a) The heat required to increase the temperature of ice from -15.00°C to 0°C without melting the ice is 837 J.
b) The heat required to melt the 40.0-g ice to water at 0°C is 1340 J.
c) The final temperature of the mixture is 0°C.
Explanation to the above given short answers are written below,
a) To calculate the heat required to increase the temperature of ice, we can use the formula:
Q = m * c * ΔT
where Q is the heat,
m is the mass,
c is the specific heat, and
ΔT is the change in temperature.
In this case, the mass of the ice is 40.0 g, the specific heat of ice is 2090 J/kg K, and the change in temperature is 0°C - (-15.00°C) = 15.00°C.
Converting the mass to kilograms (40.0 g = 0.040 kg), we can calculate:
Q = 0.040 kg * 2090 J/kg K * 15.00°C = 837 J
b) To calculate the heat required to melt the ice, we can use the formula:
Q = m * L
where Q is the heat,
m is the mass, and
L is the latent heat of fusion.
In this case, the mass of the ice is 40.0 g and the latent heat of fusion is 33.5 x 10^4 J/kg.
Converting the mass to kilograms, we can calculate:
Q = 0.040 kg * 33.5 x 10^4 J/kg = 1340 J
c) When the ice and water reach equilibrium, their final temperature will be the melting point of ice, which is 0°C. This is because during the phase change from ice to water, the temperature remains constant until all the ice has melted.
Therefore, the final temperature of the mixture is 0°C.
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Two coils A and B are wound side by side. Coil A has 8120 turns and coil B has 11842 turns. 54% of flux produced by coil A links coil B. A current of 6 A in coil A produces 0.02 mWb, while the same current in coil B produces 0.078 mWb. a) Calculate the mutual inductance and the coupling coefficient. b) Calculate the emf induced in coil B when the current is reversed in 0.015 seconds.
a) Mutual inductance = 0.108 H; Coupling coefficient = 0.482. b) - 4.95 V.
a) Mutual inductance, M between coil A and coil B can be given as:
M = k√(L_AL_B) here, k is the coupling coefficient, L_A and L_B are the inductances of the coil A and coil B respectively. Since 54% of flux produced by coil A links coil B,
So, K = 0.54
L_A = N_A Φ/I_AL_A
= 8120 × 0.02/6
= 27.07 mH
L_B = N_B Φ/I_BL_B
= 11842 × 0.078/6
= 154.63 mH
M = k√(LALB) = 0.482 × √(27.07 × 0.15463) = 0.108 H
b) The emf induced in coil B can be given as:-
ε = M (dI_B/dt)/L_B
ε = 0.108 × (-6/0.015) / 0.15463 = -4.95 V
Thus, the emf induced in coil B when the current is reversed in 0.015 seconds is -4.95 V.
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A 2.0-kg particle has an initial velocity of (5i - 4j) m/s. Some time later, its velocity is (7i ; 3j) m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process
The work done by the resultant force can be calculated using the work-energy principle, which states that the work done by all the forces acting on an object is equal to the change in its kinetic energy.
First, we need to find the change in kinetic energy of the particle. The initial kinetic energy (KEi) can be calculated using the formula KEi = (1/2)mv^2, where m is the mass of the particle and v is its initial velocity. Substituting the given values, we get KEi = (1/2)(2 kg)(√41 m/s)^2 = 41 J.
Similarly, the final kinetic energy (KEf) can be calculated using the final velocity. KEf = (1/2)mv^2 = (1/2)(2 kg)(√58 m/s)^2 = 58 J.
Therefore, the change in kinetic energy (ΔKE) = KEf - KEi = 58 J - 41 J = 17 J.
Now, using the work-energy principle, we know that the work done by the resultant force (W) = ΔKE. Since no energy is lost in the process, all the work done by the forces is converted into the change in kinetic energy of the particle.
Therefore, the work done by the resultant force during this time interval is 17 J.
The work done by the resultant force during the time interval is 17 J, which is equal to the change in kinetic energy of the particle, as per the work-energy principle.
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Which is an example of nuclear energy being converted into heat and light?
A a volcano
B The sun
C A rocket engine
D A coal burning power plant
Answer:
D. A coal burning power plantExplanation:
it is a coal power plant , nuclear power is economical and does not fluctuate as much as wind or solar power.
Unlike coal, it is considered clean in terms of the amount of greenhouse gas emissions produced by the power plant itself, although uranium mining and processing are not without risks and environmental impact
Lifestyle practice that can improve your quality of life
Explanation:
And keep changing gradually.
Eat a variety of foods. ...
Base your diet on plenty of foods rich in carbohydrates. ...
Replace saturated with unsaturated fat. ...
Enjoy plenty of fruits and vegetables. ...
Reduce salt and sugar intake. ...
Eat regularly, control the portion size. ...
Drink plenty of fluids. ...
Maintain a healthy body weight
Use Newton’s law of gravitation to show that Earth’s gravitational field has a strength of 9.8 N/kg.
The value of the Earth's gravitational field strength is 9.8 N/Kg
How do I prove that the Earth's gravitational field strength is 9.8 N/Kg?The garviational field strength or acceleration due to gravity is given by the following formula:
g = GM / R²
Where
g is garviational field strength or acceleration due to gravity M is the mass G is the gravitational constantR is the radius.With the above formula, we can prove that the acceleration due to gravity other wise know as gravitational field strength is 9.8 N/Kg. This is illustrated below:
Mass of Earth (M) = 6×10²⁴ KgRadius of Earth (R) = 6400000 mGravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²Gravitational field strength (g) =?g = GM / R²
g = (6.67×10¯¹¹ × 6×10²⁴) / (6400000)²
g = 4002×10¹¹ / 4096×10¹⁰
g = 9.8 N/Kg
From the above calculation, we can see clearly that the gravitational field strength is 9.8 N/Kg
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For a 1 efficient step down transformer voltage in primary and secondary are equal current in primary and secondary are equal input power is same as the output power output power is zero
The given condition for a 100% efficient step down transformer is not true.
How do Step-down Transformers work?Because there are fewer turns in the secondary winding of a step-down transformer, the secondary voltage is lower than the initial voltage. As a result, this kind of transformer is employed to reduce the voltage to the levels intended for the circuit. Almost all power supply incorporate a step-down transformer to keep the operating voltage range of the circuit within acceptable limits. Electronic transformers and distribution systems are often where these transformers are installed (power transformers).
What Does a Step-Down Transformer Mean by Power?Using the system voltage and current, we can calculate the power of a transformer. Volt-Amps, or VA, is the unit used to measure the power in a transformer (for larger transformers Kilo Volt-Amps, kVA).
Any transformer should, in theory, have constant power on both sides, which implies that the power available on the secondary side of the transformer should match the power available on the primary side. This also applies to step-down transformers. A step-down transformer's secondary side has a lower voltage than its primary side, hence in order to balance the transformer's total power, the secondary current would need to be increased.
What is the Step-Down Transformer's Relationship Between Voltage and Current?In a step-down transformer, the output current is greater than the input current while the output voltage is lower than the primary voltage.
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How much work is done by the force of gravity went 45 n object falls to the ground from a height of 4.6m?
The work W exerted over an object by a force F along a distance d is:
\(W=Fd\)Substitute F=45N and d=4.6m to find the work done by the force of gravity on the falling object:
\(W=(45N)(4.6m)=207J\)Therefore, the work done by the force of gravity when a 45N object falls a distance of 4.6m, is:
\(207J\)A boat floats in a lake. When the boat moves the force of resistance is proportional to the velocity of the boat. Initially the boat is at rest. A person walks from the stern to the bow of the boat. What will be the position of the boat long time after the person stopped moving?
Answer: Contant.
Explanation:
You are given that When the boat moves the force of resistance is proportional to the velocity of the boat. This means that the total momentum on the boat is equal to zero. Then the boat remains at a certain position.
When a person walks from the stern to the bow of the boat, the boat will tend to move in the opposite direction with equal magnitude of momentum. The magnitude of forces will thereby cancel out.
The person will be seen moving while the boat moves in the opposite direction.
If no external force is acting on the boat, the sum of the momentum of the person and the boat will be equal to zero. And the boat will remain at rest.
The position of the boat long time after the person stopped moving will therefore remain the same.
The Enterprise wants to orbit a4.15 x 10^24kg planet with a period of14100 s. What should the radius oftheir orbit be?
Given:
Mass of planet, m = 4.15 x 10²⁴ kg.
Period, T = 14100 s
Let's find the radius.
To find the radius, apply the formula from Kepler's Third aw:
\(\begin{gathered} \frac{T^2}{R^3}=\frac{4\pi^2}{GM} \\ \\ \end{gathered}\)Where R is the radius.
Rewrite the formula for r:
\(R=\sqrt[3]{\frac{GM*T^2}{4\pi^2}}\)Where:
G is gravitational constant = 6.67 x 10⁻¹¹ m3 kg-1 s-2
M is the mass = 4.15 x 10²⁴ kg
T is the period = 14100 s
π = 3.54
Plug in values and solve for R;
\(\begin{gathered} R=\sqrt[3]{\frac{6.67\times10^{-11}*4.15\times10^{24}*14100^2}{4\pi^2}} \\ \\ R=\sqrt[3]{\frac{5.503\times10^{22}}{39.4784}} \\ \\ \end{gathered}\)Solving further:
\(\begin{gathered} R=\sqrt[3]{1.394\times10^{21}} \\ \\ R=11170796.49\approx1.12\times10^7\text{ m} \end{gathered}\)Therefore, the orbital radius will be 1.12 x 10⁷ meters.
ANSWER:
1.12 x 10⁷ m
what is similar between scientific theory and scientific law
Answer:
Explanation:
In general, a scientific law is the description of an observed phenomenon. It doesn't explain why the phenomenon exists or what causes it. The explanation of a phenomenon is called a scientific theory.
Caregivers should begin reading to children:
When they are babies.
When they can talk.
When they show an interest.
When they are two.
When they are preschoolers.
Answer:
When they are babies. to get them familar with it
Explanation:
Pls choose brainliest.
Answer:
When they are babies
Explanation:
Because they could hear the words and laern them.
Physical Science B - Accommodated Final
1) A gardener moves 5 kilograms bag of soil at an average acceleration rate of 4 m/s to her flower bed, a distance of 5 meters. How much work does the gardener do? Equations - Work = Force x Distance, Force = mass x acceleration
a. 100 n
b.22n
2) It takes 1000 N of force to lift a go kart onto a work table. If the mechanic uses a pulley with a mechanical advantage of 4 to lift the kart, how much force is needed?
a.4000 n
b.250 n
3) What is the advantage of class 3 lever?
a. It increases the distance over which a force needs to be applied
b. It decreases the distance over which a force needs to be applied
4) One end of the lever is pushed down 2 meters to lift a heavy bag up to a surface 1 meter off the ground. If it takes 1000 N of force to lift the bag directly, what amount of force is needed to lift it with the lever?
a. 500 n
b. 2000 n
5) A team of students builds a lever as a science project. They expend 100 Joules of energy to lift some bricks with the lever. If 60 Joules of energy are applied to the bricks, what is the lever’s efficiency?
a. 160%
b. 60%
The two terms that have been included in the question are:1. Physical Science2. Accommodated FinalNow let's proceed to the question.The statement "It increases the distance over which a force needs to be applied" is describing the property of mechanical advantage.
It's important to note that there are three ways to express mechanical advantage:MA = output force / input forceMA = input distance / output distanceMA = output speed / input speedLet's examine how the different expressions for mechanical advantage apply to the given statement:a. "It increases the distance over which a force needs to be applied."We can see that this expression describes mechanical advantage in terms of distance, which means that MA = input distance / output distance. In this case, the output distance is greater than the input distance, which means that MA is greater than 1. This means that the force applied is multiplied by a factor equal to the mechanical advantage. Therefore, the correct answer is (a)It increases the distance over which a force needs to be applied.Now let's answer the second part of the question:We have to find the percentage increase from 2000 to 160%.Here's how we can do it:First, we need to find the difference between the two values:160% - 2000 = -1840Next, we need to find the percentage change from the initial value to the final value:|-1840 / 2000| × 100% = 92%Therefore, the percentage decrease from 2000 to 160% is 92%.Hence, the answer is 92% in 200 words.For such more question on mechanical
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Question 10 Marks: 1 The valley or ravine landfill method utilizes "lifts" from the bottom up with depths usually ofChoose one answer. a. 6 to 8 feet b. 8 to 10 feet c. 10 to 12 feet d. 12 to 14 feet
The valley or ravine landfill method utilizes "lifts" from the bottom up with depths usually of 6 to 8 feet.
This means that the landfill is built up in layers or lifts, with each layer being 6 to 8 feet deep. The waste is then compacted and covered with a layer of soil before the next lift is added. This method is used in valleys or ravines because it allows for the natural contours of the land to be used, minimizing the need for excavation and land disturbance. It also helps to contain the waste in a specific area, making it easier to manage and monitor. Overall, the valley or ravine landfill method is an efficient and environmentally responsible way to dispose of waste.
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Which circuit would have the most electrical power?
OA. A. 1 = 2.0 A = V = 0.17 V
B. 1 = 1.2 A V = 0.14 V
the answer is c because it has the most volts
a
2) It takes an average 19,080 seconds for light to reach Pluto (Pluto's orbit varies quite a bit!). The
speed of light is in number 1. How far would Pluto be from the Sun at that particular point in its orbit
The average distance of Pluto is 3.7 billion miles or 5.9 billion kilometers, 39 astronomical units away from the Sun.
From a median distance of three.7 billion miles. Pluto is 39 astronomical units far away from the solar. One astronomical unit is the space from the solar to Earth. From this distance, it takes daylight five.
Mild from the solar takes about 5.5 hours to reach Pluto at its common distance (39. four AU). Pluto turned into founded in 1930 and turned at the beginning considered the ninth planet from the sun.
Sunlight travels at the rate of mild. Photons emitted from the surface of the sun want to travel across the vacuum of space to attain our eyes. the short solution is that it takes daylight an average of eight mins and 20 seconds to travel from the sun to the Earth.
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At what temperature does a process with [delta]h = 20. kj and [delta]s = 300. j become spontaneous? (give the answer in 3 sig figs)
The Temperature at a process with ΔH and ΔS become spontaneous is 66.6k
Gibbs free energy - It can be defined as that can be used to calculate the amount of work done performed by a closed system at constant temperature and pressure.
It's symbol is G.
Gibbs free energy equation is given as
ΔGΔH−TΔS
where
ΔG = Gibbs free energy.
ΔH = Enthalpy change.
T = Temperature in Kelvin.
ΔS = Entropy change.
ΔH= 20kJ = 20000J
ΔS= 300J/K
if ΔG<0, process is spontaneous
if ΔG>0, process is non spontaneous
if ΔG=0, process is in equilibrium
To find the temperature at which the given reaction becomes spontaneous, the minimum T value for which we obtain a negative value of the Gibbs free energy change is
ΔH−TΔS > 0
T > ΔH/ΔS
We have ΔH=20kJ=20000J
ΔS= 300J/K
T > 20000/300
T> 66.6K
The Temperature at a process with ΔH and ΔS become spontaneous is 66.6k
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Which would ba another example of newtons first law?
A 4.0 kg mass is 1.0 m away from a 7.0 kg mass. What is the gravitational force between the two masses? (Remember to use the gravitational constant, G = 6.67 x 10-11 N x m2/ kg2, in your calculation.)
6.67 x 10 -11 N
1.9 x 10 -9N
6.67 x 10 10N
3.8 N
The gravitational force between the two masses is approximately 1.96 x 10⁻⁹ N. Option B is correct.
The gravitational force between two masses can be calculated using the formula;
F=G x (m₁ x m₂) / r²
Where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between their centers of mass.
In this case, m₁ = 4.0 kg, m₂ = 7.0 kg, r = 1.0 m, and G = 6.67 x 10⁻¹¹ N x m²/kg². Plugging these values into the formula gives;
F = (6.67 x 10⁻¹¹ N x m²/kg²) x (4.0 kg x 7.0 kg) / (1.0 m)²
F = 1.96 x 10⁻⁹ N
Therefore, the gravitational force is 1.96 x 10⁻⁹ N.
Hence, B. is the correct option.
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--The given question is incomplete, the complete question si
"A 4.0 kg mass is 1.0 m away from a 7.0 kg mass. What is the gravitational force between the two masses? (Remember to use the gravitational constant, G = 6.67 x 10-11 N x m2/ kg2, in your calculation.) A) 6.67 x 10 -11 N B) 1.9 x 10 -9N C) 6.67 x 10 10N D) 3.8 N."--
parfit thinks that claiming god as being the cause of the big bang is:
Parfit, a prominent philosopher, argues that claiming God as the cause of the Big Bang is problematic. He suggests that using God as an explanation for the origin of the universe is not satisfying, as it merely replaces one mystery with another.
Additionally, Parfit asserts that invoking God as the cause of the Big Bang raises questions about the nature of God. Furthermore, Parfit asserts that science provides a more plausible explanation for the origin of the universe. Scientists have proposed various theories, such as the inflationary model and the cyclic model, that attempt to explain the origins of the universe without the need for a divine creator.
In conclusion, Parfit does not find the argument that God caused the Big Bang to be convincing, as it raises more questions than it answers. Instead, he advocates for relying on scientific theories to explain the origins of the universe.
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A bat hits a baseball with a force of 500N. The magnitude of the force that the baseball exerts on the bat is...
Answer:
45
Explanation:
because
The magnitude of the force that the baseball exerts on the bat is 500 N.
The given parameters;
force applied on the baseball by the bat, F₁ = 500 NAccording to Newton's third law of motion, action and reaction are equal and opposite. That is, when an object A exerts a certain force on another object B, the reaction of object B is equal to the magnitude of the force exerted by object A but in opposite direction.
Let the force the baseball exerts on the bat = F₂
then, from Newton's third law, we will have the following;
F₁ = -F₂
500 = -F₂
-500 N = F₂ (500 N is magnitude while the negative sign is the direction)
Thus, the magnitude of the force that the baseball exerts on the bat is 500 N.
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q1. let us assume that, s small balls, each of mass m hit a surface elastically each second with a velocity u m/s. calculate the force witnessed by the surface.
The force witnessed by the surface would be force = number of balls × mass of each ball × velocity of each ball
The force witnessed by the surface when small balls hit it elastically can be calculated by using the principle of momentum transfer. The force is equal to the rate at which momentum is transferred to the surface. Since the balls are hitting the surface elastically, this means that the balls will rebound with the same velocity that they hit the surface.
Therefore, the force witnessed by the surface can be calculated by multiplying the number of small balls, mass of each small ball and the velocity of each small ball, by the equation:
force = number of balls × mass of each ball × velocity of each ball.
This equation assumes that all balls are identical and hit the surface at the same velocity.
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In the vertical mass spring system with air resistance the displacement is the function u(t)
mu ′′+γu ′+ku=0
Prove that when m, y and k are greater or equal to 0, the system will return to the equilibrium when t tend to infinity.
When m, γ, and k are greater than or equal to 0 in the vertical mass-spring system with air resistance, the system will return to equilibrium as time tends to infinity.
In the given differential equation mu ′′+γu ′+ku=0, where m, γ, and k represent the mass, damping coefficient, and spring constant respectively, the terms involving these variables determine the behavior of the system.
When m, γ, and k are greater than or equal to 0, it implies that the mass, damping, and spring properties are non-negative. This means that the system has physical properties that allow for stability and convergence to equilibrium.
The term mu ′′ represents the inertia force, γu ′ represents the damping force, and ku represents the spring force. When these forces are balanced and there are no external forces, the system is in equilibrium.
In the absence of external forces and with non-negative values for m, γ, and k, the system's dynamics will eventually dampen out the initial displacement, bringing the system back to equilibrium. This behavior is observed as time tends to infinity.
The non-negativity of these parameters ensures that the forces acting on the system do not cause uncontrollable oscillations or instability, leading to a return to equilibrium over time.
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which is the correct range for the temperature danger zone? question 2 options: 0-32f 40-100f 40-140f 100-200f
The correct range for the temperature danger zone is 40-140°F.
The temperature danger zone refers to the range of temperatures in which bacteria can grow and multiply rapidly, posing a risk of foodborne illnesses. The correct range for the temperature danger zone is 40-140°F (4-60°C). Within this temperature range, bacteria can multiply quickly, reaching dangerous levels that can lead to food poisoning.
Temperatures below 40°F (4°C) can slow down bacterial growth, while temperatures above 140°F (60°C) can kill most bacteria. However, between 40-140°F, bacteria thrive and can double in number every 20 minutes, increasing the risk of foodborne illnesses.
Maintaining proper temperature control is crucial in food safety to prevent bacterial growth and minimize the risk of foodborne illnesses. This is particularly important for perishable foods such as meats, poultry, fish, dairy products, cooked rice, and cooked vegetables.
To ensure food safety, it is recommended to keep cold foods below 40°F (4°C) and hot foods above 140°F (60°C).
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how many significant figures are needed in the distance?
When measuring distance, you need eight significant figures.
The range of values that can be rationally attributed to a determined quantity by contrasting a parameter with the results of a measurement is represented by uncertainty.
The formula for percent distance uncertainty is as follows:
% Uncertainty = ( uncertainty in distance) / ( original value) × 100
data provided
haziness in the distant, ⁺ 2m
satellite's distance, 20000km
Calculating the percentage of uncertainty in a distance is as follows:
% Uncertainty = ( ⁺ 2m × \(\frac{10^{-3 } km}{1 km}\)) / (20000 km) × 100
= 1 × 10⁻⁵ %
The distance should be converted as follows:
d = (20000km) (10³/1)
= 20000000 km
Uncertainty exists in the distance between the satellite and the Earth, which is:
d = 20000000 km ⁺ 2m
Thus, the measurement of distance requires eight significant figures.
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Correct question:
Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to +-2m, what percent uncertainty in the distance is required? How many significant figures are needed in the distance?
The uncertainty in the distance is 1 × 10⁻⁵ % , and eight significant figures are needed in the distance.
the stability of a isotope nucleus depends on?
Answer:
It depends on the ratio of nuetrons to protons
A 600-kg car is moving at 5 m/s then comes to a stop
in 3 seconds. How much average force is necessary?
The average force acting on the car is 1000 N.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Given that: A 600-kg car is moving at 5 m/s then comes to a stop in 3 seconds.
Now according to Newton's 2nd law of motion:
Magnitude of force applied on the body = change in momentum/time interval
= I final momentum - initial momentum I/time interval
= I 0 - 600×5 I /3 N
= 10000 N
Hence, average force acting on the car is 1000 N.
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On a keyboard, you strike middle C, whose frequency is 256. 0 Hz. Find the period of one vibration of this tone
The period of one vibration of the tone will be 0.00390625 seconds.
Period of waveThe period (T) of a waveform is the time it takes for one complete cycle or vibration. It is calculated as the inverse of the frequency (f) of the waveform.
So, if the frequency of middle C is 256.0 Hz, then the period of one vibration of this tone is:
T = 1/f
T = 1/256.0 Hz
T = 0.00390625 seconds
Therefore, the period of one vibration of middle C is approximately 0.00390625 seconds.
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Explain the image below in terms of Newton’s Laws.
The image given, is explained in terms of Newton's 1st law of motion.
What is Newton's 1st law of motion?Based on Newton's First Law of Motion (Inertia). An object at rest remains at rest, and an object in motion continues in motion at a steady speed and in a straight path until operated on by an unbalanced force.
Newton's first rule of motion states that if a pan of water were being moved along a track, the water would tend to keep moving ahead. However, the water will appear to splash to the right while it goes to the left. Space is nearly a perfect vacuum, devoid of both gravity and matter. Think about a satellite travelling 17,500 mph around the Earth. If a rock were to be launched from the satellite, it would orbit the earth adjacent to the satellite at a speed of 17,500 mph.
Here, in the given image, it is shown that the sofa is remain in the place unless a person forcefully move it from one place to another.
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What happens to the gravitational force between two objects when the distance between them is reduced by 50%?
A the gravitational force decreases by 50%
B the gravitational force increases by 50%
Cthe gravitational force decreases by 25%
the gravitational force increases by 400%
Question 8
Answer:
B
Explanation:
Water is flowing in a pipe with a varying cross-sectional area, and at all points, the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.070 m^{2}0.070m 2, and the magnitude of the fluid velocity is 3.50 m/s.
(a) What is the fluid speed at points in the pipe where the cross-sectional area is (a) 0.105 m and (b) 0.047m^2?
(c) Calculate the volume of water discharged from the open end of the pipe in 1.00 hour.
The fluids speed at a) 0.105m² and b) 0.047m² are 2.33m/s² and 5.21 m/s² respectively
For solving a) and b) we should use flow continuity for ideal fluids:
ΔQ = 0 ----1
With Q the flux of water, but Q is Av using this on (1) we have:
A2v2-A1v1 = 0---2
With A the cross sectional areas and v the velocities of the fluid.
a) Here, we use that point 2 has a cross-sectional area equal to A2 = 0.105m2 , so now we can solve (2) for :
v2= 2.33 m/s
b) Here we use point 2 as A2 = 0.047m² :
v2 = 5.21 m/s
c) Here we need to know that in this case the flow is the volume of water that passes a cross-sectional area per unit time, this is Q= V/t , so we can write:
A1v1 = V/t , solving for V:
V = A1v1t = (0.070m2)(3.5m/s)(3600s) = 882 m³
What is Bernoulli's theorem?
According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy. The mathematical concept is named after Swiss mathematician Daniel Bernoulli, who first published it in his book Hydrodynamics in 1738.
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