l.b. jefferies' trade in rear window saves him from harm once he is discovered by his potentially murderous neighbor? group of answer choices lisa and her quick thinking his dark room chemicals his camera flashbulb the sharp edge of a camera lens
Answer:
The brightness of his flashbulbs temporarily saved him by blinding his would-be assassin.
According to newton's third law of motion, when one object exerts a force on a second object, what are the forces?.
When object A exerts a force on object B, object B must exert an equal and opposite force on object A. This law essentially expresses a certain symmetry.
Forces always occur in pairs, and one body cannot exert a force on another without experiencing the force itself. Newton's third law of motion states that whenever a first object exerts a force on her second object, the first object experiences a force equal but opposite to the force it is exerting . Newton's third law of motion states that whenever the first object exerts a force on his second object, the first object experiences a force equal but opposite to the force it is exerting .
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A train travels on a track at a constant velocity of 100 kmh
. Inside one of the train cars is a table and book. The table and the book are moving with the train at constant velocity; however, the table and the book are at rest (stationary) relative to each other.
Using Newton's third law of motion, what is the force relationship between the table and the book? Does it matter that the train is moving?
A
The mass of the book is the force of the book on the table. This force is equal to the force of the table on the book. It does not matter that the train is moving, because the contents of each train car are not moving relative to the train.
B
The mass of the book exerts no force on the table because it is not accelerating; however, the table exerts a force on the book. It does matter that the train is moving, because it exerts a force on both the table and the book.
C
The weight of the book exerts a force on the table due to gravity, which is exactly balanced by the force of the table on the book. It does matter that the train is moving, because it exerts a force on both the table and the book.
D
The weight of the book is the force of gravity acting on the book, this force is exactly balanced by the force of the table on the book. It does not matter that the train is moving, because the contents of each train car are not moving relative to the train.
The weight of the book exerts a force on the table due to gravity, which is exactly balanced by the force of the table on the book. It does matter that the train is moving, because it exerts a force on both the table and the book. Thus, option C is correct.
What is acceleration?The rate at which an object's velocity changes over time, or how quickly it changes its velocity, is measured by acceleration. It has both magnitude and direction because it is a vector quantity. In physics, acceleration is typically defined as the change in velocity per unit of time and is expressed in units of metres per second squared (m/s2).
A change in direction, speed, or both can cause acceleration. When an object accelerates, it is said to be experiencing a net force, and the acceleration is inversely correlated with the mass of the object.
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A box slides down a frictionless ramp inclined at 30 degrees. What is the box’s acceleration? What is the acceleration if the coefficient of friction between the box and ramp is 0.34?
Frictionless ramp: The acceleration of a box sliding down a frictionless ramp inclined at 30 degrees can be determined using the equation for gravitational acceleration:
a = g * sin(θ)
where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the ramp (30 degrees).
a = 9.8 * sin(30) = 4.9 m/s^2
Ramp with friction: If the coefficient of friction between the box and ramp is 0.34, the acceleration can be determined using the equation:
a = g * sin(θ) - μ * g * cos(θ)
where μ is the coefficient of friction.
a = 9.8 * sin(30) - 0.34 * 9.8 * cos(30) = 2.86 m/s^2
So the acceleration of the box sliding down a frictionless ramp inclined at 30 degrees is 4.9 m/s^2, and the acceleration if the coefficient of friction is 0.34 is 2.86 m/s^2.
an arrow is in mid-flight on its way to a target. at this moment, what force keeps the arrow going forward?
At the moment, there is actually no force that keeps the arrow going forward when it is in mid-flight.
In order to accelerate an object, there must be a net force acting on the object. This is because without any force acting on, an object will be at rest or moving at a constant rate and at one direction.
Acceleration in physics is defined to be the change in velocity over the time elapsed (a = Δv/t). The equation means that an object will be accelerating when it keeps changing velocities.
When the arrow is in mid-flight, it is assumed to be moving at a constant velocity, ignoring the air friction. Therefore, the arrow is not accelerating mid-flight, which means there is no force acting on the arrow at that moment.
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using the field of view calculated in exercise 1 for the high power lens, what is the approximate diameter of each of the cells in the bacteria coccus form slide in photo 10? show your calculations.
The approximate diameter of each cell in the Bacteria Coccus Form slide in Photo 10 is 0.33 micrometers.
The formula to calculate the diameter of an object in the field of view is:
diameter = field of view (FOV) / magnification
First, we need to convert the FOV from millimeters to micrometers:
0.2mm = 200µm
Now, we can use the formula to calculate the diameter:
diameter = 200µm / 600 = 0.33µm
So, the approximate diameter of each cell in the Bacteria Coccus Form slide in Photo 10 is 0.33 micrometers.
Field of View (FOV) is the extent of the observable world that is seen at any given moment. It refers to the extent of the observable environment that is seen by an observer's eye or a camera lens. In the context of visual representation, FOV is often expressed as an angle, which defines the breadth of the visible area. A larger FOV allows more of the environment to be seen at once, while a smaller FOV provides a narrower, more focused view.
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What simple machine you would use to do the following job. You want to build a jump for your bike. Your dad said you can use the pile of dirt out behind the garage for it.
We can use a log and arock or something hard to make a pivot and place on it the log to build a jump.
BUILD HIGHER JUMPThere are several exercises that can be done to increase the height of the jump.
The exercise to train the jump is by jumping jack. Jumping jacks is a type of exercise plyometric that can help you jump higher by building lower body strength. This exercise can also increase the heart rate.
Jumping jacks are useful for improving performance in activities that require you to move quickly in different directions.
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when a spiral galaxy is observed at a distance of 2 billion light-years, what do we observe?
When a spiral galaxy is observed at a distance of 2 billion light-years, we see the galaxy as it was 2 billion years ago. This is because light travels at a constant speed, and it takes time for the light from the galaxy to reach us. Thus, the observation of a spiral galaxy 2 billion light-years away allows us to see the galaxy in the distant past and learn about its structure and evolution over time.
When observing a spiral galaxy at a distance of 2 billion light-years, we are looking at the galaxy as it appeared 2 billion years ago. We are observing the galaxy's light that has taken 2 billion years to reach us. From our viewpoint, we see the galaxy's position, brightness, and general structure as it was 2 billion years ago. We can use this information to study the galaxy's history, formation, and evolution. However, it is important to keep in mind that the galaxy has likely changed over the 2 billion years since its light was emitted, so our observation is not a completely accurate representation of the galaxy's current state.
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Sasha lifts a couch from the ground floor of her house to the attic. If
the couch has a mass of 120 kg and is lifted 8.2 m, then what is the
energy gained by the couch?
J
Use g-9.81 m/s2 and do not include units in your answer.
Work done or energy used to lift the mass is the product of the force applied on it and the displacement. The energy used for a force of 1176 N here is 9643.2 J.
What is work done ?Work done is a vector quantity measuring how effectively the force make a displacement. Thus, it is the product of force and displacement. Work done by body is equal to the energy used by it.
Here the force that has to be applied to lift the mass is equal to its weight
F = mg
m = 120 kg
g = 9.8 m/s²
then F = 120 × 9.8 m/s² = 1176 N.
Displacement of the couch = 8.2 m.
then work done = F. ds
W = 8.2 m ×1176 N = 9643 J.
Therefore, the energy gained by the coach is equal to the work done by the person that is 9643 J.
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william tell must split the apple atop his son's head from a distance of 27 m. when william aims directly at the apple, the arrow is horizontal. at what angle must he aim it to hit the apple if the arrow travels at a speed of 35 m/s?
The angle at which William Tell must aim the arrow is approximately 32.2 degrees.
To find the angle at which William Tell must aim the arrow to hit the apple, you need to use the equation of motion for a projectile under constant gravitational acceleration.
Let's call the angle at which William aims the arrow "θ". Then, the horizontal velocity of the arrow (vx) can be found using vx = 35 m/s x cos(θ). The vertical velocity of the arrow (vy) can be found using vy = 35 m/s x sin(θ).
Using the kinematic equation for vertical motion under constant acceleration, we can find the time it takes for the arrow to reach the height of the apple:
vy = v0 + a x t
0 = 35 m/s x sin(θ) - 9.8 m/s² x t
t = (35 m/s x sin(θ)) / 9.8 m/s²
Next, use the horizontal velocity of the arrow and the time found above to find the horizontal distance it travels:
x = vx x t
x = 35 m/s x cos(θ) x (35 m/s x sin(θ)) / 9.8 m/s²
Finally, set x equal to the distance to the apple (27 m) and solve for θ using trigonometry:
27 m = 35 m/s x cos(θ) x (35 m/s x sin(θ)) / 9.8 m/s²
cos(θ) = sqrt(9.8 m/s² x 27 m / (35 m/s)²)
θ = arc cos(sqrt(9.8 m/s² x 27 m / (35 m/s)²))
The angle at which William Tell must aim the arrow is approximately 32.2 degrees.
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A 0.230-kg baseball is thrown with a speed of 41 m/s.What is the ball's momentum?
The momentum of the 0.230-kg baseball thrown with a speed of 41 m/s is 9.53 kg m/s. This means that if the ball were to collide with an object with equal and opposite momentum, the combined momentum of the two objects would be zero.
Momentum is a measure of an object's motion and is calculated by multiplying its mass and velocity. In physics, it is an important concept as it is conserved in many cases and helps to predict how objects will interact with each other.
The momentum of an object can be calculated using the formula: p = mv, where p is momentum, m is the mass of the object, and v is its velocity. In this case, the mass of the baseball is 0.230 kg, and its velocity is 41 m/s. Therefore, the momentum of the baseball can be calculated as follows:
p = mv = 0.230 kg * 41 m/s = 9.53 kg m/s.
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A plastic ball of mass 400 kg moves with a velocity of 30 m/s. It collides with a second plastic ball of mass 200 kg moving in the same direction at 10 m/s. After the collision, the 200 kg ball has a velocity of 26 m/s, in the same direction. What is the new velocity of the 400 kg ball? Show your equation and work.
The total momentum during the collison is conserved. Using this concept, the final velocity of the 400 kg ball is 22m/s.
What is momentum ?Momentum of an object is the product of its mass and velocity. During collision between two bodies the total initial momentum is equal to the total final momentum.
Momentum of ball of 400 kg with 30 m/s = 400 × 30 = 12000 kg m/s.
momentum of ball of 200 kg with 10 m/s velocity = 200 × 10 = 2000 kg m/s.
total initial momentum = 2000 + 12000 kg m/s = 14000 kg m/s.
Now, final momentum of 200 kg ball with 26 m/s = 200 × 26 = 5200 kg m/s.
total final momentum = total initial momentum = 14000 kg m/s.
thus 5200 kg m/s + (400 kg × v m/s) = 14000 kg m/s
v = (14000 - 5200 kg m/s )/400 kg = 22 m/s.
Therefore, the final velocity of 400 kg ball is 22 m/s.
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a 1-megabit computer memory chip contains many 91 ff capacitors. each capacitor has a plate area of 1.22 x 10^-11 m^2. determine the pkate seperation of such a capacitor (assume an empty parallel-plate configuration.
The plate separation of such a capacitor is 1.186 nm or 11.86 Angstroms.
The question is not complete. A similar question is in the attachment. The formula for the capacitance of a parallel plate capacitor
C = ε₀ × A ÷ d
C = capacitance of the capacitor (Farad)C = ε₀ × A ÷ d
C × d = ε₀ × A
91 × 10⁻¹⁵ × d = 8.85 × 10⁻¹² × 1.22 × 10⁻¹¹
91 × 10⁻¹⁵ × d = 10.797 × 10⁻²³
d = 10.797 × 10⁻²³ ÷ 91 × 10⁻¹⁵
d = 0.1186 × 10⁻⁸
d = 1.186 × 10⁻⁹
1 nm (nanometers) = 10⁻⁹ m1 Angstroms = 10⁻¹⁰ md = 1.186 nm
d = 11.86 × 10⁻¹⁰ m
d = 11.86 Angstroms
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i use a 2 kg hammer to hit a 0.5 kg ball. if the ball accelerates at 12 m/s2 what is the acceleration of the hammer?
So the acceleration of the hammer is 3 m/s^2.
Newton's Third Law of Motion, which stipulates that there is an equal and opposite response to every action, may be used to calculate the hammer's acceleration.
In this instance, the hammer's force on the ball is the action, and the ball's force on the hammer is the response.
Since force is equal to mass times acceleration (F = ma),
The acceleration of the hammer can be calculated as follows:
a_hammer = F_ball / m_hammer
a_hammer = (m_ball * a_ball) / m_hammer
a_hammer = (0.5 kg * 12 m/s^2) / 2 kg
a_hammer = 3 m/s^2
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Numerical problem ? A load of 680N is lifted from A to C by 500N force on an inclined plane as shown in the diagram study the. diagram and calculate.? input work
The work done is 6000J
What is Work Done?The product of a force's component acting in the displacement's direction and its magnitude is known as the work done by the force. Formula.
The following formula can be used to determine work by multiplying force and distance in the direction of the force. Unit: W = F d.
Given
Load: 680 Effort: 500 Ed: 12 Meters Ld: 8 metersOutput work formula
L*Ld = 680*8 = 5440
Hence the output is 5440J
Input work
We know
the input work formula is
E*Ed
500*12= 6000J
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what will be value of mag field after capacitor fullly charged
The value of the magnetic field after a capacitor is fully charged will be zero. This is because once the capacitor is fully charged and the electric field is no longer changing, the magnetic field will disappear.
When a capacitor is fully charged, the value of the magnetic field will be zero. This is because the electric field stops changing once the capacitor is fully charged, which in turn means that the magnetic field associated with it will no longer exist.
This can be explained by the principle that magnetic fields are generated due to the changes in electric fields, which no longer exist in the case of a fully charged capacitor. Thus, it is important to note that the value of the magnetic field will be zero once the capacitor is fully charged.
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Blue and white wands are rubbed together and held 1.35 cm apart. If the charge on the white- faced wand is 1.38 x 10-10 C, what is the magnitude of the force each wand ex one? Is the force attractive or repulsive? State your assumptions. (8 pts) erts on the other
We can conclude that the force exerted on each wand is repulsive, as the charges are both of the same sign.
What is mangitude?Magnitude is a measure of the size of a physical quantity usually explain it as a numerical value of the octane used to compare the relative size of different object or phenomena it is typically used to measure the intensity soldiers trained the something magnitude is a concept applicable how many different physical quantities of the light sound and its speed and force.
The magnitude of the force exerted by each wand can be calculated using Coulomb’s Law, which states that the force is equal to the product of the two charges, divided by the square of the distance between them. Since we know the charge on the white-faced wand, we can calculate the force:
F = (1.38 x 10-10 C)2 / (1.35 cm x 10-2 m)2
F = 0.0012 N
The force between the two wands is repulsive, as the charges are both of the same sign.
Assuming that the wands are not charged before they are rubbed together and that the distance between them remains constant, we can conclude that the force exerted on each wand is repulsive, as the charges are both of the same sign.
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which of the three objects experiences the greatest buoyant force?
The highest volume of water is displaced by the lead block and aluminum, which also has the largest volume and the strongest buoyant force.
What kind of force is buoyant, for instance?Here are a few real-world instances of the buoyant force. A ship floating in the ocean, a boat moving down a river, an iceberg floating in the water, a person wearing a life jacket floating in the water, a helium balloon rising in the air, etc. The density has a direct relationship with the buoyant force.
Are heavier things subject to larger buoyant forces?An object feels a buoyant force because the bottom is deeper in the liquid than the top, which results in a stronger upward pressure. As a result, any item submerged in a liquid experiences buoyancy.
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What is the equation for a sphere?
(x-h)^2 + (y-k)^2 + (z-l)^2 = r^2 is the equation for sphere.
What is a sphere?Every point on the surface of a sphere, which has three dimensions, is equally distant from the object's centre. It has a symmetrical, circular shape, and all points that are a certain distance from the centre define the surface of the object. Numerous commonplace items, including balls, planets, and even fruits, include spheres.
The equation for a sphere in physics is given by:
(x - h)2 + (y - k)2 + (z - l)2 = r2,
where (h, k, and l) stand in for the sphere's centre and r is its radius. The distance between any point on the surface of the sphere and its centre is calculated using this equation.
The sphere is perfectly symmetrical in all directions, so if you cut it in half, both pieces would be identical.
One of the most fundamental shapes in physics, the sphere may be found in many fields including fluid mechanics, optics, and thermodynamics. Other forms like ellipses and toroids can also be constructed using the sphere as their fundamental building block.
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Why is kinetic energy not conserved in inelastic collisions? What if, theoretically, there was an inelastic collision that did not generate any heat?
Kinetic energy is not conserved in inelastic collisions because part of the energy is converted into internal energy. If there was an inelastic collision that did not generate any heat, it would still result in a decrease in total kinetic energy, as the internal energy would remain constant.
In an inelastic collision, kinetic energy is not conserved due to the conversion of some of the energy into internal energy. This is the case even if the collision does not produce any heat.
The total kinetic energy still decreases, as the internal energy remains constant. Therefore, in an inelastic collision, part of the kinetic energy is transformed into internal energy, resulting in a decrease in the total kinetic energy of the system.
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how long does it take a motor with an output of 8.0 w to lift a 2.0 kg object 88 cm?
The takes a motor with an output of 8.0 W approximately 3.632 minutes to lift a 2.0 kg object 88 cm.
The time it takes a motor with an output of 8.0 W to lift a 2.0 kg object 88 cm can be calculated using the equation for work, which is given by:
W = F * d
where W is the work done, F is the force required to lift the object, and d is the distance the object is lifted. The force required to lift the object can be calculated using the equation for weight, which is given by:
F = m * g
where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2).
Substituting the values for m and g into the equation for weight, we get:
F = 2.0 kg * 9.8 m/s^2 = 19.6 N
Now that we know the force required to lift the object, we can substitute this value into the equation for work to calculate the work done:
W = F * d = 19.6 N * 88 cm = 1717.28 J
Finally, we can use the equation for power, which is given by:
P = W / t
where P is the power of the motor and t is the time it takes to lift the object. We know the power of the motor (8.0 W) and the work done (1717.28 J), so we can calculate the time it takes to lift the object:
t = W / P = 1717.28 J / 8.0 W = 215.91 seconds = 3.632 minutes
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what is the speed of light with a frequency of 2.4 x 1013 1/s? give your answer in m/s.
The 299,792,458 m/s is the speed of light with a frequency of 2.4 x 1013 1/s.
What is speed ?
The rate of a directionally changing object's location. The SI unit of speed is created by combining the fundamental units of length and time. Meters per second (m/s) is the unit of speed in the metric system.
What is frequency?
The frequency is expressed in Hertz. A sound wave's frequency is determined by how many vibrations it produces ( f ). Another way to think of frequency is as the quantity of waves that pass a specific spot in a second.
Therefore, 299,792,458 m/s is the speed of light with a frequency of 2.4 x 1013 1/s.
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a gaseous substance with a molecular weight of 50 is at 200 psia, 300f, and it has a density of 1.5 lbm/ft3. can this gas be treated as an ideal gas?
Yes, this gas can be treated as an ideal gas with a molecular weight of 50 is at 200 psia, 300f, and it has a density of 1.5 lbm/ft3.
This is because the molecular weight of the gas is relatively low, at 50, and the pressure and temperature of the gas are both within the range of the ideal gas law. The ideal gas law states that for a gas at a given temperature and pressure, the product of its pressure and volume is equal to the product of its temperature and molar gas constant. In this case, the pressure, temperature, and molar gas constant are all within the range of the ideal gas law, so the gas can be treated as an ideal gas.
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two equally charged particles are held 3.2 ' 10$3 m apart and then released from rest. the initial acceleration of the first particle is observed to be 7.0 m/s2 and that of the second to be 9.0 m/s2 . if the mass of the first particle is 6.3 ' 10$7 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle?
[tex]a) 4.9X 10^{-7} Kg\\ b) 7.09X10^{-11} C[/tex]
We know that (from Newton’s third law) the magnitude of the force on the second particle due to the first particle [tex]F_{12}[/tex] equals the magnitude of the force on the first particle due to the second particle [tex]F_{21}[/tex] , so:
[tex]F_{12} = F_{21}[/tex]
Given:
The initial acceleration of the first particle, a1 = 7.0 m/s^2
The initial acceleration of the second particle, a2 = 9.0 m/s^2
Mass of the first particle, m1 = 6.3 * 10^(-7) kg
Separation between the two particles, d = 3.2 * 10^(-3) m
Using Coulomb's law, the force between two charges q1 and q2 is given by:
F = k * |q1 * q2| / d^2
Where k is Coulomb's constant.
Coulomb's law is a fundamental law of electrostatics that describes the interaction between charged particles. It states that the force between two point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Since the acceleration of a particle is directly proportional to the net force acting on it, we can write:
m1 * a1 = k * |q1^2| / d^2
m2 * a2 = k * |q2^2| / d^2
Dividing the first equation by the second equation, we get:
m1 * a1 / m2 * a2 = q1^2 / q2^2
(m1 * a1) / (m2 * a2) = (q1^2) / (q2^2)
m2 = m1 * (a1 / a2)
Substituting the known values:
m2 = 6.3 * 10^(-7) kg * (7.0 m/s^2 / 9.0 m/s^2)
m2 = 4.9 * 10^(-7) kg
The mass of the second particle is 4.9 * 10^(-7) kg.
To find the magnitude of the charge of each particle, we can rearrange the first equation:
q1^2 = m1 * a1 * d^2 / k
Substituting the known values:
q1^2 = 6.3 * 10^(-7) kg * 7.0 m/s^2 * (3.2 * 10^(-3) m)^2 / k
q1 = sqrt(6.3 * 10^(-7) kg * 7.0 m/s^2 * (3.2 * 10^(-3) m)^2 / k
=> q1 = q2 = 7.09 × 10^-11 C
Therefore, the correct answers are:
[tex]a) 4.9X 10^{-7} Kg\\ b) 7.09X10^{-11} C[/tex]
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if earth shrank to a smaller radius but kept the same mass, the gravitational force between earth and the moon would
The gravitational force between the earth and the moon would not change if earth shrank to a smaller radius but kept the same mass.
The gravitational force between two objects is directly proportional to their individual masses and inversely proportional to the distance between them.
So, if we shrank the Earth to a smaller radius keeping the mass constant then the density of the earth goes up but as the distance between the center of the earth and the moon doesn't change the gravitational force also would not change.
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