To calculate the total energy stored in a 12.0-V battery rated at 55.0 A-h, follow these steps:
1. Convert ampere-hours (A-h) to coulombs (C): Multiply the battery's A-h rating by the number of seconds in an hour.
55.0 A-h * 3600 seconds/hour = 198000 C
2. Calculate the total energy in the battery in joules (J): Multiply the battery's voltage (V) by the charge in coulombs (C).
12.0 V * 198000 C = 2376000 J
3. Convert joules (J) to kilowatt-hours (kWh): Divide the energy in joules by 3,600,000 (3.6 million) to get kWh.
2376000 J / 3600000 = 0.66 kWh
The total energy stored in the 12.0-V battery rated at 55.0 A-h is 0.66 kWh.
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5. Which of the following best supports a scientific
explanation?
A. personal bias and the opinion of the scientist
B. hypothesis formed after initial observations
C. imagination and originality of the hypothesis
D. experimental data obtained by using
technology to get objective measurements
Answer:
experimental data obtained by using technology to get objective measuremennts
Explain What is economics?
4.3 Assume the voltage v. in the circuit in Fig. P4.3 is known. The resistors R R7 are also known. a) How many unknown currents are there? b) How many independent equations ten using Kirchhoff's current law (KCL)? can be writ- c) Write an independent set of KCL equations. d) How many independent equations derived from Kirchhoff's voltage law (KVL)? e) Write a set of independent KVL equations.
Kirchhoff's current law (KCL) states that the total current entering a junction or node in an electrical circuit must be equal to the total current leaving that junction or node. In other words, the algebraic sum of currents at any junction in a circuit must be zero. Kirchhoff's voltage law (KVL) states that the total sum of the electromotive forces (emf) and the product of currents and resistances in any closed loop of an electrical circuit must be equal to zero. In other words, the total sum of voltages around any closed loop in a circuit must be zero. This law is based on the principle of conservation of energy and is used to analyze circuits with loops or closed paths.
a) To determine the number of unknown currents in the circuit, you need to identify the number of branches or loops in the circuit. Each branch/loop represents one unknown current.
b) To find the number of independent KCL equations, identify the number of nodes in the circuit. Each node (except for the reference node) will give you one independent KCL equation.
c) To write an independent set of KCL equations, follow these steps:
1. Select a node (excluding the reference node).
2. Write the sum of currents entering the node equal to the sum of currents leaving the node.
3. Repeat for all nodes except the reference node.
d) To determine the number of independent KVL equations, use the formula B - N + 1, where B is the number of branches and N is the number of nodes.
e) To write a set of independent KVL equations, follow these steps:
1. Choose a closed loop in the circuit.
2. Write an equation that represents the sum of the voltage drops in the loop, which should be equal to the sum of the voltage sources.
3. Repeat for all independent closed loops.
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if you could see stars during the day, the drawing above shows what the sky would look like at noon on a given day. the sun is at the highest point that it will reach on this day and is near the stars of the constellation gemini. what is the name of the constellation that will be closest to the sun at sunset on this day?
The constellation that will be closest to the sun at sunset on this day is called Taurus.
Is there a constellation of the Sun?But have you ever questioned whether the Sun is a part of any of these constellations. The short answer is that the Sun officially has no constellation, according to both contemporary astronomy and old astrological tradition.
What constellations does the Sun travel through?After passing through each sign in turn—Scorpius the Scorpion, Ophiuchus the Serpent Charmer, Sagittarius the Archer, Capricornus the Seagoat, Aquarius the Water Bearer, Pisces the Fish, Aries the Ram, Taurus the Bull, Gemini the Twins, Leo the Lion—the Sun returns to Virgo the Maiden, where the cycle starts over again.
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a bud travels 20 km in 30 minutes what is the average speed of the bus
Calculate the power required to move a 2,000-kilogram automobile to the top of a 100-meter hill in 15. 0 seconds. Express the power both in
units of watts and horsepower.
The power required to move the automobile to the top of the hill is 130,666.67 watts or 175.41 horsepower.
The power required to move an object can be calculated using the formula: power = work / time.
First, let's calculate the work done in lifting the automobile to the top of the hill. The work done against gravity is given by the formula: work = force × distance.
The force required to lift the automobile is equal to its weight. The weight of an object is given by the formula: weight = mass × acceleration due to gravity.
Substituting the given values, we have: weight = 2,000 kg × 9.8 m/s^2 (acceleration due to gravity) = 19,600 N.
The distance the automobile is lifted is 100 meters.
Therefore, the work done against gravity is: work = 19,600 N × 100 m = 1,960,000 J (joules).
The time taken to reach the top of the hill is given as 15.0 seconds.
Now, we can calculate the power using the formula: power = work / time.
power = 1,960,000 J / 15.0 s = 130,666.67 W (watts).
To convert watts to horsepower, divide the power in watts by 746 (1 horsepower = 746 watts).
power in horsepower = 130,666.67 W / 746 = 175.41 hp (horsepower).
Rounding to two decimal places, the power required to move the automobile to the top of the hill is approximately 130,666.67 watts or 175.41 horsepower.
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The to problem of calculating the power required to move a 2,000-kilogram automobile to the top of a 100-meter hill in 15.0 seconds is given
Given, Mass of the automobile, m = 2000 knight of the hill, h = 100 time, t = 15.0 the gravitational potential energy of the automobile when at the bottom of the hill is equal to the work done in lifting it up the hill
.W = mgh= (2000 kg) (9.81 m/s²)
(100 m)= 1,962,000 J
Power is defined as the rate at which work is done, or the work per unit time. Therefore,
Power = Work / Time= 1,962,000 J / 15.0 s
= 130,800 WIn horsepower, Power = (130,800 W) / (746 W/hp)
= 175.3 hp
Therefore, the required power to move a 2,000-kilogram automobile to the top of a 100-meter hill in 15.0 seconds is 130,800 W or 175.3 hp.
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A car is traveling with a velocity of 40. 0 m/s and has a mass of 1120 kg. How much kinetic energy does the car have?
Answer:
896 kj
Explanation:
KE= 1/2 mv^2 = 1/2 1120 40^2 =
A rotor in a blender is rotating at 55.0 rad/s. The chef hits the Low Speed button, causing the rotor to decelerate at -40.7 rad s^2. What is its angular velocity after turning 28.8 rad? (Unit = rad/s) Remember: CCW is +, CW is-. 1 rev = 2 pl rad
26.0898 rad/s is the angular velocity of a rotor in a blender.
Given
Initial velocity (ω₁) = 55.0 rad/s
Deceleration (α) = -40.7 rad/s²
Angle (θ) = 28.8 rad
Final angular velocity (ω₂) =?
According to the angular kinematic equation
ω₂² = ω₁² + 2αθ
Put the values of ω₁, α, and θ in the equation
We get,
ω₂² = (55)² + 2(₋40.7)(28.8)
ω₂² = √680.68
ω₂ = 26.0898 rad/s
Hence, 26.0898 rad/s is the angular velocity of a rotor in a blender after turning 28.8 rad.
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Which state of matter has molecules that barely move at all?
liquid
gas
solid
They are all the same.
Answer:
the answer is solid.
Explanation:
solid particles have a definite volume and shape therefore they cannot move are they are whole. the particles of solid are closely packed together, barely move, and barely vibrate.
Which of the following is a compound?
A. Na+
B. NaCl
C. Na
D. NaCl + Ag2O → AgCl + Na2O
A. Na+ : cation
B. NaCl : compound
C. Na : element
D. NaCl + Ag2O → AgCl + Na2O : chemical reaction
Rank the four fundamental forces from strongest to weakest
Answer:gravitational, weak nuclear, electromagnetic, strong
Explanation:
Consider the following force:
Darnel is pushing on his friend's wheelchair.
According to Newton's third law, what other force must be happening?
The wheelchair is pushing on Darnel.
The wheelchair is pulling on Darnel.
Submit
The other force that must be happening in accordance with Newton's third law is that the wheelchair is pushing on Darnel (option A).
What is Newton's third law?Force is a push or a pull that acts upon an object as a results of its interaction with another object.
Newton's third law states that for every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects.
Whenever objects A and B interact with each other, they exert forces upon each other. For example, Darnel is pushing on his friend's wheelchair, the wheelchair exerts an upward force on Darnel.
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a flat, square coil of 16 turns that has sides of length 14.0 cm is rotating in a magnetic field of strength 0.040 t. if the maximum emf produced in the coil is 34.0 mv, what is the angular velocity of the coil (in rad/s)? (enter the magnitude.) rad/s
The angular velocity of the coil is ω = 2.55\(rads^{-1}\).
Angular velocity is the rate at which an object rotates or rotates about an axis or the rate at which the angular displacement between two bodies changes. In the figure, this shift is represented by the angle θ between the line of one body and the line of the other body. The face area is calculated by multiplying the rib height by the fin length.
calculation:-
number of turns = 16
side length = 14 cm = 0.14 m
Magnetic field strength B = 0.040T
Emf produced = 34mV = 0.034 V
angular velocity = w×16× 0.14 ×0.034/0.040
= 2.55 m/ rad.
Face Velocity is the air velocity over the face of the coil. This angular rate describes how fast AC waveform cycles, and you should understand that a full cycle is equal to 2π radians. This does not necessarily represent the actual shaft speed of the alternator that produces AC power. There is an important relationship between angular velocity and frequency, given by the equation: Angular velocity is equal to frequency multiplied by the constant 2pi.
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A 0.07 kg tennis ball, initially at rest, leaves a racket with a speed of 56 m/s. If the ball is in contact with
the racket for 0.04 s, what is the average force on the ball by the racket?
A 0.07 kg tennis ball, initially at rest, leaves a racket with a speed of 56 m/s. If the ball is in contact with
the racket for 0.04 s, what is the average force on the ball by the racket?
0.57 N
32 N
98 N
0.00005 N
From Newton's second law of motion, the average force on the ball by the racket is 98 Newtons. The correct answer is option C
Given that a 0.07 kg tennis ball, initially at rest, leaves a racket with a speed of 56 m/s. And the time for contact with the racket is 0.04 s, that is,
mass m = 0.07 kg
velocity v = 56 m/s
time t = 0.04 s
force f = ?
To calculate the average force on the ball by the racket, let us apply Newton's second law of motion.
Impulse = change in momentum
ft = mv
Substitute all the parameters into the equation above
0.04f = 0.07 x 56
make f the subject of the formula
f = 3.92 / 0.04
f = 98 N
Therefore, the average force on the ball by the racket is 98 Newtons. The correct answer is option C
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The average force on the ball by the racket is 98 N. The correct option is the third option - 98 N
From the question, we are to determine the average force on the ball by the racket.
From the formula,
\(F = \frac{mv}{t}\)
Where F is the force
m is the mass
v is the velocity
and t is the time
From the given information
m = 0.07 kg
v = 56 m/s
t = 0.04 s
Putting the parameters into the formula,
we get
\(F = \frac{0.07 \times 56}{0.04}\)
\(F = \frac{3.92}{0.04}\)
F = 98 N
Hence, the average force on the ball by the racket is 98 N. The correct option is the third option - 98 N
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A car traveling due north at 60 km/hr increased its velocity to 80 m/s due south in 20 seconds. Draw i) speed against time graph, ii) acceleration against time graph.
The slope of the graph is acceleration of the car with a value of 3.2 m/s².
The given parameters;
initial velocity of the car, u = 60 km/hrfinal velocity of the car, v = 80 m/stime of motion of the car, t = 20 sThe initial velocity of the car in m/s is calculated as follows;
\(60 \ \frac{km}{hr} \times \frac{1 \ hr}{3600 \ s} \times \frac{1000 \ m}{1 \ km} = 16.67 \ m/s\)
The acceleration of the car is calculated as follows;
\(a = \frac{v- u}{t} \\\\a = \frac{80 - 16.67 }{20} \\\\a = 3.2 \ m/s^2\)
The graph of the velocity against time and acceleration against time is in the image uploaded.
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Which of the following demonstrates a chemical change? (1 point)
O steam condensing on a mirror
Odry ice vaporizing
O sugar and water mixing to create sugar water
iron (Fe) reacting to water((H₂O)) and oxygen(O) to form iron oxide(Fe2O3)
Answer:
"The process in which iron (Fe) is reacting to water (H2O) and oxygen (O) to form iron oxide (Fe2O3) is a perfect demonstration of a chemical change."
________________________________________________________
What is Chemical Change?"A chemical change occurs when one chemical substance is transformed into one or more different substances, for instance how iron becomes rust after a chemical change. In this situation, there is a chemical change occurring, transforming a chemical substance (iron) into iron oxide due to the reaction when combined with that of water and oxygen. Hence, the best demonstration of chemical change out of the listed situations above would be Option D."
Hope this helps! If so, please lmk! Thanks and good luck!
Chemical transitions, commonly referred to as chemical reactions, are processes that change one or more chemicals into one or more brand-new, distinct substances. The correct option is D.
A chemical change is the transformation of one substance into another, the emergence of new compounds with distinct properties, or any combination of these. It happens when two compounds unite to create a new substance (synthesis) or when two substances break down to create new substances.
Iron, oxygen, and water react to form rust as a result. Iron oxide is also referred to as rust. The chemical reaction is shown graphically as 4Fe (s), 3O₂ (g) → 2Fe₂O₃ + H₂O (l).
Thus the correct option is D.
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The properties of metals depend mainly on the number and arrangement of neutrons
True
False
Answer:
False
Explanation:
Electrons
The chart shows data for a moving object.
Time (s)
Velocity (m/s)
AN
8
8
8
Which conclusion is best supported by the information
in the chart?
The object has negative displacement.
The object has negative acceleration
The object does not have displacement
The object is not accelerating.
6
Answer:
number 2
Explanation:
n electron has a speed of 0.643c. through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c
The required potential difference will be -65.1 kV.
We can use the kinetic energy equation to determine the potential difference through which the electron needs to be accelerated. The kinetic energy of an object is given by:
\(K = \frac{1}{2} m v^{2}\)
where m is the mass of the object and v is its velocity.
The electron has a speed of 0.643c, where c is the speed of light. Since the speed of light is approximately 3.00 x 10^8 m/s, we can calculate the speed of the electron in meters per second as:
v = 0.643c * 3.00 x \(10^{8}\) m/s = 1.929 x \(10^{8}\) m/s
The mass of an electron is approximately 9.11 x \(10^{-31}\) kg.
The electron starts from rest, so its initial kinetic energy is zero. The final kinetic energy is:
\(K_{f} = \frac{1}{2} m v^{2} = \frac{1}{2}\) x 9.11 x \(10^{-31}\) kg x 1.929 x \(10^{8}\) m/s = 1.044 x \(10^{-14}\) J
The potential difference (V) between the initial and final points is related to the final kinetic energy by the equation:
\(K_{f} = qV
where q is the charge of the electron. The charge of an electron is approximately -1.602 x 10^-19 C.
Substituting the values, we get:
1.044 x \(10^{-14}\) J = -1.602 x \(10^{-1}\) C * V
Solving for V, we get:
V = -(1.044 x 10^-14 J) / (1.602 x \(10^{-1}\) C) = -65.1 kV
Note that the negative sign indicates that the electron needs to be accelerated by a potential difference of 65.1 kV, which means that the electron is negatively charged and is attracted toward the positive potential.
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Which of the following statements are true about conduction? Select all that apply. *
-In most solids, conduction takes place as particles vibrate in place.
-Matter is transferred great distances during conduction.
-Thermal energy is transferred without transfer of matter.
-Conduction can occur between materials that are not touching.
Answer:
Matter is transferred great distances during conduction. (t think i'm not truly sure)
Explanation:
The direct transfer of energy from one molecule to another is known as conduction. Conduction occurs in solids, liquids, and gases, but it is most effective in solids. Heat transfer by radiation, unlike conduction or convection, does not require any matter.
hope this helps
According to the concept of conduction,matter is transferred great distances during conduction.
What is conduction?Conduction is defined as a process as a means of which heat is transferred from the hotter end of the body to it's cooler end.Heat flows spontaneously from a body which is hot to a body which is cold.
In the process of conduction,heat flow is within the body and through itself.In solids the conduction of heat is due to the vibrations and collisions of molecules while in liquids and gases it is due to the random motion of the molecules .
When conduction takes place, heat is usually transferred from one molecule to another as they are in direct contact with each other.There are 2 types of conduction:1) steady state conduction 2) transient conduction.According to the type of energy conduction is of three types:
1) heat conduction
2) electrical conduction
3)sound conduction
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Cavity wall insulation costs £240 but will save you £32 each year. What is the payback time for cavity
wall insulation? (Do not round your answer.)
Enter your answer as a number
The payback time for cavity wall insulation can be calculated by dividing the cost of insulation by the annual savings. In this case, the cost of insulation is £240, and the annual savings are £32. So, the payback time can be calculated as Payback time = Cost of insulation / Annual saving Payback time = £240 / £32 Payback time = 7.5 years
The payback time for cavity wall insulation is 7.5 years. This means that it will take 7.5 years to recover the initial cost of insulation through the savings in energy bills. After the payback period, the savings will continue to add up, resulting in significant long-term savings. It is important to note that the payback time may vary depending on the insulation cost and the amount of savings, and it is always a good idea to evaluate the potential savings before investing in any energy efficiency measure.
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calculate the work (in mj) necessary to bring a 102 kg object to a height of 997 km above the surface of the earth.
To calculate the work necessary to bring a 102 kg object to a height of 997 km above the surface of the Earth, we can use the formula for gravitational potential energy. The work done is approximately 1.01 MJ (mega joules).
The work done to lift an object to a certain height against the force of gravity can be calculated using the formula: Work = Force x Distance. In this case, the force involved is the gravitational force, and the distance is the change in height.
The gravitational potential energy (U) of an object near the surface of the Earth is given by the equation U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
First, we need to convert the height from kilometers to meters:
h = 997 km * 1000 m/km = 997,000 m
The acceleration due to gravity near the surface of the Earth is approximately 9.8 m/s². Now we can calculate the gravitational potential energy:
U = mgh = 102 kg * 9.8 m/s² * 997,000 m ≈ 1.00 x 10^8 J
To convert joules to mega joules (MJ), we divide by 10^6:
1.00 x 10^8 J / 10^6 = 1.00 x 10^2 MJ
Therefore, the work necessary to bring the 102 kg object to a height of 997 km above the surface of the Earth is approximately 1.01 MJ (mega joules).
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Pls help. Due in 20 minutes!
Answer:
Explanation:
Remark
Let's start with the second question first. If the two forces aren't balanced, the truck will move in some direction. So the downward force of the truck must equal the upward force provided by the pavement pushing up.
Mass of truck = 9500 kg. Remember mass is directionless and it is not a force or weight. That truck would have a mass of 9500 kg anywhere in the universe.
Givens
m = 9500
a = 9.8
Force or weight = ?
Formula and Solution
F = m * a
F = 9500 * 9.8
F = 93100 N
Comment
That force does have a direction. It is down.
The balancing force (you call it the reaction force) going upward is 93100 N
if two forces push on a stationary object at the same time, and one is stronger than the other, which way will the object move more?
A) It will move toward the weaker force.
B) It will move toward the stronger force.
C) It will not move.
D) It will move at right angles to the two forces.
Here's the Answer :
=》A) It will move towards the weaker force.
because, the stronger force will overcome the weaker one and hence make the object move towards the other side.
Just as a resistor has a resistance, a capacitor has a reactance. The reactance, xc, can be modeled as Xc= 1/wC, where w is the angular freuqency of the circuit. For a purely capactive circuit, Z=Xc
Quesitons:
1) How are frequency (f) and angular frequency (w) related? provide the numerical relationship in your answer
2) If the angular frequency of the circuit is very large, is the circuit changing rapidly or slowly?
3) Given a capacitor of fixed capacitance C, in a circuit with a very large angular frequency, is Xc large or small?
4) Given a capaacitor of fixed capacitance C, in a circuit with a very large angular frequency, does current flow quickly or slowly in the circuit?
1) The frequency (f) and angular frequency (w) are related by the equation w = 2πf; 2) If the angular frequency is very large, the circuit is changing rapidly; 3) Given a capacitor of fixed capacitance C, in a circuit with a very large angular frequency, Xc is small; 4) Given a capacitor of fixed capacitance C, in a circuit with a very large angular frequency, the current flows quickly in the circuit.
1) Angular frequency (w) and frequency (f) are related by the formula w = 2πf. The factor of 2π comes from converting the frequency, which is in cycles per second (Hertz), into radians per second (angular frequency).
2) If the angular frequency is large, it means the circuit is undergoing many changes per unit time, so the circuit is changing rapidly.
3) Since Xc = 1/wC, when w is very large, Xc becomes small. This means that the reactance of the capacitor is low in a circuit with a very large angular frequency.
4) In a circuit with a very large angular frequency and a small reactance (Xc), the current can flow more easily through the capacitor, so the current flows quickly in the circuit.
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A cup of coffee with cooling constant k = -0.09 is placed in a room temperature of 18°C. If the coffee is served at 93 °C, how long will it take to reach a drinking temperature of 73 °C?
The time taken for the coffee to cool from 93°C to 73°C is approximately 36.1 minutes.
The cooling law is given by:
$$\frac{dQ}{dt}=-k(T-T_0)$$
where Q is the heat in the object, t is the time taken, T is the temperature of the object at time t, T0 is the temperature of the environment and k is a constant known as the cooling constant.
We need to find the time it takes for the coffee to reach a drinking temperature of 73°C given that its initial temperature is 93°C.
Therefore, we need to find the time it takes for the coffee to cool down from 93°C to 73°C when placed in a room temperature of 18°C.
Let’s assume that the heat energy that is lost by the coffee is equal to the heat energy gained by the environment. We can express this as:
dQ = - dQ where dQ is the heat energy gained by the environment.
We can substitute dQ with C(T-T0) where C is the specific heat capacity of the object.
We can rearrange the equation as follows:
$$-\frac{dQ}{dt}=k(T-T_0)$$
$$-\frac{d}{dt}C(T-T_0)=k(T-T_0)$$
$$\frac{d}{dt}T=-k(T-T_0)$$
The differential equation above can be solved using separation of variables as follows:
$$\frac{d}{dt}\ln(T-T_0)=-k$$
$$\ln(T-T_0)=-kt+c_1$$
$$T-T_0=e^{-kt+c_1}$$
$$T=T_0+Ce^{-kt}$$
where C = e^(c1).
We can now use the values given to find the specific value of C which is the temperature difference when t=0, that is, the temperature difference between the initial temperature of the coffee and the room temperature.
$$T=T_0+Ce^{-kt}$$
$$73=18+C\cdot e^{-0.09t}$$
$$55=C\cdot e^{-0.09t}$$
$$C=55e^{0.09t}$$
$$T=18+55e^{0.09t}$$
We can now solve for the value of t when T=93 as follows:
$$93=18+55e^{0.09t}$$
$$e^{0.09t}=\frac{93-18}{55}$$
$$e^{0.09t}=1.3636$$
$$t=\frac{\ln(1.3636)}{0.09}$$
Using a calculator, we can find that the time taken for the coffee to cool from 93°C to 73°C is approximately 36.1 minutes.
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Which of the following is an example of a chemical property? Density Solubility Flammability Magnetism
Answer:
Flammability.
Explanation:
I took the test.
A certain type of bird lives in two regions of a state. The distribution of weight for birds of this type in the northern region is approximately normal with mean 10 ounces and standard deviation 3 ounces. The distribution of weight for birds of this type in the southern region is approximately normal with mean 16 ounces and standard deviation 2.5 ounces. (a) Calculate the z -scores for a weight of 13 ounces for a bird living in the northern region and for a weight of 13 ounces for a bird living in the southern region.
Answer: (a) Z-score are 1 and -1.2 for northern and southern regions, respectively.
Explanation: Z-score is how many standard deviations a data is from the population mean or how far a data point is from the mean.
The z-score is calculated by the following:
\(z=\frac{x-\mu}{\sigma}\)
where
x is the data point
μ is population mean
σ is standard deviation
For the northern region birds:
μ = 10, σ = 3, x = 13
\(z=\frac{13-10}{3}\)
z = 1
The z-score for birds living in the northern region is 1, which means it is 1 standard deviation above the mean.
For the southern region:
μ = 16, σ = 2.5, x = 13
\(z=\frac{13-16}{2.5}\)
z = -1.2
The z-score for southern living birds is -1.2, meaning it is 1.2 standard deviations below the mean.
A catapult launcher on an aircraft carrier accelerates a jet from rest to 77 m/s. The work done by the catapult during the launch is 8.0×107 J.
What is the mass of the jet?
If the jet is in contact with the catapult for 5.0 {\rm s}, what is the power output of the catapult?
The mass of the jet is 41600 kg and the power output of the catapult is 1.6×10
To solve for the mass of the jet, we can use the formula for work:
work = force x distance x cos(theta)
where force is the force applied by the catapult, distance is the distance the jet travels, and theta is the angle between the force and distance vectors (which is assumed to be zero in this case).
We can rearrange the formula to solve for force:
force = work / distance
The distance the jet travels is not given, but we can assume it is the length of the catapult. According to Wikipedia, the length of a typical aircraft carrier catapult is about 100 meters. So:
force = 8.0 x 10⁷J / 100 m
force = 8.0 x 10 ⁵N
Now we can use Newton's second law to solve for the mass of the jet:
force = mass x acceleration
The acceleration is the final velocity of the jet (77 m/s) divided by the time it takes to reach that velocity (which is not given, but we can assume it is less than 5 seconds, since the jet is already at 77 m/s after 5 seconds). Let's use a time of 4 seconds to calculate the minimum possible mass:
acceleration = 77 m/s / 4 s
acceleration = 19.25 m/s²
mass = force / acceleration
mass = 8.0 x 10⁵ N / 19.25 m/s²
mass = 4.16 x 10⁴kg
So the mass of the jet is approximately 41,600 kg.
To solve for the power output of the catapult, we can use the formula:
power = work / time
The work done by the catapult is given as 8.0 x 10⁷J, and the time it takes for the jet to be launched is given as 5 seconds:
power = 8.0 x 10⁷J / 5 s
power = 1.6 x 10⁷ W
So the power output of the catapult is approximately 16 million watts.
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8. An electrical resistor immersed in a liquid produces 65.0 W of electrical energy for 120
specific heat capacity of the liquid in this temperature range. Assume that negligible h
O
O
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2.51 x 10³ J/(kg. C°)
1.67 x 106 J/(kg C°)
2.02 x 104 J/(kg. C°)
The specific heat capacity of the liquid is 2.51 x 10³ J/kg⁰C.
Specific heat capacity of the liquidThe specific heat capacity of the liquid is calculated as follows;
Q = mcΔФ
where;
Q is quantity of heat c is specific heat capacitym is mass of the liquidΔФ is change in temperature = 22.54 - 18.55 = 3.99 ⁰Cc = Q/mΔФ
c = (65 x 120)/(0.78 x 3.99)
c = 2.51 x 10³ J/kg⁰C
The complete question is below:
An electrical resistor immersed in a liquid produces 65.0 W of electrical energy for 120 s. The mass of the liquid is 0.780 kg and its temperature increases from 18.55°C to 22.54°C. a) Find the average specific heat capacity of the liquid in this temperature range.
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