Answer:
No
Explanation:
Suppose, you are driving a car with certain velocity and see a man crossing the road. So, you hit the brakes to stop the car. From the point, you hit brakes until you stop (final velocity = 0) you are decelerating.
A ball is thrown up into the air. When it gets to the very top,
what kind of energy does it have?
At the highest attitude, the velocity of the ball is 0 m/s, so the kinetic energy is 0 as well.
Hence the answer is potential energy because it doesn't depend on velocity .
An 11-kilogram cart is pulled with a horizontal force at a constant velocity of 8.0 meters per second, as shown in the diagram. The force of friction between the cart and the floor is 12 newtons. What is the magnitude of the horizontal force?
The cart is pulled at a constant velocity, so it is in equilibrium. In particular, the net horizontal force is zero, and consists of only the pulling force and friction such that
p - f = 0
where p and f denote the magnitudes of the pulling force and friction.
So we have
p - 12 N = 0
p = 12 N
A cubic box is completely filled with 2800 g of water. What is the length of one side of the box, in meters?
m
Explain your reasoning.
Since the density of water is
cm3 is
g/cm3, then the volume of 2800 g of water is
cm on each side. Converting [ cm to meters, the cube is
Proy
13 of 15
⠀⠀⠀
Next
cm³. A cubic box with a volume of [
m on each side.
The density of water is approximately 1 g/cm^3. Therefore, the volume of 2800 g of water would be 2800 cm^3 because density is mass/volume, and so volume is mass/density.
Since this volume is inside a cubic box, the length of each side of the cube (a, for instance) could be found by taking the cubic root of the volume. This is because the volume of a cube is calculated by a^3 (length of one side cubed). Hence, a = cube root of 2800 cm^3 ≈ 14.1 cm.
Converting centimeters to meters (as 1 meter is equal to 100 centimeters), we get approximately 0.141 meters.
So the filled cubic box has a side length of approximately 0.141 m.
What voltage would be measured across the 15 ohm resistor?
Answer: That depends on what other components are in the same circuit
along with the 15-ohm resistor.
If there's nothing else, and the battery is connected across the 15-ohm
resistor, then when you measure the voltage across the 15-ohm resistor,
your voltmeter is also connected straight across the battery, and you read
10 volts.
Explanation:
Scientists launch a rocket, and they monitor its acceleration and the force exerted by its engines. As the rocket gets higher, the monitors show that the acceleration of the rocket is increasing but the force exerted stays the same. How do Newton’s laws explain why the scientists could expect this to happen? The total force stays the same, but the action force is increasing as the reaction decreases. The mass of the rocket decreases as fuel is burned, so the acceleration increases. The inertia of the rocket increases, which reduces the force needed to change its speed. The reaction force is increasing as fuel is burned, which causes a greater acceleration.
Newton’s laws explain why scientists could expect this to happen , The mass of the rocket decreases as fuel is burned, so the acceleration increases, therefore the correct answer is option B.
What is Newton's second law?Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum. The mathematical expression for Newton's second law is as follows
As given in the problem Scientists launch a rocket, and they monitor its acceleration and the force exerted by its engines. As the rocket gets higher, the monitors show that the acceleration of the rocket is increasing but the force exerted stays the same.
Newton's laws clarify why scientists may anticipate this to occur. The right response is option B because as fuel is burnt, the rocket's mass reduces, and its acceleration rises.
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Help please, view attachment below
Answer: you are right, its entodermic
Explanation:
The enthalpy of the products in an entodermic reaction is greater than the enthalpy in the reactants.
If the height of an object is doubled, the potential energy will
OA. increase by 4 times
OB. decrease by 1/2
OC. stay the same
O D. double
SUB
The height of the object, given that the potential energy of the object doubled will be double (option D)
How do i determine the height of the object?First, we shall list out the given parameters. Details below:
Initial potential energy (PE₁) = PInitial volume height (h₁) = hNew potential energy (PE₂) = 2PNew volume height (h₂) = ?Potential energy is given as:
PE = mgh
Keeping mg constant, we have
PE₁ / h₁ = PE₂ / h₂
Inputting the given parameters, we have
P / h = 2P / h₂
Cross multiply
P × h₂ = h × 2P
Divide both sides by P
h₂ = (h × 2P) / P
h₂ = h × 2
h₂ = 2h
Thus, we can conclude that the new height of the object will also double (option D)
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a force is represented by a ____ the choice of a ____ is necessary
Answer:
a force is represented by a vector the choice of a reference frame is necessary
Explanation:
Two charged particles are a distance of 1.72 m from each other. One of the particles has a charge of 8.01 nC, and the other has a charge of 4.22 nC.
a. The magnitude of the electric force that one particle exerts on the other is 1.72 millinewtons (mN). and b. the force is repulsive
To calculate the magnitude of the electric force between two charged particles, we can use Coulomb's Law, which states that the magnitude of the electric force (F) between two charged objects is given by:
F = k * (|q1| * |q2|) / r^2
where k is the electrostatic constant (k = 8.99 x 10^9 N·m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
Given:
q1 = 8.01 nC (nanocoulombs)
q2 = 4.22 nC (nanocoulombs)
r = 1.72 m
Converting the charges to coulombs:
q1 = 8.01 x 10^-9 C
q2 = 4.22 x 10^-9 C
Plugging the values into Coulomb's Law:
F = (8.99 x 10^9 N·m^2/C^2) * ((8.01 x 10^-9 C) * (4.22 x 10^-9 C)) / (1.72 m)^2
Calculating the magnitude of the force:
F ≈ 1.72 x 10^-3 N
Therefore, the magnitude of the electric force that one particle exerts on the other is approximately 1.72 millinewtons (mN).
To determine if the force is attractive or repulsive, we need to consider the signs of the charges. If the charges have opposite signs (one positive and one negative), the force is attractive. If the charges have the same sign (both positive or both negative), the force is repulsive.
In this case, both charges are positive, so the force between them is repulsive. The particles will experience a repelling force due to their like charges, causing them to push away from each other.
The question was incomplete. find the full content below:
Two charged particles are a distance of 1.72 m from each other. One of the particles has a charge of 8.01 nC, and the other has a charge of 4.22 nC.
(a) What is the magnitude (in N) of the electric force that one particle exerts on the other?
(b) Is the force attractive or repulsive?
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Rocks in the asteroid belt are traveling around the Sun at a distance of 3.2 Astronomical Units (AU). According to Kepler's Third Law, what is the orbital period of these rocks?
Recall Kepler's Third Law can be written as
P 2 = a 3
if the period is measured in (Earth) years and the distance is measured in AU. Follow the steps in Example 3.1 (just with a different distance value).
Pick the answer that's closest to your result:
The orbital period of the rocks in the asteroid belt is approximately 5.73 years.
What is the average distance, a, between the sun and the asteroid, expressed in astronomical units?
The distance from the Sun to the asteroid belt is between 2-4 AU, or between 300 and 600 million kilometers (186-272 million mi).
Using Kepler's Third Law, we have:
P² = a³
where P is the orbital period of the rocks in years, and a is the semi-major axis of their orbit in astronomical units (AU).
Substituting a = 3.2 AU, we get:
P² = (3.2 AU)³
P² = 32.768 AU³
P = \(\sqrt{32.768}\) years
P ≈ 5.73 years
Therefore, the orbital period of the rocks in the asteroid belt is approximately 5.73 years.
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Heather and Jerry are standing on a bridge 46 m
above a river. Heather throws a rock straight down with a speed of 14 m/s
. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. How much time elapses between the first splash and the second splash?
The time elapsed between the first splash and the second splash is approximately 0.69 seconds.
To calculate this, we consider the motion of two rocks thrown simultaneously from a bridge. Heather throws a rock straight down with a speed of 14 m/s, while Jerry throws a rock straight up with the same speed.
We use the equation for displacement in uniformly accelerated motion: s = ut + (1/2)at^2.
For Heather's rock, which is thrown downwards, the initial velocity (u) is positive and the acceleration (a) due to gravity is negative (-9.8 m/s^2). The displacement (s) is the height of the bridge (46 m).
Solving the equation, we find two possible values for the time (t): t ≈ -4.91 s and t ≈ 1.91 s.
Since time cannot be negative in this context, we discard the negative value and consider t ≈ 1.91 s as the time it takes for Heather's rock to hit the water.
For Jerry's rock, thrown upwards, we use the same equation with the same initial velocity and acceleration. The displacement is also the height of the bridge, but negative.
Solving the equation, we find t ≈ -5.68 s and t ≈ 1.22 s. Again, we discard the negative value and consider t ≈ 1.22 s as the time it takes for Jerry's rock to reach its maximum height before falling back down.
To find the time difference between the first and second splash, we subtract t ≈ 1.91 s (Heather's rock) from t ≈ 1.22 s (Jerry's rock). This gives us a time difference of approximately 0.69 seconds.
Therefore, the time elapsed between the first splash and the second splash is approximately 0.69 seconds.
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Two of the smallest particles known to man, the Kauaion and the Waimeaon have just been discovered! The Kauaion has a mass that is 3 times larger than the Waimeaon. The particles were discovered in a 1-D collision travelling towards each other where the Kauaion had a velocity of 50000m/s and the Waimeaon had a velocity of 100000m/s . The particles underwent a completely elastic collision. Find the velocity of the Kauaion and the Waimeaon after the collision.
Part A:
After the collision, the Kauaion has a velocity of:
_____ m/s
Part B:
After the collision, the Waimeaon has a velocity of:
_____ m/s
A. After the collision, the Kauaion has a velocity of 75,000 m/s.
B. After the collision, the Waimeaon has a velocity of 25,000 m/s.
Velocity of the Kauaion and the Waimeaon after the collisionThe velocity of the Kauaion and the Waimeaon after the collision is calculated by applying the principle of conservation of linear momentum as follows;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is mass Kauaionm₂ is mass of Waimeaonu is the initial velocity of the objectsv is the final velocity of the objectsLet the mass of the Waimeaon = m
3m(50000) + m(100000) = 3mv₁ + mv₂
m(150,000) + m(100000) = m(3v₁ + v₂)
150,000 + 100000 = 3v₁ + v₂
250,000 = 3v₁ + v₂
v₂ = 250,000 - 3v₁ --------(1)
One directional linear velocityu₁ + v₁ = u₂ + v₂
v₂ = u₁ + v₁ - u₂
v₂ = 50000 + v₁ - 100000
v₂ = v₁ - 50000 ----(2)
Solve (1) and (2) together
v₁ - 50000 = 250,000 - 3v₁
4v₁ = 300,000
v₁ = 300,000/4
v₁ = 75,000 m/s
v₂ = v₁ - 50000
v₂ = 75,000 - 50,000
v₂ = 25,000 m/s
Thus, after the collision, the Kauaion has a velocity of 75,000 m/s.
After the collision, the Waimeaon has a velocity of 25,000 m/s.
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Moving sideways on the balls of the feet.
Question 4 options:
galloping
sliding
striding
skipping
Two blocks, 1 and 2, are connected by a massless string that passes over a massless pulley. 1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. 2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105
. The figure illustrates the configuration.
A system of two blocks connected by a rope passing over a pulley. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle. Box M subscript 1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M sub 1 and the surface is mu subscript 1. Box M subscript 2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle. The coefficient of friction between box M sub 2 and the surface is mu subscript 2.
The force acting on the system of two blocks connected by a rope passing over a pulley is -13.26 N.
The system of two blocks connected by a rope passing over a pulley are M1 and M2, where M1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M1 and the surface is mu subscript 1. M2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle.
The coefficient of friction between box M2 and the surface is mu subscript 2. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle.M1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. M2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105.The free-body diagram of M1 shows that the weight of M1 acts straight downwards (vertically) and the normal force acts perpendicular to the slope.
The force of friction opposes the motion and acts opposite to the direction of motion.M1 = 2.25 kgTheta subscript 1 = 42.5 degreesMu subscript 1 = 0.205g = 9.81 m/s²In the free-body diagram of M2, the normal force acts perpendicular to the incline of the slope, the weight of the object acts vertically downwards and parallel to the incline, and the force of friction opposes the motion and acts opposite to the direction of motion.M2 = 5.55 kgTheta subscript 2 = 33.5 degreesMu subscript 2 = 0.105g = 9.81 m/s²The tension in the string is the same throughout the rope. Since the masses are being pulled by the same rope, the acceleration of the objects is the same as the acceleration of the rope.
The tension in the string is directly proportional to the acceleration of the objects and the rope.A system of two blocks connected by a rope passing over a pulley has a total mass of M. The acceleration of the system is given by the formula below:a = [(m1-m2)gsin(θ1) - μ1(m1+m2)gcos(θ1)] / (m1 + m2)Where, μ1 = 0.205 is the coefficient of friction of block M1θ1 = 42.5 degrees is the angle of the incline of block M1M1 = 2.25 kg is the mass of block M1M2 = 5.55 kg is the mass of block M2g = 9.81 m/s² is the acceleration due to gravitysinθ1 = sin 42.5 = 0.67cosθ1 = cos 42.5 = 0.75The acceleration of the system is:a = [(2.25-5.55)(9.81)(0.67) - (0.205)(2.25+5.55)(9.81)(0.75)] / (2.25 + 5.55)a = -1.7 m/s² (the negative sign indicates that the system is accelerating in the opposite direction).
The force acting on the system is given by:F = MaWhere M is the total mass of the system and a is the acceleration of the system. The total mass of the system is:M = m1 + m2M = 2.25 + 5.55M = 7.8 kgThe force acting on the system is:F = 7.8(-1.7)F = -13.26 N (the negative sign indicates that the force is acting in the opposite direction).
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The water hyacinth was a major weed in Australian
and overseas' waterways until biological control
was used. Looking at the photo below, what
impact would this weed have on biodiversity in the
waterways it infests?
Whoever answers i will give branliest
An oxygen atom can absorb any frequency of light to cause its electrons to increase in energy.
Answer:
that's true.
Explanation:
that's the reason why oxygen supports burning.
Using complete sentences and correct punctuation and grammar answer the following question. Must be at least 3 sentences.
Explain why Eclipses do not occur every month.
Answer: A solar eclipse occurs when the moon passes in between the Earth and sun, casting a shadow down on the surface of our planet. If you're in the path of the shadow, the moon destroys the sun. No, wait, I mean the moon blocks the sun briefly.A lunar eclipse happens when the moon passes through the Earth's shadow. We see one limb of the moon darken until the entire thing is in shadow.An eclipse does not occur every month, because one month after an eclipse the relative geometry of the Sun, Moon, and Earth has changed. As seen from the Earth, the time it takes for the Moon to return to a node, the draconic month, is less than the time it takes for the Moon to return to the same ecliptic longitude as the Sun.
Explanation:
Answer:
Because the moon's orbit wobbles up and down with respect to the Earth, the satellite's shadow can be too high or too low to cause a solar eclipse. If the moon partially covers the sun for a given location, that area experiences a partial solar eclipse. But if the moon fully covers the sun, it will cause either a total solar eclipse or an annular solar eclipse; that's when a bright ring of light is still visible in the sky around the dark silhouette of the moon.
What is a lower fixed point in physics
In physics, a lower fixed point refers to the minimum temperature at which a particular substance or system can reach and below which it cannot be cooled further.
It is a fundamental concept in the study of thermodynamics, specifically in relation to phase transitions and the behavior of substances at low temperatures.
The lower fixed point is often associated with the concept of absolute zero, which is the lowest possible temperature in the Kelvin scale (-273.15 degrees Celsius or -459.67 degrees Fahrenheit).
At absolute zero, particles in a substance possess the minimum amount of energy and their motion ceases, resulting in the absence of thermal energy.
The lower fixed point serves as a reference point for temperature scales, such as the International Temperature Scale of 1990 (ITS-90), which defines temperature measurements based on fixed points like the melting point of certain substances and the triple point of water.
These fixed points provide reproducible and well-defined temperature values for calibration and measurement purposes.
Understanding the lower fixed point is crucial for various scientific and technological applications, such as cryogenics, superconductivity, and the study of quantum phenomena at extremely low temperatures.
By pushing the boundaries of cooling techniques, researchers aim to approach the lower fixed point and explore the fascinating properties and behaviors of matter at such extreme conditions.
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You can test the flexibility in the backs of your legs, hips, and lower back with the “sit-and-reach” activity.
true or false
I NEED ANSWER TODAY RN!!!
5.5A Two similar dielectric ellipsoids are placed in an electric field as shown in Fig. P5.5. For which orientation is the depolarization factor larger? Give qualitative reasons. Fig. P5.5 (a) (b) E
In order to determine which orientation results in a larger depolarization factor for the similar dielectric ellipsoids placed in an electric field, we need to consider the shape and alignment of the ellipsoids with respect to the electric field.
The depolarization factor measures the reduction in the electric polarization of a material due to its shape and alignment in an electric field. It is influenced by the geometry of the material and how it interacts with the electric field.
Qualitatively, if the ellipsoids are aligned in such a way that their major axes are parallel to the electric field lines, the depolarization factor would be smaller. This is because the electric field would act along the long axis of the ellipsoid, resulting in less distortion of the polarized charges inside the material. The polarization would be more effectively aligned with the electric field, minimizing the depolarization effect.
On the other hand, if the ellipsoids are oriented such that their major axes are perpendicular or at an angle to the electric field lines, the depolarization factor would be larger. In this case, the electric field would act in a direction that is not aligned with the major axis of the ellipsoid, causing more distortion and misalignment of the polarized charges inside the material. This results in a larger depolarization effect.
Without a specific diagram or more information about the orientations shown in Figure P5.5, it is difficult to determine the exact orientation with the larger depolarization factor. However, based on the general understanding of the relationship between alignment and the depolarization effect, the orientation where the major axes of the ellipsoids are perpendicular or at an angle to the electric field lines is likely to result in a larger depolarization factor.
Match the following. Match the items in the left column to the items in the right column.
1. index fossil
study of fossils
2. law of original lateral continuity
study of rock layers and the processes that form them
3. law of superposition
a fossil that is widespread geographically but only occurs in one layer or a small number of layers of rock
4. paleontology
sediment deposited into water will spread in a horizontal and continuous sheet
5. stratigraphy
any undisturbed sequence of layered rocks has the oldest rock on the bottom and newest rock on the top
Answer:
1. A fossil that is widespread geographically but only occurs in one layer or a small number of layers of rock
2. Sediment deposited into water will spread in a horizontal and continuous sheet
3. Any undisturbed sequence of layered rocks has the oldest rock on the bottom and newest rock on the top
4. Study of fossils
5. Study of rock layers and the process that form them
Sorry if any of these are wrong
What is the cost per month to operate an A.C. 10hours per day whose power is 3kW and 1KWH cost 79francs
The cost of operation for an A.C for 10 hours per day for a month will be 71,100 francs.
What is Power?Power is the amount of energy transferred or converted per unit time. The unit of power is the watt, equal to one joule per second. Power is a scalar quantity.
Cost of operation for 10 hours a day;
Daily consumption = 3kW x 10 hours
Daily Consumption = 30kW
Since 1kWH = 79 francs;
Daily consumption amount = 30 x 79 francs
Daily consumption amount = 2,370 francs
Therefore, the monthly consumption (using 30days) will be;
2,370 francs x 30 = 71,100 francs
In conclusion, 71,100 francs will be spent in a month (30 days) to run the 3kW rated A.C for 10 hours a day at 1kWH.
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Which energy transformation occurs when a butane lighter is lit?
When a butane lighter is lit, chemical energy transforms into heat energy.
What is law of conservation of energy?
Energy cannot be created or destroyed, says the law of conservation of energy. However, it has the ability to change its form. The total energy of an isolated system is constant when all sources of energy are taken into account.
The chemical energy is the bonds of chemical molecules contain energy. Exothermic reactions are those in which chemical energy is released during the reaction, frequently in the form of heat.
In butane energy is stored as a chemical energy as bonds of chemical molecules and when it is lit, the chemical energy of the butane transforms into heat energy.
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Technician A says that a radio may be able to receive AM signals, but not FM signals if the antenna is defective. Technician B says that a good antenna should give a reading of about 500 ohms when
tested with an ohmmeter between the center antenna wire and ground. Which technician is correct?
A. Technician A only
B. Technician B only
C. Both Technician A and Technician B
D. Neither Technician A nor Technician B
Neither Technician A nor Technician B is correct about the
statements they made.
What is an Antenna?This is referred to as an interface between radio waves and
helps in their propagation through currents moving in metal
conductors. It is mostly used with a transmitter or receiver for
an excellent output.
If an antenna is defective, it can't receive any type of signal If
the resistance is greater than zero then it means the antenna is
defective which is why neither of the technicians are correct.
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How does light of different frequency react when they pass through a prism (material with higher refractive index)?
Answer:
I believe the answer is that the light with the higher frequency refracts more than light with a lower frequency
Explanation:
I know this isn’t the right subject but i need help
Expository with an a anecdote and explain how specific life even impact the character of an individual
The current state of research offers some evidence that life events can cause changes in personality traits and that various life events may connect differently to various trait domains.
What is anecdote?
A brief narrative or account abou life events changet a person or event that is typically humorous, instructive, entertaining, or biographical in nature is known as an anecdote.
How do life events change your personality?
These ideas contend that because life events alter, interrupt, or reroute people's habits of thought, feeling, and action, they have long-lasting consequences on personality traits.
Hence is a changes in personality traits a correct answer.
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Which 5 are examples of locomotor movements? Select all that apply.
Question 1 options:
Hopping
Galloping
Sitting
Sleeping
Walking
Running
Skipping
Eating
Answer:
Five examples of locomotor movements are:
Hopping
Galloping
Walking
Running
Skipping
Explanation:
I hope it helps ❤❤
Select all that are true regarding natural resources (Hint: Pick 3)
There is a big difference between renewable and nonrenewable resources.
Tectonic plates are one reason why certain materials are found only at certain places.
Not every resource is found everywhere on earth
A person can find all resources everywhere
The distinction among renewable and nonrenewable is substantial. One explanation for why some materials are unique to specific locations is the movement of tectonic plates. On Earth, not every resource can be found.
Simply put, what do tectonic plates mean?Huge fragments of the Planet's crust and upper mantle make up tectonic plates. They are composed of both continental and oceanic crust. Along pre ridges and the significant faults that define the plate boundaries, earthquakes happen.
How do tectonic plates function? What are they?According to the idea of plate tectonics, Earth's crust is made up of enormous solid rock slabs called "plates" that move across the beneath, the rock inner layer above the planet's core. The crust is a part of the solid outer layer of the earth.
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A fuel tank for a rocket in space under a zero-g environment is rotated to keep the fuel in one end of the tank. The system is rotated at 3 rev/min. The end of the tank (point A) is 1.5 m from the axis of rotation, and the fuel level is 1 m from the rotation axis. The pressure in the nonliquid end of the tank is 0.1 kPa, and the density of the fuel is 800 kg/m3 . What is the pressure at the exit (point A)
Answer:
P₂ = 4098.96 Pa
Explanation:
For this exercise let's use Bernoulli's equation
Let's use the subscript 1 for the point of the liquid surface and the subscript 2 for the ends (point A)
P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂
the velocity at the end of the tank
v₂ = w r₂
the velocity at the surface of the liquid is
v₁ - w r₁
where r₂ = 1.5 m and r₁ = 1 m
the tank pressure is P₁ = P₀ = 0.1 10³ Pa
P₂ = P₁ + ½ ρ [w² (r₁² - r₂²)] + ρ g (y₁ -y₂)
We must remember that the pressure measurements the distances are measured from the lowest part to the surface that has zero height
let's reduce the magnitudes to the SI system
w = 3 rev / min (2π rad / 1rev) (1 min / 60 s) = 0.314159 rad / s
let's calculate
P₂ = 0.1 10³ + ½ 800 0.314159² |(1² -1.5²)| + 800 9.8 |(1-1.5)|
P₂ = 0.1 103 +78.96 + 3920
P₂ = 4098.96 Pa
A 10-kg package drops from chute into a 25-kg cart with a velocity of 3 m/s. The cart is initially at rest and can roll freely with no friction. Determine: a) the final velocity of the cart, b) the impulse exerted by the cart on the package, c) the fraction of the initial energy lost in the impact.
Answer:
(a) the final velocity of the cart is 0.857 m/s
(b) the impulse experienced by the package is 21.43 kg.m/s
(c) the fraction of the initial energy lost is 0.71
Explanation:
Given;
mass of the package, m₁ = 10 kg
mass of the cart, m₂ = 25 kg
initial velocity of the package, u₁ = 3 m/s
initial velocity of the cart, u₂ = 0
let the final velocity of the cart = v
(a) Apply the principle of conservation of linear momentum to determine common final velocity for ineleastic collision;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
10 x 3 + 25 x 0 = v(10 + 25)
30 = 35v
v = 30 / 35
v = 0.857 m/s
(b) the impulse experienced by the package;
The impulse = change in momentum of the package
J = ΔP = m₁v - m₁u₁
J = m₁(v - u₁)
J = 10(0.857 - 3)
J = -21.43 kg.m/s
the magnitude of the impulse experienced by the package = 21.43 kg.m/s
(c)
the initial kinetic energy of the package is calculated as;
\(K.E_i = \frac{1}{2} mu_1^2\\\\K.E_i = \frac{1}{2} \times 10 \times (3)^2\\\\K.E_i = 45 \ J\\\\\)
the final kinetic energy of the package;
\(K.E_f = \frac{1}{2} (m_1 + m_2)v^2\\\\K.E_f = \frac{1}{2} \times (10 + 25) \times 0.857^2\\\\K.E_f = 12.85 \ J\)
the fraction of the initial energy lost;
\(= \frac{\Delta K.E}{K.E_i} = \frac{45 -12.85}{45} = 0.71\)