Answer: Law of conservation of mass
Explanation:
two horizontal force are exerted on a large crate. the first force in 1200N to the right. the second force is 650 N to the left. the crate is initially at rest. five seconds later, its velocity is 7.5m/s to the right. what is the mass of the crate
With the knowledge of kinematic and dynamics, the mass of the crate is 366.7 kg
What is Force ?Force can simply be defined as a pull or push. It is the product of mass and acceleration. It is a vector quantity.
Given that two horizontal force are exerted on a large crate. the first force in 1200N to the right. the second force is 650 N to the left. the crate is initially at rest. five seconds later, its velocity is 7.5m/s to the right.
Let us first list all the parameters involved
Net Force F = 1200 - 650 = 550 NInitial velocity u = 0Time t = 5 sFinal velocity v = 7.5 m/sAcceleration a = ?Mass m = ?The net Force F = ma
We can find acceleration with formula
v = u + at
7.5 = 0 + 5a
5a = 7.5
a = 7.5/5
a = 1.5 m/s²
Then, F = ma
550 = 1.5m
m = 550/1.5
m = 366.7 kg
Therefore, the mass of the crate is 366.7 kg
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While standing, twisting your lower limb at the hip so that your toes point off to the side is called ________ rotation. Twisting your lower limb at the hip so that your toes point toward your other foot is called __________ rotation.
Lateral; medial
Lateral rotation is an anatomical term of motion used to describe rotation along the long axis of a joint. In lateral rotation, this movement is away from the midline of the body and occurs in the transverse plane.
On the other hand, medial rotation is a rotational movement towards the midline. It is sometimes referred to as internal rotation.
According to this question, twisting one's lower limb at the hip while standing, so that the toes point off to the side is an example of lateral rotation while doing the above but in such a way that it points towards the other foot is an example of medial rotation.
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consider the given result of a chromatography experiment. developed chromatography plate with three spots. spot a has travelled about half of the distance between the starting line and the solvent front. spot b has travelled about one third of the distance between the starting line and the solvent front. spot c has travelled about three quarters of the distance between the starting line and the solvent front. identify which spot corresponds to the compound in each description. has a retention factor of about 0.60 choose... corresponds to the compound with the highest affinity for the solvent choose... corresponds to the compound with the lowest affinity for the solvent choose...
TLC is a frequently used technique in organic chemistry labs because it can provide immediate and important information about the purity of a sample and whether or not a reaction is taking place. Using low polarity solvents, a TLC plate can be finished in less than five minutes.
What will happen if sample spots are too close to each other in chromatography?Problems with the separation can result from a location that is overly large or dense. 6. If you are using multiple samples on the same plate, be sure their spots do not overlap. In order to avoid colliding during the separation, adjacent dots must be spaced by at least 0.5 cm.
Since the ratio between the distances stays constant, the Rf value won't change if the solvent is only permitted to move halfway up the plate. After marking the front line of the solvent on the TLC plate and removing it from the developing chamber, let the plate air dry. When a substance is placed to a TLC plate in excess, the dot may streak over the plate or touch nearby samples that are being evaluated.
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Oil with a density of 817kg/m3817kg/m3 is flowing smoothly through a pipe, as shown. In the lower portion, the oil is flowing at v1=2.09m/sv1=2.09m/s, and the pressure gauge indicates P1=247kPaP1=247kPa. In the upper portion of the pipe, oil is flowing at v2=3.41m/sv2=3.41m/s at a height that is 10.68m10.68m above the lower portion.What is the pressure reading, in kilopascals, on the gauge on the upper portion of the pipe?
The pressure in the upper portion of the pipe is calculated by applying Bernoulli's equation,
P₁ + ¹/₂ρv₁² + ρgh₁ = P₂ + ¹/₂ρv₂² + ρgh₂
given is
p1 =247kPa
v1=2.09 m/s
h1= 0
v2 =3.41 m/s
h2 = 10.68 m
p=817 [tex]m^{3[/tex]
p2 = ?
Solving for this we can get the required value.
Bernoulli's equation formula shows the relation between pressure, kinetic energy, and gravitational potential energy of a fluid in a container. We have the formula for Bernoulli's principle as follows: p + 1 2 ρ v 2 + ρ g h = A constant.
Bernoulli's principle is based on the principle of conservation of energy. According to it, "in a steady flow, the sum of all forms of energy in a fluid is the same at all points that are free of viscous forces". This required the sum of kinetic energy, potential energy and internal energy to be constant.
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Both balls fall from the same height above the ground.
(a) Use the graphs to find
(i) the average acceleration of the falling rubber ball during the first 3.0 s
Think of a book at rest on a flat leveled surface and another book (same type) that is sliding and slowing down to a complete stop on the
same surface.
a. What force(s) is on the sliding book that is not on the book at rest? Explain why.
b. If the sliding book was speeding up instead, describe how the free body diagram would be drawn differently than the book at rest.
Each lightbulb provides 90 M of resistance. The batteries are 1.5 V. Calculate the current in your circuit.
The current in the circuit will be 0.0167 Amperes when a light bulb is providing resistance and the batteries with 1.5 voltage.
What is current?A stream of charged particles, such as electrons or ions, travelling through an electrical conductor or a vacuum is known as an electric current. The net rate of electric charge flowing through a surface or into a control volume is how it is measured.
What are the calculations?To calculate current the formula used is V= IR
1.5/90 = I
0.016 A = I
What is a circuit?Electronic components such as resistors, transistors, capacitors, inductors, and diodes are connected via conductive wires or traces that allow an electric current to pass between them.
Hence, the current in the circuit will be 0.0167 Amperes when a light bulb is providing resistance and the batteries with 1.5 voltage.
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which one of the following is not a typical consequence associated with open pit mines. apes
One of the things that are NOT a typical consequence that is associated with open pit mines is the release of high concentrations of ozone into the local environment, causing long-term respiratory harm to individuals and the environment.
The open-pit mine is a surface mining technique used to extract rocks or minerals from the earth using an open-air pit. This technique is used when ore or rock deposits are found near the surface, which makes digging a tunnel unnecessary.
The main consequence of open-pit mine that concerns most people is that it generates a large amount of dust that contains heavy metals to the environment, as well as creating deposits of toxic waste ponds. Ozone is not considered a heavy metal.
Attached below is an image of the Sunrise Dam Gold Mine open pit mine in Australia.
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various processes and events can obscure impact craters that are present on the surface of a moon or planet. separate the items into those that obscure impact craters and those that are not likely to obscure impact craters
Plate tectonics, comet strikes, enormous floods, including wind-blown sediments hide or deteriorate impact craters, whereas the following do not: radiation degradation and solar heating.
What does "moon science" mean?An object that circles a planet or another object that doesn't belong to a star is called a moon. Moons can also orbit exoplanets, large comets, and other things in addition to planets. Moons are also referred to as natural satellites since they orbit other objects, which is another name for a satellite.
A moon personality is what?Your appearance shows the roiling cauldron of emotions, worries, longings, and obsessions that lies beneath your sun sign-based identity. It emphasizes the real self, along with its motivations and issues.
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The star forming interiors of molecular clouds are best studied at which of the following wavelengths gamma ray x ray visible infared
If you wanted to see stars hidden behind a molecular cloud, you would probably look at light with an infrared wavelength.
What are wavelength and frequency?The duration, which will also apply to troughs, seems to be the distance between the two wave crests. The unit of frequency by cycles per second (Hz), which is the quantity of vibrations that cross a specific area in a second (Hertz).
Is frequency the same as wavelength?The connection between wavelength and frequency is inversely proportional. The wavelength of a wave with highest frequency is the shortest. Double the wavelength corresponds to twice the frequency. The wavelengths ratio is therefore the inverse of an applied frequency.
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The complete question is-
If you wanted to observe stars behind a molecular cloud, in what wavelength of light would you most likely observe?
A. visible
B. gamma-ray
C. X-ray
D. infrared
E. ultraviolet
If a chimpanzee were to throw darts at a Periodic Table, he would most likely hit an
element with which of the following characteristics:
a) a naturally radioactive element
b) a solid at room temperature
c) a gas at room temperature
d) a liquid at room temperature
Answer:he would most likely hit an element with which of the following characteristics: W) a naturally radioactive element X) a solid at room temperature Y) a gas at room temperature Z) a liquid at room temperature ANSWER: X) A SOLID AT ROOM TEMPERATURE
Explanation:
b
3.5 Press
The seesaw will balance when the moments on both sides are equal.
Zara weighs 400 N.
Calculate the distance from the pivot to where Zara should sit to
balance the seesaw.
Show your working and give the unit.
Because Newton as Pressure = Thrust/Area, the answer will be 7.5.
What happens when two kids of different weights balance on a seesaw and each generates an equal amount of torque in the opposing direction?The rotating equivalent of Newton's first law is this. When each child's weight exerts an equal amount of torque about the pivot in opposing directions, two kids can balance on a seesaw (clockwise and counter clockwise).
Can two people of different weights balance on a seesaw?The idea of the seesaw You are probably aware that any two people, regardless of their weights, can balance each other while seated on opposite sides of a seesaw. All that is required is for each individual to contribute an equal moment, which is determined by multiplying the person's weight by the distance from the fulcrum.
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Suppose you hear an echo 0.15 seconds after banging. How long
is the barn?
With the use of echo formula, the length of the barn is 24.75 m
What is an Echo ?An echo is a sound heard after the reflection of sound waves from a plane surface. It is simply the reflection of sound waves.
Suppose you hear an echo 0.15 seconds after banging.
Then,
Time T = 0.15 sSpeed of sound in air V = 330 m/sLength L = ?V = 2L/T
330 = 2L/0.15
2L = 330 × 0.15
2L = 49.5
L = 49.5/2
L = 24.75 m
Therefore, the barn is 24.75 m long.
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Which statement best describes the period of the mass on a spring above?
Start at C, go through D, stop at E
Start at B, hop to D, back to C, then to A, stop at E
Start at A, go through B, C, and D, turn at E, go back through D, C, and B to A
Start at A, go through B, C, and D, stop at E
The statement will best describe the period of mass on spring, Start at A, go through B, C, and D, turn at E, go back through D, C, and B to A
define mass ?
The density and kind of atoms in any specific thing are referred to as the object's mass in science. Although mass can also be measured in pounds, the kilogramme (kg) is the SI unit of mass (lb).
Think of a pillowcase stuffed with feathers and one packed with bricks to rapidly grasp the notion of mass. Which one is heavier? The bricks have a larger mass because their atoms are heavier and denser. Because of this, although though both pillowcases are the same size and level of fill, one has a significantly higher mass than the other.
according to the hooks law statement will best describe the period of mass on spring, Start at A, go through B, C, and D, turn at E, go back through D, C, and B to A will describes the image.
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On his most recent trip to the running store, Andy noticed that the water bottles for his favorite hydration belt were on sale. They were usually priced at $8, but they were on sale for $5.
The store owner told Andy that he was surprised that people were not only buying more water bottles due to the sale, but also more of the hydration belt, even though the belts were not on sale.
Based on the scenario above, what type of goods are the water bottles and hydration belts?
Explanation: It is not clear from the information given what type of goods the water bottles and hydration belts are. The only information provided is that they are sold at a running store, which suggests that they may be related to running or fitness. However, without more information it is impossible to determine their specific type or classification.
g the pressure of air in your house can stay constant during the day if the temperature rises. let the temperatures be 298 kk during the day, and 288 kk at night, and volume of the house be 900 m3m3.
There have been 903.73 moles of air that are expelled from the residence each day.
What is pressure and its types?Force is the term used to describe the physical violence applied to something. A perpendicular force is applied to the surface of the objects for each unit of area. The basic formula for pressures is F/A. (Force per unit area). Project phases are a pressure unit (Pa). Different types of pressure include absolute, atmospheric, differential, and gauge pressures.
Briefing:Since the pressures are steady:
V1/T1 = V2/T2
In the evening, V1 = 900 m^3, and T1 = 288K.
In the daytime, T2 = 298K, and V2 =?
V2 = V1*T2/T1 = 900*295/288 = 921.875 m^3
921.875 - 900 = 21.875 m^3
who venture outside during the day
V2/T2 = Vs/Ts
Vs = V2*Ts/T2 = 21.875*273/295 = 20.24 m^3
22.24 liters per mole, and 1000 liters per m^3, so
N = 20.24*1000/22.4
N = 903.73 moles.
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Abbey and Mia are in the basement playing pool. On Abbey's recent shot, the cue ball was moving east at 91 cm/s when it struck the slower 8-ball moving in the same direction at 18 cm/s. The 8-ball immediately speeds up to 62 cm/s. Determine the post-collision velocity of the cue ball. (Assume all balls have the same mass.)
Answer:
[tex]47\; {\rm cm\cdot s^{-1}}[/tex] to the east.
Explanation:
When an object of mass [tex]m[/tex] travels at a velocity of [tex]v[/tex], the momentum [tex]p[/tex] of that object will be [tex]p = m\, v[/tex].
Let [tex]m[/tex] denote the mass of one ball.
Before the collision:
Momentum of the cue ball: [tex]p(\text{cue, before}) = m\, v(\text{cue, before})[/tex].Momentum of the numbered ball: [tex]p(\text{number, before}) = m\, v(\text{number, before})[/tex].Hence, the total momentum before the collision was:
[tex]\begin{aligned} & p(\text{cue, before}) + p(\text{number, before}) \\ &= m\, v(\text{cue, before}) + m\, v(\text{number, before})\end{aligned}[/tex].
Likewise, the total momentum right after the collision would be:
[tex]\begin{aligned} & p(\text{cue, after}) + p(\text{number, after}) \\ &= m\, v(\text{cue,after}) + m\, v(\text{number, after})\end{aligned}[/tex].
Momentum is supposed to be conserved during the collision. In other words, total momentum should be the same immediately before and after the collision. Hence:
[tex]\begin{aligned} & p(\text{cue, before}) + p(\text{number, before}) \\ &= p(\text{cue, after}) + p(\text{number, after})\end{aligned}[/tex].
[tex]\begin{aligned} & m\, v(\text{cue, before}) + m\, v(\text{number, before}) \\ &= m\, v(\text{cue, after}) + m\, v(\text{number, after})\end{aligned}[/tex].
Assume that positive velocities denote motion to the east.
In this question, [tex]v(\text{cue, before})[/tex], [tex]v(\text{number, before})[/tex], and [tex]v(\text{number, after})[/tex] are all given. Rearrange this equation to find [tex]v(\text{cue, after})[/tex]:
[tex]\begin{aligned}& m \, v(\text{cue, after}) \\ &= m\, v(\text{cue, before}) \\ &\quad\quad + m\, v(\text{number, before}) \\ &\quad\quad - m\, v(\text{number, after}) \end{aligned}[/tex].
[tex]\begin{aligned}& v(\text{cue, after}) \\ &= v(\text{cue, before}) \\ &\quad\quad + v(\text{number, before}) \\ &\quad\quad - v(\text{number, after}) \\ &= 91\; {\rm cm \cdot s^{-1}} + 18\; {\rm cm\cdot s^{-1}} - 62\; {\rm cm\cdot s^{-1}} \\ &= 47\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Since the result is greater than zero, the direction of motion of the cue ball after the collision will also be to the east.
Distance (height) and mass determine the amount of ________ energy in an object.
Answer:
potential
Explanation:
Answer:
Gravitational potential energy
Explanation:
GPE = MGH
M - MASS
G - GRAVITATIONAL
H - HEIGHT
Which of the following statements about spherical mirrors is correct? (There could be more than one correct choice.)
A - A concave mirror always produces a virtual image.
B - A convex mirror always produces an upright image.
C - A concave mirror always produces a real image.
D - A convex mirror always produces a real image.
E - A convex mirror always produces a virtual image
Convex mirror always produces virtual images is the correct option.
A real image is not always formed by a concave mirror , concave mirror's rays do not converge, and it is only when the rays do converge that a real image is formed.When the subject is maintained between the main focus and the mirror's pole, a virtual image is also created by the concave mirror. Behind the mirror is where the image is created. The image is therefore virtual, upright, and enlarged.A concave mirror creates a real, reversed image in all the other scenarios.As a result, depending on the object distances, a concave mirror can create both real and virtual images.Virtual images are always created by convex mirrors. This is so because the convex mirror's focal point and curvature center are fictitious points that are impossible to reach. As a result, the image is created inside the mirror and cannot be displayed on a screen.To study about Convex mirror -
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use the following terms to create a concept map: gravity, force, falling object, net force, and air resistance.
Net force , gravity, falling object, air resistance, force . this is the concept map obtained from the above given terms.
An item often experiences some air resistance as it descends through the air. The leading surface of the item collides with air molecules, creating air resistance. Several variables affect how much air resistance the item really experiences. To keep things straightforward, it may be noted that the object's speed and cross-sectional area are the two most frequent variables that directly affect the amount of air resistance. The quantity of air resistance rises with increasing speed. Greater air resistance is brought on by larger cross-sectional areas and gravity.
What causes an item to finally attain a terminal velocity when it encounters air resistance?
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A spaceship is moving in a straight line on it's way to a planet . The pilot sees that the planet is ahead and to the left .She claims that she does not need to use the engines to push the ship toward the planet . Explain why the pilot is corrrect or incorrect ?
The pilot is correct since the planet's gravitational force will drag the spaceship toward the planet on its own.
What is gravitational force?Gravity, also known as gravitational force, pulls things with mass toward one other. Gravitational pull from Earth is a topic that we frequently consider. This force is responsible for keeping the body on the ground. Any item with mass, on the other hand, exerts a gravitational attraction on all other things with mass.
The gravitational force is called attractive because it constantly strives to bring masses together rather than pushing them apart. It is obvious that the gravitational force directly relates to the masses of the two interacting objects; larger, more massive objects will pull apart with a stronger gravitational force.
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Pls help need to get this done asap
Answer:
I would say B. would be the answer.
Explanation:
Sorry if I'm wrong
If the spaceship whips around the planet to the other side so that the angle is ϕ=30.9∘ and is moving at 178m/s, how far, in kilometers, from the planet is it?
Having said that,
Gravitational Constant: g=GMR2
G=6.621011Nm2kg2 R=Radius Earth's M stands for Earth's mass.
The spacecraft is currently far away. R′=2R
As a result, g will be as follows: g′=GMR′2 R′=2R g′=GM4R2 g′=g4 g′=9.84 g′=2.45ms2
At any point on its surface, a non-rotating perfect sphere with equal mass density or one whose density varies exclusively with distance from the centre (spherical symmetry) will produce a constant gravitational field. The Earth is an oblate spheroid because it rotates and is not spherically symmetric; rather, it is slightly flatter towards the poles and bulges at the Equator. As a result, the magnitude of gravity varies slightly throughout the surface.
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Classify each phase change based on whether it describes a transition between a gas and a liquid, a gas and a solid, or a liquid and a solid.
The classification of the phase changes include the following:
A gas and a liquid= Condensation and evaporation.
A gas and a solid= sublimation and deposition
A liquid and a solid= freezing.
What is phase change?Phase change is defined as the ability of matter to change from one form to another ( solid, liquid or gas) due to changes in its surrounding environment.
The classification of 0hase changes include the following:
Condensation : This is the change of gas to liquid.Evaporation: This is the change of liquid to gas.Sublimation: This is the change of solid to gas.Deposition: This is the change of gas to solid.Freezing: This is the change of liquid to solid.Therefore, in the classification of pase change of matter, A gas and a liquid= Condensation and evaporation, a gas and a solid= sublimation and deposition, a liquid and a solid= freezing.
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The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n = 2 as shown in the figure below. Consider the photon of longest wavelength corresponding to a transition shown in the figure. (a) Determine its energy. eV (b) Determine its wavelength. nm Consider the spectral line of shortest wavelength corresponding to a transition shown in the figure. (c) Find its photon energy. eV (d) Find its wavelength. nm (e) What is the shortest possible wavelength in the Balmer series? (Be sure to consider all values of n, not just those indicated by the arrows in the figure.) nm
Electronic transitions that end up in the state with quantum number n = 2 are what the Balmer series for the hydrogen atom refers to. The longest wavelength is 656.3x10-9 m, and the energy is 3.03X10^33J
Given quantum number (n) = 2
This will be transition 3-2 photon energy (E)= hc/λ since we must take into account the photon with the longest wavelength that completes the electron transition in the state with the quantum number n=2
photon energy (E)= hc/λ
(a) Then the energy (El) of longest wavelength= 6.63×10 −34 x 3x10^8/656.3x10-9
E = 3.03x10^33J = 1.89eV
(b) We know that 1/λl = R(1/n1^2 - 1/n2^2) where R = Rydberg constant
1/λl = 1.097×107m−1× (1/2^2 - 1/3^2)= 656.3x10-9m
(c) From given diagram we say thee shortest transition is from level 6 to level 2
n1 = 2 and n2 = 6
Its photon energy (Es) = 6.63×10 −34 x 3x10^8/411x10-9 = 3.023eV
(d) Wavelength of shortest transition series 1/λ = 1.097×107x(1/2^2 -1/6^2) = 411nm
(e)Shortest wavelength is emitted in Balmer series if the transition of electron takes place from n2=∞ to n1=2.
Shortest wavelength in Balmer series 1/λ = R(1/2^2 -1/∞)=364.6nm
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pitch depends on which of the following? number of hair cells stimulated amplitude of a sound wave number of sound waves that reach the ear in a given time strength of neural impulses traveling up the auditory nerve
Strength the neural impulses flowing up an auditory nerve in relationship to the amount of sound waves who reach my ear in a particular amount of time.
A sound wave is what?A blast wave seems to be the pattern of disruption brought on by the motion of energy moving through a medium as it spreads from the source of sound (such as air, water, and any other fluid or solid matter).
What causes sound waves to move?Sound is a type of energy produced by vibrations. These vibrations result in sound waves, which move through various media such as wood, sea, and the atmosphere. When an object is in motion, the particles of the medium also change position. This motion, which lasts on until particle runs out of power, is known as sound waves.
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An 18 v battery connected to a resistor produces a 5 mA( milliamp) current. What is the resistance? Show work
what is a mirror's radius of curvature if cars 17.0 m away appear 0.37 their normal size? follow the sign conventions.
Therefore, if cars 17.0 m away appear 0.37 their normal size, the mirror's radius of curvature is -6.29.
What is radius of curvature?In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. Its radius is the same as the radius of the circular path that, at that specific moment, most closely matches the curve. The diameter of the a circle that, individually and collectively, fits a normal section the best seems to be the radius of curvature of surfaces. The curvature's length and radius is denoted by R, and its derivative by K, where R=1/K.
The diameter of a hollow sphere in which the spherical mirror was housed determines its radius of curvature. The radius of curvature is the distance between the pole and center of a spherical mirror.
How do you use radius formula?Radius = Diameter/ 2 applies when the diameter is known. Radius = Circumference/2 can be calculated after the circumference is known. The radius is calculated using the formula Radius = ⎷(Area of the circle/π) when the area is known.
Briefing:For the mirror, we can solve two equations:
1/f=1/d_0 -1/d_i
M= -d_i/d_0
Index I stands for a picture, while index 0 stands for the object.
Magnification in this instance is 0.37:
0.37= -d_i/d_0
-0.37d0 = di d0 =17.0m
di= -0.37 × 17.0
di = 6.29m
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The water supply of a building is fed through a main pipe 6.00 cm in diameter. A 2.00−cm -diameter faucet tap, located 2.00 m above the main pipe, is observed to fill a 25.0−L container in 30.0 s . (a) What is the speed at which the water leaves the faucet? (b) What is the gauge pres- sure in the 6 -cm main pipe? (Assume the faucet is the only "leak" in the building.)
The pressure difference in the 6 cm supply line is 2.31 * 10⁴Pa, and the rate at which water exits the valve is 2.65 m/s.
What do distance and speed mean in physics?The ability of an object to move quickly or slowly is a very fundamental idea in motion. Distance is exactly proportional to velocity if time is constant, hence speed is merely distance divided by time. You will be asked to perform calculations for one of three supplied variables in incidents affecting speed, distance, and time.
Briefing:The primary pipe's R1 radius is 3.0 cm.
The faucet's radius is R2 = 1.0 cm.
The faucet's height is h = 2.0 cm.
(a) The flow rate
[tex]$$\mathrm{R}=\mathrm{Av}=\frac{25 \mathrm{~L}}{30}=0.833 \mathrm{~L} / \mathrm{s}=833 \mathrm{~cm}^3 / \mathrm{s}$$[/tex]
The area of faucet [tex]$\mathrm{A}_2=\pi r_2{ }^2$[/tex]
[tex]$$=\pi(1 \mathrm{~cm})^2=\pi \mathrm{cm}^2$$[/tex]
then the speed
[tex]$$\begin{aligned}\mathrm{v}=\frac{\mathrm{R}}{\mathrm{A}} & =\frac{833 \mathrm{~cm}^2 / \mathrm{s}}{\pi \mathrm{cm}^2}=265 \mathrm{~cm} / \mathrm{s} \\& =2.65 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]
b) from continuity equation
[tex]$$\begin{aligned}A_1 v_1 & =A_2 v_2 \\\text { then } \mathrm{v}_1=\frac{A_2 v_2}{A_1} & =\frac{(\pi)}{\pi(3 \mathrm{~cm})^2}(265) \\& =0.295 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]
From Bernoulli's theorem
[tex]$$\begin{aligned}\mathrm{P}_1 & +\frac{1}{2} \rho v_1^2+\rho g y_1=\mathrm{P}_2+\frac{1}{2} \rho v_2^2+\rho g y_2 \\P_1-P_2 & =\frac{1}{2} \rho\left(v_2^2-v_1^2\right)+\rho g\left(y_2-y_1\right) \\& =\frac{1}{2}\left(10^3\right)\left[(2.65)^2-(0.295)^2\right]+\left(10^3\right)(9.8)(2) \\& =2.31 \times 10^4 \mathrm{~Pa}\end{aligned}$$[/tex]
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A mass m at the end of a spring oscillates with a frequency of 0.71 Hz . When an additional 780 g mass is added to m, the frequency is 0.64 Hz .
a)What is the value of m ?
A mass m at the end of a spring oscillates with a frequency of 0.71 Hz . When an additional 780 g mass is added to m, the frequency is 0.64 Hz, thus the value of mass is 3.376 kg
What is frequency?In terms of physics, frequency refers to the quantity of waves that pass through a given point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences over the course of a single unit of time.
Given that,
Frequency = 0.71 Hz
Mass = 780 g
After added to m, frequency becomes = 0.64 Hz.
Let the spring constant is k
k=m × w²
from the given info.
m × (0.71)² = (m+0.78) × (0.64)²
m ×[(0.71)²- (0.64)²] = 0.78 × (0.64)²
m = 0.78 × (0.64)² /[(0.71)²- (0.64)²]
m = 0.319 / 0.0945
m = 3.376 kg
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