when the temperature is kept constant, to increase the volume of the gas, you will decrease the pressure (Option D)
How do I increase the volume at constant temperature?The volume of a gas at constant temperature is explained by the Boyle's law equation which is states as follow:
The volume of a fixed mass of gas is inversely proportional to the pressure at conctant temperature. Mathematically, it is expressed as follow:
P ∝ = 1/V
P = K / V
P₁V₁ = P₂V₂
Where
P₁ and P₂ are initial and new pressure V₁ and V₂ are initial and new volume
From the above formula, we can see that volume and pressure exist in inverse proportionality. This means that when the volume increases, the pressure will decrease and also, when the volume decreases, the presure will increase.
With the above information, we can conclude that the correct answer to the question is: You would decrease the pressure (Option D)
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What is pasteurization?
A. A method of creating vaccine invented by Pasteur
B. The use of heat to kill any microorganisms living in a substance
C. The use of radiation to sterilize substances
D. A method of speeding up fermentation
Which of the following is a cause of climate change?
A. A decrease in greenhouse gases in the atmosphere
B. Burning coal to produce electricity
C. Rising sea levels
D. All of the above
After writing Wonderful Life, Stephen Jay Gould was criticized by his follow scientists
A. Because he misinterpreted the Burgess Shale fossil data
B. Because his hypothesis was incorrect.
C. Because they thought he was arguing against natural selection.
D. Because he claimed the Burgess Shale fossils weren't real.
Answer:
1) B. The use of heat to kill any microorganisms living in a substance
2) B. Burning coal to produce electricity
3) A. Because he misinterpreted the Burgess Shale fossil data
During take-off a 6kg model rocket is burning fuel causing its speed to increase at a
rate of 7m/s² despite experiencing a 100N drag. What is the magnitude of the net force on the rocket
The magnitude of the net force on the rocket was found to be 42N
Define magnitude ?
What is magnitude in Physics, is surely an issue of tremendous relevance in science. Magnitude often relates to the quantity or distance. In regard to the movement, we may associate magnitude with the size and speed of the item while moving.
The magnitude of a thing or a quantity is its size. Like in terms of speed, a car is driving quicker than a motorbike. In this situation, the car's speed is greater than the motorbike's. Let's now discuss what magnitude in physics means.
the magnitude of the net force was determined by the equation.
∑F= ma
=6(7m/s²)
=42 N
the force was exerted upwards.
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A 1.55-m-tall fisherman stands at the edge of a lake, being watched by a suspicious trout who is 3.50 m from the fisherman in the horizontal direction and 45.0 cm below the surface of the water.
A. At what angle from the vertical does the fish see the top of the fisherman�s head?
The angle from the vertical does the fish see the top of the fishermans head is 42.24 degrees and can be finded out by snells law.
According to Snell’s Law when light is incident on an interface separating two media, the angles of incidence and refraction, θ1 and θ2, are related,
n1 sin(θ1) = n2 sin(θ2)
where θ1 or θ2 is the angle between the normal to the interface and the direction in which incident or refracted wave is propagating. The quantities n1 and n2 are the indices of refraction of the two media.
While the speed of light is constant in a vacuum, the speed of light in air and in transparent solids is somewhat less. The ratio of the speed of light in a vacuum (c) to the speed of light in a solid (v) is called the index of refraction (n) of the solid.
Applying snells law,
nwater *sinα = nair *sinβ
nwater *sinα = sinβ
sinα = sinβ/nwater
sinβ = 1.33 sinα
AB = 3.5m-BC
AB = 3.5m-CDtanβ
AB = 3.5m-1.55*tanβ
Also, AB = 4.5m*tandα
4.5m*tandα = 3.5m-1.55*tanβ
4.5m*tandα = 3.5m-1.55*(sinβ/cosβ)
4.5m*tandα = 3.5m-1.55*1.33sinα/[tex]\sqrt{1-(1.33)^2*(sin\alpha )^2}[/tex]
α=42.24 degrees.
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2KI → 2
+
2
Which chemical symbols will complete the equation for this decomposition reaction?
The chemical symbol used is 2K + 2I to complete the equation for the decomposition reaction.
What is decomposition reaction?Decomposition reaction is defined as a chemical reaction when the reactant or molecule breaks down into less complex compounds Consequently, when a single reactant splits into two or more products. Because two or more reactants are combined to create a single product in a combination reaction, they are known as the opposite of a combination reaction.
One reactant produces two or more products during a decomposition process. Iodine and potassium will be produced as potassium iodide breaks down. With two K and two I on each side, this equation is balanced. It can be described using the all-inclusive formula: AB --> A + B.
Thus, the chemical symbol used is 2K + 2I to complete the equation for the decomposition reaction.
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I want to know anwser
The wave speed of a wave is equal to its frequency multiplied by its wavelength.
What is wavelength?Wavelength is a measure of the distance between two successive peaks of a wave. It is most commonly associated with light, sound, and other forms of electromagnetic radiation. It is the distance from one peak of the wave to the next, measured in meters. Wavelength is an important factor in determining the properties of a wave, such as its frequency, amplitude, and speed. It is also used to measure the wavelength of sound, radio waves, and other forms of electromagnetic radiation.
Therefore, the wave speed of a 44 Hz wave with a wavelength of 1 m is 44 m/s. This is because frequency is the number of waves passing a certain point in a certain amount of time (measured in hertz or Hz), while wavelength is the distance between two successive wave crests (measured in meters). Thus, when multiplied, these two values give us the wave speed, which is measured in meters per second (m/s).
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What initiative regarding Native Americans did the government begin in 1954, but stop by 1962?
A. Expanding the role of the federal government in daily governance of reservations
B. Providing additional federal funds for Native American education
C. Allowing Native American reservations to use federal funds as they found fit
D. Abolishing reservations and relocating Native Americans
The government started allowing reservations for Native Americans to use federal monies in 1954, but stopped by 1962.
What makes them reservations, exactly?The earliest phase of Indian encounters with Europeans is when the word "exclusive" originally appeared. A sizable portion of the Indians' country was "reserved" for their exclusive use through treaties. Indians were intended to live on reserves, which are frequently sparsely populated areas of land.
What use did reservations serve?Displacement to reservations had two purposes for the United States. Native Americans were originally removed from the area to create room for westward territories. Second, it made it possible for the US to carry out a strategy to transform tribal villages into modest farming settlements.
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a_____ force can cause a greater change in velocity.
Answer:
A stronger force can cause a greater change in velocity.
Explanation:
Forces affect how objects move. They may cause motion; they may also slow, stop, or change the direction of motion of an object that is already moving. Since force cause changes in the speed or direction of an object, we can say that forces cause changes in velocity. Remember that acceleration is a change in velocity.
Three boxes are pulled to the left by strings with negligible mass on a horizontal surface, as shown above. The masses of the boxes are m1, m2, and m3, where m3>m2>m1. Friction between the boxes and the surface is negligible. The figure below shows force diagrams for each box. A student is trying to determine the tensions in the strings connecting the boxes. If the acceleration of the system and the pulling force F are known, which of the following pairs of equations could be used to find the tensions?
m3a3=TB and m2a2=TA−TB
The two quantities agree within experimental uncertainty but not agree numerically.
There is no frictional force exerted on the puck, and the gravitational force and normal force are exerted on the puck and are equal in magnitude.
The mean value of F is: 10.52 N
The mean value of TA is: 10.6 N
So, the two quantities agree within experimental uncertainty but not agree numerically.
The puck on the table relates to a planet orbiting the sun because the force of tension is acted on the puck with its connection to the table using the string. Similarly, a planet has the force of gravity acting upon it is allowing it to orbit in its path.
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72pts
What is the mechanical advantage of the wheel and axle shown below?
0.8 cm 26 cm
Answer:
Explanation:
The correct answer is A. 32.5
Mechanical advantage is the ratio of force that is input into a machine to the force output.
Mechanical advantage of a wheel and axle is calculated by dividing the radius of the wheel by that of the axle.
MA=R/r where R is the radius of the wheel and r is the radius of the axle.
Substituting for the values in the question gives:
MA=26cm/0.8cm
=32.5
A 70 kg mountain climber dangling in a crevasse stretches a 50-m-long, 1.0-cm-diameter rope by 8.0 cm. Part A What is Young's modulus for the rope? Express your answer with the appropriate units. HAO ? Value Units
Young's modulus for the rope 5.462 × [tex]10^{9}[/tex]N/m²
Mass is 70 kg
F = mg = 70 × 9.8N
F = 686N
ΔL = 8cm
A = πr² = 0.785 ×[tex]10^{-4}[/tex]
Y = F/A l/Δl = 686 × 50 / 0.785 ×[tex]10^{-4}[/tex] × 8 × [tex]10^{-2}[/tex]
Y = 5.462 × [tex]10^{9}[/tex]N/m²
Young's modulus (displaystyle E), also known as the Young modulus or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical characteristic that gauges the stiffness of a solid material under tensile or compressive tension when a force is applied longitudinally. Using the formula, it quantifies the relationship between axial strain and tensile/compressive stress in the linear elastic zone of a material. Axial strain is measured as the proportionate deformation of the relationship between axial strain and tensile/compressive stress. Young's modulus was first introduced by Leonhard Euler in 1727, while being named after the 19th-century British scientist Thomas Young. Giordano Riccati, an Italian physicist, conducted the first experiments in 1782 that utilized the idea of Young's modulus in its current form, 25 years before Young's work.
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A model rocket is launched with an initial upward velocity of 125 ft/s. The rocket's height h (in feet) after t seconds is given by the following.
h=125t-16
Find all values of t for which the rocket's height is 71 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
The values of time (t) = 7.20, 0.62, and the model rocket is launched with an initial upward velocity of 125 ft/s and height of h.
What is Velocity?The directional speed of an object in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
What is the calculation?height of the rocket is given as,
h = 125t - 16t²
now, when h = 71 then,
71 = 125 t - 16 t²
16 t² - 125t + 71 = 0
Using the quadratic formula, we have:
- (-125) + √ (-125)² - 4 × 16 × 71
t = ____________________
2 × 16
125 + √11081 125 - √11081
t = _________ t = _________
32 32
t = 7.20, t = 0.62
Hence, the values of time (t) = 7.20, 0.62.
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Raise your hand and hold it flat. Think of the space between your index finger and your middle finger as one slit, and think of the space between middle finger and ring finger as a second slit.(a) Consider the interference resulting from sending coherent visible light perpendicularly through this pair of openings. Calculate the angle between adjacent zones of constructive interference, assuming the width of your middle finger to be 2.7 cm and the wavelength of the light to be 700 nm.(b) To make the angles in the interference pattern easy to measure with a plastic protractor (e.g., for which the angle between the central maximum and the adjacent ones is 15�), you should use an electromagnetic wave with what frequency?HzHow is this wave classified on the electromagnetic spectrum?
Angle and frequency between neighboring zones for constructive interference are both 1.846 * 103⁻³ degrees and 6.44 * 10¹⁰ Hz, respectively.
What exactly is regularity and why is it significant?The quantity of oscillations that pass a given point in one unit of time, as well as the number of passes or oscillations that an object in periodic motion experiences in one unit of time Multiple electrical frequencies cannot coexist without causing device damage, hence keeping a constant electrical rate is crucial. When it comes to supplying power on a national basis, this has important ramifications.
Briefing:a). For Constructive interference;
[tex]$$\begin{aligned}& d \sin \theta=m \lambda \\& \theta=\sin ^{-1}\left(\frac{m \lambda}{d}\right)=\sin ^{-1}\left(\frac{1 \times 580 \times 10^{-9}}{0.018}\right) \\& \theta=1.846 \times 10^{-3} \text { degreees }\end{aligned}$$[/tex]
Angle between nearby constructive interference zones;
[tex]$$\Delta \theta=1.846 \times 10^{-3}-0=1.846 \times 10^{-3} \text { degrees }$$[/tex]
b). [tex]$0.018 \sin 15=1 \times \lambda$[/tex]
[tex]$\lambda=4.66 \mathrm{~mm}$[/tex]
Frequency;
[tex]$$\begin{aligned}& \mathrm{f}=\mathrm{c} / \mathrm{lambda}=\left(3^* 10^8\right) /\left(4.66^* 10^{-3}\right) \\& \mathrm{f}=6.44^* 10^{10} \mathrm{~Hz}\end{aligned}$$[/tex]
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The complete question is-
Raise your hand and hold it flat. Think of the space between your index finger and your middle finger as one slit, and think of the space between middle finger and ring finger as a second slit.
(a) Consider the interference resulting from sending coherent visible light perpendicularly through this pair of openings. Calculate the angle between adjacent zones of constructive interference, assuming the width of your middle finger to be 2.7 cm and the wavelength of the light to be 700 nm.
(b) To make the angles in the interference pattern easy to measure with a plastic protractor (e.g., for which the angle between the central maximum and the adjacent ones is 15), you should use an electromagnetic wave with what frequency?
Hz
How is this wave classified on the electromagnetic spectrum?
"n 25 kg object is moving at a velocity or 10 ml. the obec has energy. Calculate it.
The energy of 25 kg object is moving at a velocity or 10 ml is 1250J.
What does a 25 kilogram object travelling at 10 m/s kinetic energy look like?KE = 1/2mv²
The mass is m = 25kg
The velocity is v = 10ms⁻¹
KE = 1/2 × 25 × 10²
⇒ KE = 1250J
Hence, Kinetic energy is 1250J
What is Kinetic energy?The energy an object has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.
What is velocity?The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
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I attached these picture
A bowling ball rolls 32 meters in 0.8 seconds. Find the average speed (in m/s) of the bowling ball in m/s
The average speed of the bowling ball 40 meter/second..
What is speed?
The pace at which an object's position changes in any direction is referred to as speed.
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. Si unit of speed be meter/second.
Given parameters:
Distance travelled by the ball: s = 32 meter.
Time taken by the ball: t = 0.8 second.
So, average speed of the ball = distance travelled/ time taken
= 32 meter/ 0.8 second
= 40 meter/second.
Hence, the average speed of the bowling ball 40 meter/second.
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The total volume occupied by two internal cable clamps, six 12AWG conductors, and single pole switch is
The total volume occupied by two internal clamps, six 12 AWG conductors and one grounding conductor, and a single-pole switch is 20.25 cu in.
When counting the number of conductors in a box a conductor running through the box is counted as conductor S?
An unbroken conductor, passing through the box without splice or termination, can be counted as one conductor if it is less than two times the minimum length required for the free conductor in 300.14. For example, two conduits are entering opposite sides of a four-inch square metal box that has a depth of 1 1/2 inches.
How many amps can 12 AWG handle?
The twelve-gauge wire is good for 20 amps, 10-gauge wire is good for 30 amps, 8-gauge is good for 40 amps, and 6-gauge is good for 55 amps, and The circuit breaker or fuse is always sized to protect the conductor [wire].
12 AWG =2.25 cu. in. ( 6 x 2.25 = 13.5)
Device( 2 x 12 AWG cu. in.)= ( 2 x 2.25 = 4.5)
Clamp ( 1 x 12 AWG cu. in.)= ( 1 x 2.25 = 2.25)
13.5 + 4.5 + 2.25 = 20.25 cu. in.
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A student makes a sound by blowing into the mouth of an empty soda bottle. How could the student make the sound louder?
A. Increase the frequency by adding water to the bottle.
B. Decrease the frequency by blowing into a different bottle.
C. Decrease the amplitude by blowing with less force.
D. Increase the amplitude by blowing with more force.
D. is correct.
Answer:
I think D is the answer to the question
6) Your classmate doesn't want to leave
physics class. You apply a force to drag
him to lunch to the right.
Answer:
Answer: I would apply a force to the right in order to push him in the direction of lunch.
Explanation:
A) How high (in m) a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 74.0 km/h? (Enter a number.)
B) If, in actuality, a 750 kg car with an initial speed of 74.0 km/h is observed to coast up a hill to a height 10.0 m above its starting point, how much thermal energy (in J) was generated by friction? (Enter a number.)
C) What is the average force of friction (down the slope) if the hill has a slope 2.5° above the horizontal? (Enter your answer in N. Enter a number.)
(a) The maximum height attained by the car is 21.57 m.
(b) The thermal energy generated by friction is 85,017.6 J.
(c) The average force of friction of the hill is 370.8 N.
What is the maximum height reached by the car?
The maximum height attained by the car is calculated by applying the principle of conservation of energy as follows;
P.E = K.E
mgh = ¹/₂mv²
h = (v²) / (2g)
where;
v is the initial speed of the car = 74 km/h = 20.56 m/sg is acceleration due to gravityh = (20.56²) / (2 x 9.8)
h = 21.57 m
The thermal energy generated by friction is determined from the change in the mechanical energy of the car.
ΔE = K.E - P.E
ΔE = ¹/₂mv² - mgh
where;
m is mass of the carh is the height attainedv is the initial velocityΔE = ¹/₂(750)(20.56)² - (750)(9.8)(10)
ΔE = 85,017.6 J
The average force of friction of the hill is calculated as follows;
Fd = ΔE
where;
d is the horizontal distance travelled by the car along the hilld = h/sin(2.5) = 10 m / sin(2.5) = 229.26 m
F(229.26) = 85,017.6
F = (85,017.6) / (229.26)
F = 370.8 N
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billiard ball is rolled off of a table onto the floor below in projectile motion. If the speed at which the bowling ball left the table was 12m/s, then what is the x-component of the velocity of the bowling ball at the instant before it strikes the
ground?
The components of velocity v have magnitudes of v x = v cos and v y = v sin, where v seems to be the magnitude of something like the speed and is its direction with respect to the horizontal.
What does velocity vs. speed mean?Velocity, as opposed to speed, refers to the pace and direction of the an object's movement as it moves down a path. In other words, whereas velocity is a vector, speed is a scalar quantity.
How do velocity and acceleration differ?Velocity is the rate at which displacement changes Since it consists both of magnitude and direction, velocity is a vector quantity. Since acceleration is merely the rate at which velocity changes, it too is a vector quantity.
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A rock appears to lie 17 cm below the surface of a smooth stream when viewed from above the surface of the stream at an angle. If the index of refraction of water is assumed to be 1.33 and that of air is approximately 1, what is the actual distance of the rock below the surface?
The actual distance of the rock below the surface is ____cm.
The rock is actually 22.61 cm beneath the surface. For When viewed from above the surface of the stream at an angle with force, a boulder appears to be 17 cm below the surface of a smooth stream.
The length of a straight line, which is the shortest route between any two points in space, is the distance between them. In classical physics, particularly Newtonian mechanics, this is how distance is typically understood. In two- and three-dimensional space, the straight-line distance is mathematically codified as the Euclidean distance. A force in physics is an effect that has the power to alter an object's motion.
I = O na/nw
17 = O * 1/1.33
O = 17 * 1.33 = 22.61 cm
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5. Which of the following correctly describes the above situation?
6. The final velocity of the two cars after they hit and stick together is:
In this case, the magnitude of the momentum of vehicle 2 is greater than the vehicle 1.
What is momentum?
In Newtonian mechanics, an object's mass and velocity are combined to form momentum, more precisely linear momentum or translational momentum. It has both a magnitude and a direction, making it a vector quantity.
The kilogramme metre per second (kg m/s), or newton-second in the International System of Units (SI), is the unit used to measure momentum.
The rate of change of a body's momentum is equal to the net force exerted on it, according to Newton's second law of motion. Although momentum varies depending on the frame of reference, it is a conserved quantity in any inertial frame, which means that if a closed system is not impacted by outside forces.
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What was the speed of a space shuttle that orbited Earth at an altitude of 882 km?
Answer:
Explanation:
Given:
h = 882 km
R = 6371 km
___________
V - ?
Since the height of the orbit is much less than the radius of the Earth, then the acceleration of free fall g = 9.81 m/s²
Speed:
V = √ (g·(R+h)) = √ ( 9.81·(6371+882)·10³ ) ≈ 8 440 m/s or
V = 8.44 km/s
A spring scale that reads in grams uses a 10.0-cm-long spring. Hanging a water bottle from the scale stretches the spring to 11.5 cm and causes the scale to read 350 g.
To determine the spring constant of the scale, you can use the formula:
k = (F / x)
where k is the spring constant, F is the force acting on the spring, and x is the displacement of the spring.
In this case, the force acting on the spring is the weight of the water bottle, which can be calculated using the weight = mass * gravitational acceleration formula:
F = m * g
where m is the mass of the water bottle in kilograms and g is the gravitational acceleration of 9.8 m/s^2.
Plugging in the values given, we get:
k = (F / x) = (m * g / x)
= (350 g / (11.5 cm - 10.0 cm))
= 307.8 g/cm
This is the spring constant of the scale. It represents the force required to stretch the spring by 1 centimeter.
In this circuit, the following values apply:
What is the voltage drop across resistor R 2 in volts
Answer: [tex]8.93 V[/tex]
Explanation: By applying ohm's law, V=IR
for R2 resistance , current flowing through it is [tex]1.9[/tex] ampere,and it's value is [tex]4.7 \ohm[/tex] ohmV=1.9*4.7
=8.93 V
In an orthogonal cutting operation, the rake angle = -5°, chip thickness before the cut = 0.2 mm and width of cut = 4.0 mm. The chip ratio 3 = 0.4. Determine (a) the chip thickness after the cut, (b) shear angle, (c) shear strain.
a. The chip thickness after the cut is 0.5 mm
b. The shear angle is 21.05
c. The shear strain is 3.086
a. the chip thickness after the cutThe formula is
r = t / tc
where we have r = 0.4
t = 0.2
0.4 = 0.2 / tc
cross multiply
tc = 0.5 mm
b. The shear angle is the angle at which a chip will detach from the work piece when cutting metal.
tan ∅ = r cos α / 1 - r sin α
= 0.4 cos (-0.5) / 1 - 0.4 sin(-5)
= 0.385
∅ = tan ⁻¹0.385
∅ = 21.05
c. When a medium is subjected to a lateral force, shear strain results. It is possible to produce a shear force wave that moves perpendicular to the direction of the applied force.
r = cot ∅ + tan(∅ - α)
r = cot (21.05)+ tan(22.05 -(-5)
r = 2.598 + 0.488
= 3.086
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the maximum allowed coefficient of performance for a heat pump operating between temperatures of 2 oc and 15 o c is:
A heat pump's operating overall efficiency is just 15.88, claims the inquiry.
What is heat in reality? What is the name of heat energy?Heat energy is created by the movement of tiny atoms, ions, or atoms in solid, liquids, and gases. Overheating can be transferred of one thing to another. When two items are already at varying temperatures from one another, a movement or exchange called heat occurs. Atoms and molecules move more quickly and clash when the temperature rises, producing heat generated (also known as heat energy). The power that comes from the heated object's temperature is referred to as thermal energy.
Briefing:Maximum COP of heat pump:
COP = [tex]T_{H} /T_{H} - T_{C}[/tex]
Here, [tex]T_{H}[/tex] = 271 K and [tex]T_{C}[/tex] = 288 K
Hence, COP = 271/288-271
COP = 15.88
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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:
I think the answer is 54 cm
the four particles in figure are connected by rigid rod of negligible mass the origin is at the center if the rectangle the system rotates in the xy plane about the z axis with an angular speed of 6 rad/s calculate the moment of the inertia of the system about the z axis and the rotational kinetic energy of the system
The moment of the inertia of the system about the z axis and the rotational kinetic energy of the system is 143 Kg/m².
What is moment of inertia?A body's resistance to having the speed of its rotation along an axis changed by the application of a torque is quantified by the term "moment of inertia" in physics (turning force). The axis might be internal or exterior, and it can be fixed or not.
Let, the distance of mass 2 kg from O to r₁
Therefore, r₁ = [tex]\sqrt{2^2 +3^2}[/tex]
r₁ = [tex]\sqrt{13}[/tex] m
the distance of masses to the rotational axis are same.
So, r₁ = r₂ = r₃ = r₄ = r = [tex]\sqrt{13}[/tex]
Hence, I = ∑ [tex]m_i r^2[/tex]
I = r² (m₁ + m₂ + m₃+ m₄)
I = 13 × (11)
I = 143 Kg/m²
So, the moment of the inertia of the system about the z axis and the rotational kinetic energy of the system is 143 Kg/m².
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A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.3 meters, and a mass M = 231 kg. A small boy of mass m = 48 kg runs tangentially to the merry-go-round at a speed of v = 2.5 m/s, and jumps on.
Required the moment of inertia of the merry go round.
a. I = 12 MR2 is the formula for the merry-go-moment round's of inertia.
I = ½ * 231 * (1.3 * 1.3)
I = 195.195 kgm2
b. The boy's angular speed is specified as = v/R = 2.5/1.3 = 1.92 rad/s.
c. I' = I + mR2 is the formula for the merry-go-moment round's of inertia following the boy's jump on it.
I’ = 195.195 + 48 * (1.3 * 1.3)
I’ = 276.315 kg/m2
The conservation of angular momentum principle determines the merry-go-angular round's speed. As a result, I (0) + m R = 'I' and = (48 * 1.92* 1.3) / 276.315 = 0.433 rad/s
To learn more about conservation of angular momentum.
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