The complex power was determined for three cases: (i) P = P1 W, Q = Q1 VAR (capacitive), resulting in (P1 + jQ1) W; (ii) Q = Q2 VAR, pf = 0.8 (leading), resulting in 1.25Q ∠ 53.13°; and (iii) S = S1 VA, Q = Q2 VAR (inductive), resulting in (S1 + jQ2) VA.
(i) P = P1 W, Q = Q1 VAR (capacitive)
We have:
Q = |Vrms||Irms|sin(θ) < 0
which implies
Irms = |Irms| ∠ θ = -j|Irms|sin(θ)
Using the formula for complex power, we have:
P + jQ = VrmsIrms* = |Vrms||Irms|∠θ
Substituting the given values, we get:
P + jQ = (P1 + jQ1) W
Therefore, the complex power is (P1 + jQ1) W.
(ii) Q = Q2 VAR, pf = 0.8 (leading)
We can calculate the real power as follows:
cos(θ) = pf = 0.8
sin(θ) = -√(1 - cos^2(θ)) = -0.6
|Vrms||Irms| = S = Q/cos(θ) = Q/0.8 = 1.25Q
Using the formula for complex power, we have:
P + jQ = VrmsIrms* = |Vrms||Irms|∠θ
Substituting the calculated values, we get:
P + jQ = 1.25Q ∠ -θ = 1.25Q ∠ 53.13°
The complex power is 1.25Q ∠ 53.13°.
(iii) S = S1 VA, Q = Q2 VAR (inductive)
We can calculate the real power using the formula for apparent power:
|Vrms||Irms| = S/|cos(θ)| = S/1 = S
Using the formula for complex power, we have:
P + jQ = VrmsIrms* = |Vrms||Irms|∠θ
Substituting the given values, we get:
P + jQ = (S1 + jQ2) VA
Therefore, the complex power is (S1 + jQ2) VA.
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Rasheed ran down the football field at a speed of 7m/s. If he got to the end in 23
seconds, how far did he actually run?
Answer:
The answer is 161 mExplanation:
To find the distance covered we use the formula
distance = velocity × timeFrom the question
velocity = 7 m/s
time = 23 s
We have
distance = 7 × 23
We have the final answer as
161 mHope this helps you
HELP ME a hot air balloon is rising upward with a constant velocity of 4.0 m/s. As the balloon reaches a height of 4.0 m above the ground, the balloonist accidently drops a can of pop over the edge of the basket. How long does it take the pop can to reach the ground?
It takes approximately 1.2 seconds for the pop can to reach the ground after being dropped by the balloonist. To answer your question, we can use the kinematic equation is given below.
h = vi*t + 0.5*a*t²
we need to consider the initial conditions of the falling pop can. When the balloonist accidentally drops the can, it has an initial velocity equal to the upward velocity of the hot air balloon, which is 4.0 m/s. Also, the initial height of the can is 4.0 meters above the ground.
Since the can is now in free fall, it will be acted upon by gravity, which has an acceleration of -9.8 m/s² (negative because it's downward). We can use the following equation of motion to find the time it takes for the pop can to reach the ground:
h = vi*t + 0.5*a*t²
Where h is the height (4.0 m), vi is the initial velocity (4.0 m/s), a is the acceleration due to gravity (-9.8 m/s²), and t is the time we want to find.
Rearranging the equation for t, we get:
t = [(-2*h) / (vi - 0.5*a)]^(1/2)
Plugging in the given values:
t = [(-2*4) / (4 - 0.5*(-9.8))]^(1/2)
t ≈ 1.2 seconds
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Which force is most important inside an atom?
O A. Gravity
O B. Air resistance
O C. Friction
O D. Strong nuclear force
Answer:
D- fuerza nuclear fuerte
Explanation:
The density of lead is 30.2g/cm³. What is the value in kg/cm³
Answer:
30.2 g / cm^3 = 30.2 g/cm^3 * 1 kg / 1000 g = .0302 kg/cm^3
A pendulum makes 50 complete swings in 2 min 40 second . what is time period for 1 complete swing?
Answer:
3.2 seconds
Explanation:
50 swings = 2 mins 40 secs
= 50 swings = 2 x 60 + 40 secs
= 50 swings = 160 secs
= 1 swing = 160 / 50 secs
= 1 swing -= 3.2 secs
what is the standard unit for measuring temperature in the metric system?
The metric system uses Celsius as the primary unit of measurement for temperature.
Nearly all nations in the world use the metric system as their official unit of measurement, which includes Celsius. The Celsius scale is used to measure temperature in most scientific disciplines. The freezing point of water is zero degrees Celsius, and the boiling point is one hundred degrees Celsius. By the middle of the 20th century, Celsius, the most widely used temperature unit in the modern metric system, had been adopted by the majority of the world. Anders Celsius, a Swedish astronomer, created the Celsius scale in 1742.
Most places in the globe measure temperature using the Celsius system (°C). The historical development of this empirical scale led to the definition of its zero point, 0 °C, as the freezing point.
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a 120-v power supple connected to a 10-ohm resistor will produce ____ amps of current
Hello!
a 120-v power supple connected to a 10-ohm resistor will produce 3.464 amps of current
P = 120 V
r = 10Ω
P = r * I²
I² = P ÷ r
I² = 120 ÷ 10
I² = 12
I = √12
I ≈ 3.464
Explain how your car's inertia affects how quickly it starts up from rest or comes
to a stop
Inertia is the tendency of an object to stay in the current state. Hence, the stationary car has a tendency to continue in the state of rest. Quick starts up will make it move backward or if stop quickly while moving, it goes forward.
What is inertia ?According to Newton's first law of motion, an objects tends to continue in its state of motion or rest until an external force acting on it. This tendency of the objects is called inertia.
The impacts of inertia can be well explained based on on real life examples. If we might had the experience of moving to front in a vehicle which suddenly breakes. It is the tendency of the vehicle to stay in motion.
Similarly the car when started from rest initially tends to stay at rest and that's why we feel it moves back ward. Similarly the car will move forward when it is suddenly stops.
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write two closest isotopes for gold-197. express your answer as isotopes separated by a comma.
The two closest isotopes for gold-197 are gold-196 and gold-198.
The atomic number of gold is 79, which means it has 79 protons. Gold-197 refers to the isotope of gold with a mass number of 197, indicating the total number of protons and neutrons in the nucleus.
The two closest isotopes to gold-197 are:
1. Gold-196: It has 79 protons and 117 neutrons (197 - 79 = 118).
2. Gold-198: It has 79 protons and 119 neutrons (197 - 79 = 118).
Therefore, the two closest isotopes to gold-197 are gold-196 and gold-198, with the number of neutrons being the only difference between them.
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A sound wave has a speed of 345 m/s and a wavelength of 4.15 meters. what is the frequency of this wave?
a. 83 hertz
b. 67 hertz
c. 125 hertz
d. 145 hertz
Answer:
a is the correct answer
from the formula of wave length=v/f
therefore f= v/wave length
these implies f= 345/4.15 = 83.1hertz
what is the correct tight asymptotic bound for T(n) in 1,2,3 where T(1)=c ?
T(n) = 10T(n/10)+100n
T(n) =T(n/10)+100n
T(n) = T(n/10)+100
The correct tight asymptotic bound for T(n) in 1, 2, 3 where T(1)=c is Θ(n log n).
To find the tight asymptotic bound of T(n), we will use the Master Theorem. So, let's take a look at each recurrence relation:
1. T(n) = 10T(n/10)+100nApplying the Master Theorem: a = 10, b = 10, f(n) = 100nlogb a = log10 10 = 1 Since f(n) = Θ(n) = Θ(n1), Case 2 of the Master Theorem applies. The solution, therefore, is Θ(n log n).
2. T(n) = T(n/10)+100n Here, a = 1, b = 10, f(n) = 100nlogb a = log10 1 = 0 Since f(n) = Θ(n0) = Θ(1), Case 1 of the Master Theorem applies. The solution, therefore, is Θ(n).
3. T(n) = T(n/10)+100 Here, a = 1, b = 10, f(n) = 100logb a = log10 1 = 0 Since f(n) = Θ(1) = Θ(n0), Case 2 of the Master Theorem applies. The solution, therefore, is Θ(log n).Therefore, the correct tight asymptotic bound for T(n) in 1, 2, 3 where T(1)=c is Θ(n log n).
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Let's use the Master Theorem to find the asymptotic tight bound for each of the three recurrence relations given in the problem statement.
1. T(n) = 10T(n/10) + 100n Here, a = 10, b = 10, and f(n) = 100n. We can calculate the value of logb a as follows: log10 10 = 1 Since f(n) = Θ(n1), we can apply Case 2 of the Master Theorem and get: T(n) = Θ(n log n)Therefore, the correct tight asymptotic bound for T(n) in the first case is Θ(n log n).
2. T(n) = T(n/10) + 100n Here, a = 1, b = 10, and f(n) = 100n. We can calculate the value of logb a as follows: log10 1 = 0 Since f(n) = Θ(n1), we can apply Case 1 of the Master Theorem and get: T(n) = Θ(n)Therefore, the correct tight asymptotic bound for T(n) in the second case is Θ(n).
3. T(n) = T(n/10) + 100 Here, a = 1, b = 10, and f(n) = 100. We can calculate the value of logb a as follows: log10 1 = 0 Since f(n) = Θ(1), we can apply Case 2 of the Master Theorem and get: T(n) = Θ(log n) Therefore, the correct tight asymptotic bound for T(n) in the third case is Θ(log n). Hence, the three asymptotic tight bounds for T(n) are Θ(n log n), Θ(n), and Θ(log n), respectively.
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a player hit a serve in a racket sport that was clocked at 61 mph. how much work did have to do on the -oz ball to get it to that speed?
The work we have to do on the -oz ball to get it to that speed is 62.20 ft.lb.
1 ounce = 0.0625 pound
1 mile per hour is = 1.46667 \(\frac{ft}{sec}\)
Now, the speed of ball is =89.46687 \(\frac{ft}{sec}\)
Now, to find the weight of the ball=0.0625 ×8
weight of ball=0.5lb
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. Kinetic energy is the type of energy that is transferred and is dependent on the mass and speed attained.
Kinetic Energy=\(\frac{1}{2} mv^{2}\)
Kinetic Energy=\(\frac{1}{2}\times0.5\times89.46687^{2}\)
Kinetic Energy=2001.082 \(\frac{ft^{2} }{sec^{2} }\times lb\)
Now, 1lbf =32.174049\(\frac{ft}{sec^{2} }\times lb\)
Now, kinetic energy=\(\frac{2001.082}{32.174049}\)
kinetic energy=62.20 ft.lb
Now, kinetic energy will always be equal to work done.
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.) Which of the following statements is true?
a) A scalar quantity can be added to a vector
b) It is possible for the magnitude of a vector to equal zero even though one of its components
is non-zero
c) Scalar quantities are path dependent, while vectors are not.
d) Scalar quantities and vector quantities can both be added algebraically
find the speed of the bicycle in feet per second and miles per hour.
To find the speed of a bicycle in feet per second (fps) and miles per hour (mph), we need to know the distance traveled and the time taken.
Let's assume the bicycle traveled a distance of d feet and the time taken to cover that distance is t seconds.
The speed of the bicycle in feet per second (fps) can be calculated using the formula:
\(\[ \text{Speed (fps)} = \frac{\text{Distance (feet)}}{\text{Time (seconds)}} = \frac{d}{t} \]\)
To convert the speed from feet per second (fps) to miles per hour (mph), we can use the conversion factor that 1 mile is equal to 5280 feet, and 1 hour is equal to 3600 seconds.
The speed of the bicycle in miles per hour (mph) can be calculated using the formula:
\(\[ \text{Speed (mph)} = \left(\frac{\text{Distance (feet)}}{\text{Time (seconds)}}\right) \times \left(\frac{1 \text{ mile}}{5280 \text{ feet}}\right) \times \left(\frac{3600 \text{ seconds}}{1 \text{ hour}}\right) \]\)
So, to find the speed of the bicycle in both feet per second (fps) and miles per hour (mph), we need the values of distance traveled and time taken.
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A student wants to test the force of magnetism by placing objects on top of a piece of cardboard and then moving them with a magnet placed under the cardboard. Which items will help the student with this investigation?
Answer:
Any material that has ferromagnetic property
Explanation:
Materials such as iron, nickel or cobalt are ferromagnetic element as they behave as small magnets in the presence of moving electric charge or static magnetic field.
When an external magnetic field is applied these ferromagnetic material align in a way that they contribute to produce a stronger magnetic field in the material and remain aligned even after removal of the external magnetic field.
Starting from rest, you pushed a 10.0 kg lawnmower a distance of 25 meters by applying a force of 75 N at an angle 35 degrees below horizontal, as shown below. Use work and energy principles to calculate how fast the lawn mower is moving (in m/s) at the end of the 25 meters.
The lawn mower is moving with a velocity of 17.53 m/s
Energy is the ability to do work while Work is defined as the product of force and distance moved in the direction of the force. Both work and energy are measured in Joule (J)
Work = Force (F) × distance (d) = FdCosθ
With the above formula, we can obtain the energy used in pushing the lawn mower as illustrated below
From the question given above, the following data were obtained:
•Force (F) = 75 N
•Distance (d) = 25 m
•Angle (θ) = 35°
•Energy (E) =?
E = FdCosθ
E = 75 × 25 × Cos 35
E = 1535.91 J
Definition and Determination of the velocityVelocity is the rate of change of displacement with time.
Velocity and energy are related according to the following equation:
E = ½ × mass (m) × square velocity (v²)
E = ½mv²
With the above formula, we can obtain the velocity of the lawn mower as follow
•Mass (m) = 10 Kg
•Energy (E) = 1535.91 J
•Velocity (v) =?
E = ½mv²
1535.91 = ½ × 10 × v²
1535.91 = 5 × v²
Divide both side by 5
v² = 1535.91 / 5
Take the square root of both side
v = √(1535.91 / 5)
v = 17.53 m/s
Thus, the lawn mower is moving with a velocity of 17.53 m/s
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Since monsoons are storms that usually occur during a specific time of year in certain regions, you could not compare them to thunderstorms. please select the best answer from the choices provided t f
The statement "Since monsoons are storms that usually occur during a specific time of year in certain regions, you could not compare them to thunderstorms" is absolutely false.
What is monsoon?Monsoon may be characterized as a seasonal transformation in the direction of the predominant, most potent, currents of a region. It blows from cold to warmer regions of the geographical locations.
Thunderstorms basically originated identically with monsoons more frequently. Monsoon involves sudden and gradual rainfall, extreme wind, and a drop-down in temperature.
The occurrence of monsoon is fixed at different geographical locations, but the occurrence of thunderstorms will not be definite or predominantly known.
Thus, the statement "Since monsoons are storms that usually occur during a specific time of year in certain regions, you could not compare them to thunderstorms" is absolutely false.
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Answer:
False
Explanation:
Which of the following is required to have a backfire flame arrestor?
Flares are rated for day, night or combined day/night use.
VHF radios work by the line of sight principle.
A boat with a gasoline inboard engine.
A boat with a gasoline inboard engine requires a backfire flame arrestor.
This safety device is designed to prevent the occurrence of a backfire in the engine compartment, which could lead to a dangerous fire or explosion. The backfire flame arrestor is typically installed in the air intake system of the engine and is responsible for trapping and extinguishing any flames or sparks that may be generated during the engine operation.
By doing so, it helps to prevent the ignition of fuel vapors in the engine compartment. It is an essential component for the safe operation of gasoline-powered inboard engines, ensuring the protection of the vessel and its occupants from potential hazards associated with backfires.
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You walk 2 minutes at 2 m/s and then 5 minutes at 1 m/s what is your average speed
5 mins
Explanation:
because speed ÷ to distance since the distance is 5 miles the answer is 5mins if not it's 0.2 if the teacher incorrect it
the most popular electrode diameters range from ____ to ____. *
The most popular electrode diameters range from small sizes, typically around 1 mm, to larger sizes, often up to 10 mm or more.
Electrodes are commonly used in various fields such as medical applications, electrical engineering, and material science. The diameter of an electrode plays a crucial role in its functionality and application. Smaller electrode diameters, typically around 1 mm, are commonly used in precision applications where fine control and high resolution are required. These smaller electrodes are suitable for intricate tasks such as microsurgery, microelectronics, and microfabrication.
On the other hand, larger electrode diameters are utilized for applications that require higher current-carrying capacity and greater durability. These larger electrodes, which can range from several millimeters to centimeters in diameter, are commonly used in industries such as welding, metal fabrication, and power generation. The larger diameter allows for efficient heat dissipation, better electrical conductivity, and improved mechanical stability.
It's important to note that the specific range of popular electrode diameters can vary depending on the specific application, industry standards, and technological advancements. Therefore, it is always recommended to consult the relevant guidelines or industry practices to determine the appropriate electrode diameter for a particular use case.
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The distance between Carol's house and her uncle's house is 24 km. What is her speed in kilometers per hour in order to get to her uncles house in 40 minutes by motorcycle.
Carol's speed in kilometers per hour in order to get to her uncles house in 40 minutes by motorcycle is 36km/hr.
How to calculate average speed?The average speed of a moving body can be calculated by dividing the distance moved by the time taken.
According to this question, the distance between Carol's house and her uncle's house is 24 km. The speed it will take her to get to her uncle's house in 40 minutes by motorcycle is as follows:
Average speed = 24km ÷ 40/60 hour
Average speed = 36km/hr
Therefore, Carol's speed in kilometers per hour in order to get to her uncles house in 40 minutes by motorcycle is 36km/hr.
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An observer measures a 100 Hz Doppler shift as an ambulance goes by. At rest, the frequency of the ambulance's siren is 2,000 Hz. What is the speed of the ambulance?
The change in the frequency of the sound, due to the relative motion of the source of sound and the observer, is determined by the Doppler's Effect.
The speed of the ambulance (source) is "6517 m/s"
The equation of Doppler's Effect is given as follows:
\(f_o = \frac{v+v_o}{v+v_s}f_s\)
where,
\(f_o\\\) = frequency of sound measure by observer = 100 Hz
v = speed of sound = 343 m/s
\(v_o\) = speed of observer = 0 m/s
\(v_s\) = speed of ambulance (source) = ?
\(f_s\) = actual frequency = 2000 Hz
Therefore, using the values, we get:
\(100\ Hz = \frac{343\ m/s + 0\ m/s}{343\ m/s + v_s}(2000\ Hz)\\\\(100\ Hz)(343\ m/s + v_s) = (343\ m/s)(2000\ Hz)\\\\v_s = \frac{686000\ Hz.m/s - 34300\ Hz.m/s}{100\ Hz}\)
v_s = 6517 m/s
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Jalen combines two substances in science class. Once combined, only one of the two substances
is visible. When he placed this combination into a filter, substance 1 stayed in the filter while
substance 2 went through it. Which of the following claims regarding Jalen's combination is the
most accurate?
a. This combination is not a mixture because he cannot see one of the substances.
b. The combination is a mixture because the substances can be separated.
c. The combination is not a mixture because the substances can be separated.
d. The combination is a mixture only because he cannot see one of the substances,
Answer: b. The combination is a mixture because the substances can be separated
Explanation: Based on the facts presented above, the combination of both both substances can be referred to as a mixture due to the following:
A mixture is obtained when two or more substances or materials are combined without a chemical reaction. This is observed when Jalen combined substance 1 and 2 with only one of the substances becoming visible after the combination.
The other reason is that, a mixture can be separated back into its original constituent, this is evident when the combination was filtered with only substance 2 going through the filter and substance 1 remaining in the filter
what is the energy density (energy per mass) of butter and similar foods? group of answer choices 4.5 mj/kg 4500 mj/kg 45 mj/kg 450 mj/kg 0.45 mj/kg
The energy density of butter and similar foods is 4.5 MJ/kg. This value represents the amount of energy stored in a given mass of food and is related to the food's calorie content.
The energy density (energy per mass) of butter and similar foods can be measured in megajoules per kilogram (MJ/kg). Energy density is important for understanding the amount of energy stored in a given mass of food, which is related to its calorie content.
1. Determine the macronutrient content of the food (i.e., grams of fat, carbohydrates, and protein per serving).
2. Multiply the grams of fat by 9 kcal/g, as fat provides 9 kcal of energy per gram.
3. Multiply the grams of carbohydrates and protein by 4 kcal/g, as both carbohydrates and proteins provide 4 kcal of energy per gram.
4. Add the energy content from each macronutrient to get the total energy content of the food.
5. Divide the total energy content by the mass of the food (in kg) to obtain the energy density (in MJ/kg).
Among the given answer choices, the correct energy density for butter and similar foods is 4.5 MJ/kg. This value is equivalent to 1,000 kcal/kg, as there are approximately 0.004184 MJ in 1 kcal. Butter and similar high-fat foods have high energy densities due to their high fat content, which provides more energy per gram compared to carbohydrates and proteins.
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A baseball is thrown straight up with a velocity of 60 m/s. C) how many seconds later will the baseball reach its maximum height?
The baseball will reach its maximum height after approximately 6.11 seconds using equations of motion where velocity is given
When a baseball is thrown straight up with an initial velocity of 60 m/s, it will eventually reach a maximum height before falling back down due to gravity. To determine how many seconds later the baseball will reach its maximum height, we need to use the equations of motion.
The equation we can use to find the time taken for the baseball to reach its maximum height is:
t = Vf / g
where t is the time taken, Vf is the final velocity (which is zero at the maximum height), and g is the acceleration due to gravity, which is approximately \(9.81 m/s^2\).
Substituting:
t = 60 / 9.81
t ≈ 6.11 seconds
Therefore, the baseball will reach its maximum height after approximately 6.11 seconds. After this point, the baseball will begin to fall back down to the ground due to the force of gravity, with its velocity increasing at a rate of \(9.81 m/s^2\)
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Analyze the relationship between total internal reflection and the critical angle.
Answer:
5.15 when the angle of incidence is equal to critical angle the angle of reflection is equal to 90 if the angle of incidence is bigger than the critical anger the reflected ray will not emerge from the medium but will be reflected back into the medium this is called total internet reflection
Explanation:
hope it's helpful
Tell how the volume of a material i related to temperature. Ue the term thermal expanion and thermal contraction in your repone
The volume of a material is related to temperature through thermal expansion and thermal contraction. Different materials will expand and contract at different rates, and the amount of expansion or contraction also depends on the magnitude of the temperature change.
Temperature and volume are related through the phenomenon of thermal expansion and thermal contraction. Thermal expansion occurs when the temperature of a material increases, causing the material to expand or increase in volume. Thermal contraction is the opposite; when the temperature of a material decreases, the material contracts or decreases in volume.
The amount of thermal expansion or contraction that occurs depends on the type of material, as different materials will respond differently to temperature changes. Generally, solids experience more thermal expansion than liquids, and metals experience more thermal expansion than non-metals. This means that when the temperature of a material increases, the volume of a solid material will increase more than the volume of a liquid material; the volume of a metal material will increase more than the volume of a non-metal material.
The amount of thermal expansion or contraction also depends on the magnitude of the temperature change. Generally, the greater the temperature change, the greater the amount of thermal expansion or contraction. For example, if the temperature of a material is increased from 10°C to 20°C, the material may experience a small amount of thermal expansion. However, if the temperature is increased from 10°C to 100°C, the material may experience a large amount of thermal expansion.
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PLEASE HELP!!! ILL MARK BRAINLYEST!!
How many atoms are in 5 C?
7
5
3
4
6
Answer:
Explanation:
3.011 x 10^24 atoms
Answer:
jskskskssksksksskssksksksksks
It is better to use crow bar to displace a heavy load than with hands . Give reason .
Explanation:
Cause it multiples force which makes it easier to move.
A(n) 0.52 kg softball is pitched at a speed of 11 m/s. The batter hits it back directly at the pitcher at a speed of 29 m/s. The bat acts on the ball for 0.01 s. What is the magnitude of the impulse imparted by the bat to the ball?
The magnitude of the impulse imparted by the bat to the ball is 20.80 kg m/s.
To find the impulse imparted by the bat to the ball, we can use the impulse-momentum theorem, which states that the impulse applied to an object is equal to the change in momentum of the object.
The initial momentum of the ball is given by:
p₁ = m₁v₁ = (0.52 kg)(11 m/s) = 5.72 kg m/s (taking the direction of motion towards the batter as positive)
The final momentum of the ball is given by:
p₂ = m₁v₂ = (0.52 kg)(-29 m/s) = -15.08 kg m/s (taking the direction of motion towards the pitcher as positive)
The change in momentum is:
Δp = p₂ - p₁ = (-15.08 kg m/s) - (5.72 kg m/s) = -20.80 kg m/s
The impulse imparted by the bat to the ball is equal to the change in momentum, so:
J = Δp = -20.80 kg m/s
Note that the negative sign indicates that the impulse is in the opposite direction to the initial motion of the ball. The magnitude of the impulse is simply the absolute value of J, which is:
|J| = 20.80 kg m/s
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