Answer:
Overgrazing, which refers to the overutilization of grazing resources, by livestock promotes the increase in undesirable herbaceous plant species and bush encroachment, which are all indicators of rangeland degradation
What role do hypnosis in scientific inquiry
hypnosis, a growing body of scientific research supports its benefits in treating a wide range of conditions, including pain, depression, anxiety and phobias. "Hypnosis works and the empirical support is unequivocal in that regard.
A 48.0-kg diver jumped to a maximum height of 11.0 meters. From there, the diver falls from rest and hits the pool at a speed of 8.81 m/s. How much energy was transferred into thermal energy during the fall?
Approximately 3,299.9 J of energy was transferred into thermal energy during the fall of the diver.
To determine the amount of energy transferred into thermal energy during the fall of the diver, we can use the principle of conservation of energy.
The initial potential energy of the diver at the maximum height is given by:
Potential Energy (PE) = m * g * h
Where:
m = mass of the diver (48.0 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = maximum height (11.0 m)
Substituting the given values:
PE = 48.0 kg * 9.8 m/s^2 * 11.0 m = 5,219.2 J
The final kinetic energy of the diver just before hitting the pool is given by:
Kinetic Energy (KE) = (1/2) * m * v^2
Where:
m = mass of the diver (48.0 kg)
v = speed of the diver (8.81 m/s)
Substituting the given values:
KE = (1/2) * 48.0 kg * (8.81 m/s)^2 = 1,919.3 J
The difference between the initial potential energy and the final kinetic energy represents the energy transferred into thermal energy:
Energy transferred into thermal energy = PE - KE
= 5,219.2 J - 1,919.3 J
= 3,299.9 J
Therefore, approximately 3,299.9 J of energy was transferred into thermal energy during the fall of the diver.
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5. To push a box up an inclined plane, is the force required smaller if you push horizontally
or if you push parallel to the incline? Why?
To push a box up an inclined plane, the force required is smaller if you push parallel to the incline.
What is an Inclined plane?This is also referred to as a ramp and is a flat surface which is tilted at an angle.
Pushing parallel to the plane doesn't generate friction which means a smaller amount of force will be required.
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please ans. Ill mark brainliest.
a. The value of t is 5 seconds.
b. The maximum velocity of the particle is 20 m/s.
c. The distance traveled with uniform velocity is 50 meters.
How to calculate the valueFrom the graph, we can see that the velocity (V) decreases linearly with time (t) until it reaches zero at t = 10 seconds. After that, the velocity increases linearly until t = 20 seconds.
a) We can use the equation of motion:
V = U + at,
0 = 20 + (-4)t,
-4t = -20,
t = 5 seconds.
Therefore, the value of t is 5 seconds.
b) From the graph, we can see that the maximum velocity occurs at t = 20 seconds, where the velocity is 20 m/s. This is the maximum velocity during the journey. Therefore, the maximum velocity of the particle is 20 m/s.
c) The distance traveled with uniform velocity: During the acceleration phase (0 seconds to 5 seconds):
We can calculate the distance using the equation:
d = (U + V) * t / 2,
d = (0 + 20) * 5 / 2,
d = 50 meters.
Therefore, the distance traveled with uniform velocity is 50 meters.
Overall, the particle travels a total distance of 50 meters with uniform velocity during the motion.
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What is the fastest bird
Answer:
Peregrine Falcon/hawk
Explanation:
i really dunno if you are talking about brids that can't fly or not.
2. What is the mass of an object that was accelerated at a rate of 1 m/s with a force of 2 N
Answer:
2 kilograms
Explanation:
F = ma
2 = 1m = 2
6. A 286 kg gold nugget is attached to the ceiling by a spring with a constant of 9500 N/m and
released from a height of 1.70 m above the floor. If the spring stretches 59.0 cm, what is the elastic
potential energy associated with the spring-nugget system?
4764 joule is potential energy associated with the spring-nugget system
Potential energy ,P =mgh
mass= 286 kg
g=9.8 m/s^2
h= 1.70 m
P =mgh
P=×286 kg×9.8×1.70
P=4764 joule
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is squeezed or extended, its potential energy increases. If a steel ball is lifted above the ground as opposed to falling to the ground, it has higher potential energy. It is capable of performing more work when raised. Potential energy is a characteristic of systems rather than of particular bodies or particles; for instance, the system made up of Earth and the elevated ball has greater potential energy as they get further apart.
Potential energy develops in systems having components whose configurations, or relative positions, determine the amount of the forces they apply to one another.
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a car with a mass of 1200 kg travels a distance of 150 M as it moves from one stoplight to the next at its fastest the car travels at 22 m per second what is its kinetic energy at this point
Answer:
ke = 1/2mv^2
= 1/2 * 1200 * 22^2
= 600 * 484
= 290400 J
Hope it helped u,
pls mark this as brainliest
and put thanks
^_^
Answer:
The kinetic energy at this point 290,400
A ball is thrown up into the air. When it gets to the very top,
what kind of energy does it have?
At the highest attitude, the velocity of the ball is 0 m/s, so the kinetic energy is 0 as well.
Hence the answer is potential energy because it doesn't depend on velocity .
A crate with a mass of 35.0 kg is pushed with a horizontal force of 150 N. The crate moves at a constant speed across a level, rough surface a distance of 5.85 m
(a) The work done by the 150 N force is 877.5 Joules.
(b) The coefficient of kinetic friction between the crate and the surface is approximately 0.437.
To answer this problem, we must take into account the work done by the applied force as well as the work done by friction.
(a) The applied force's work may be estimated using the following formula:
Work = Force * Distance * cos(theta)
where the force is 150 N and the distance is 5.85 m. Since the force is applied horizontally and the displacement is also horizontal, the angle theta between them is 0 degrees, and the cosine of 0 degrees is 1.
As a result, the applied force's work is:
Work = 150 N * 5.85 m * cos(0) = 877.5 J
So, the work done by the 150 N force is 877.5 Joules.
(b) Frictional work is equal to the force of friction multiplied by the distance. The work done by friction is identical in amount but opposite in direction to the work done by the applied force since the crate travels at a constant speed.
The frictional work may be estimated using the following formula:
Work = Force of Friction * Distance * cos(theta)
The net force applied on the crate is zero since it is travelling at a constant pace. As a result, the friction force must be equal to the applied force, which is 150 N.
Thus, the work done by friction is:
Work = 150 N * 5.85 m * cos(180) = -877.5 J
Since the work done by friction is negative, it indicates that the direction of the frictional force is opposite to the direction of motion.
The coefficient of kinetic friction may be calculated using the following equation:
Friction Force = Kinetic Friction Coefficient * Normal Force
The normal force equals the crate's weight, which may be computed as:
Normal Force = mass * gravity
where the mass is 35.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Normal Force = 35.0 kg * 9.8 m/s^2 = 343 N
Now, we can rearrange the equation for the force of friction to solve for the coefficient of kinetic friction:
Force of Friction = coefficient of kinetic friction * Normal Force
150 N = coefficient of kinetic friction * 343 N
coefficient of kinetic friction = 150 N / 343 N ≈ 0.437
As a result, the kinetic friction coefficient between the container and the surface is roughly 0.437.
In summary, the work done by the 150 N force is 877.5 Joules, and the coefficient of kinetic friction between the crate and the surface is approximately 0.437.
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mention examples of linear motion
Answer:
firing a bullet
parade
swimming on a straight line
elevators
playing slide
In albinism is not produced?
Explanation:
The term albinism typically refers to oculocutaneous (ok-u-low-ku-TAY-nee-us) albinism (OCA) — a group of inherited disorders where there is little or no production of the pigment melanin. The type and amount of melanin your body produces determines the color of your skin, hair and eyes.
A) The motor speed is less than wheel speed.
B) The output power of the motor is positive during hill climbing.
C) The wheel torque is more than motor torque.
For the following statements
A) The motor speed is less than wheel speed.
B) The output power of the motor is positive during hill climbing.
C) The wheel torque is more than motor torque
These assertions are given respectively as
falsetruefalseWhat are speed, power, and Torque?Speed: defined as the ratio of operation with respect to distance and time
Power: defined as the ability to work
Torque: This is the speed of a rotating object
Generally, the equation for Speed, Power, Torque is mathematically given as
V=m/s
P=w/t
T=rfsin\theta
In conclusion
For a moving car, the wheels speed is in equilibrium with the motor speed Hence false
The output power during a hill climb is positive cause work is been done, Hence true
The wheel torque also is in equilibrium with the motor Torque, Hence false
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explain why a wrecking ball can destroy a building, but a yo-yo cant. Use the term kinetic energy in your explanation.
The kinetic energy of a body determines it's level of impact on the object in which it comes in contact with. Hence, the much larger kinetic energy exhibited by a wrecking ball compared to a yo-yo means that is has a much larger impact on a building than a yo-yo.
Kinetic Energy = 0.5mv²The kinetic energy of a body is a factor of it's velocity and mass as they are directly proportional.
The wrecking ball has a very large mass which is thousands of times larger than that of a yo-yo. Also, the velocity at which a wrecking ball is launched is higher than the velocity of a yo-yo.
This means that the kinetic energy of a wrecking ball is much higher than that of yo-yo. Hence, having much greater impact on a building compared to a yo-yo.
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Which event causes the formation of trenches in Earth’s crust?
magma rising
mantle emerging
volcanoes erupting
lithosphere colliding
Answer:
D lithosphere colliding
Reason:
Image result for what causes the formation of trenches in Earth’s crust
Trenches are formed by subduction, a geophysical process in which two or more of Earth's tectonic plates converge and the older, denser plate is pushed beneath the lighter plate and deep into the mantle, causing the seafloor and outermost crust (the lithosphere) to bend and form a steep, V-shaped depression.
The formation of trenches in Earth's crust is caused by the collision of lithospheric plates, so the correct answer is "lithosphere colliding."
What are trenches in Earth's crust?Trenches are long, narrow depressions or canyons in the Earth's crust that form at subduction zones, where one lithospheric plate is forced beneath another plate into the Earth's mantle. Trenches are primarily found on the ocean floor, where they can be several kilometers deep and hundreds of kilometers long.
Trenches are formed by the process of subduction, which occurs when one tectonic plate moves beneath another plate. As the denser plate sinks into the mantle, it creates a deep trench in the ocean floor. This process is associated with volcanic activity, as the sinking plate often triggers the melting of rock in the mantle, which can then rise to the surface and form volcanic islands or arcs.
Trenches are important features of the Earth's crust because they provide evidence for the movement and interaction of tectonic plates over time. Additionally, they are often associated with earthquakes and can serve as warning signs of potential seismic hazards in the surrounding region.
Therefore, lithosphere colliding causes the formation of trenches in Earth’s crust.
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A bike accelerates uniformly from rest to a speed of 10 m/s over a distance of 50 m. (a) Determine the acceleration of the bike. (b) how long will take to do that?
Answer:
a) 0.2m/s
b) 5m/s
Explanation:
a) acceleration=∆v/∆t
v=10
t=50
10/50=1/5
=0.2m/s
b) time= d/s
d=50m
s=10
50/10
=5m/s
Answer:
See below
Explanation:
Average speed = (0+ 10)/2 = 5 m/s
then to cover 50 m will take 50 m / 5 m/s = 10 seconds
change in velocity/ change in time = acceleration = 10/10 = 1 m/s^2
Experiment to find ways to make rainbows.
a) Insert at least one setup where light passing through a prism gives a rainbow and describe why a rainbow is formed.
b) Explain why only some types of light will yield rainbows.
Answer:
Explanation:
a) To get a rainbow from a prism arrangement, we will need
A triangular prismA black cardboard boxA source of white light (light from the window will suffice)A pocket knifeFirst, you cut a slit in one end of the cardboard with the pen knife.
Next you open up a space on top of the cardboard through which you can observe the experiment and its result.
Next, you place the triangular prism with its slant face facing the the cut slit.
Finally, position the slit to face the light from the open window, and adjust the prism till the projected bands of colored light (rainbow) is very much obvious on the other end of the box, opposite the slit.
b) For a light to yield rainbow, it most be composed of different component colors of light. The colors of light is due to the difference in wavelength, and dispersion is due to the different in the wavelengths of the component light. So to get rainbow from a light source, the light must not be monochromatic. This means that only light composed of component light of different colors can produce rainbow. Light from the sun for example is composed of 7 distinct colors of light, and white light can be created with just three colors; blue, green, and red light.
Three loads are applied attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P = 0. as shown to a light beam supported by cables 7.5 kN Q P С E А В 1.5 m- 0.75 m 0.5 m 0.75 m Fig. P4.9
When\(P = 0, Q\)must be in the range between \(4.3 kN and 12.9 kN\) to prevent either cable from becoming slack.
We may examine the forces operating on the beam to find the range of values for Q. The sum of the vertical forces must be zero when \(P = 0,\)which indicates that the beam is in equilibrium. Our result is the equation:
\(Q + 7.5 - 3 - 4 = 0\)
When Q is solved for, we obtain \(Q = 0.5 kN to 12.9 kN.\) To prevent either wire from going slack, we must also ensure that both cables are under positive stress. We can accomplish this by searching for the extreme values of Q in each cable's tensions.
\(Q = 0.5 kN\)results in a positive 7.5 kN tension in cable AB. However, cable DE's tension is negative\((-2.5 kN)\), indicating that cable DE is under tension. is loose.
\(Q = 12.9 kN\) results in a positive \(3.4 kN\) tension in cable DE. Cable AB, however, has negative tension \((-5.4 kN),\) indicating that it is slack.
The range of Q values that satisfy the requirement that neither cable sags when \(P = 0 is 4.3 kN to 12.9 kN.\)
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According to the Keynesian view, manipulating foreign sector spending is not a reliable way to move the U.S. economy toward a more acceptable equilibrium because __________.
According to the Keynesian view, manipulating foreign sector spending is not a reliable way to move the U.S. economy toward a more acceptable equilibrium because it does not address the fundamental causes of economic instability.
Keynesian economics focuses on the role of domestic demand in driving economic growth and stability. The government can use fiscal and monetary policy to stimulate aggregate demand and promote full employment. However, changes in foreign sector spending can be unpredictable and beyond the control of domestic policymakers. For instance, an increase in foreign demand for U.S. exports could boost economic growth and employment in the short run, but it may not be sustainable if the foreign demand later decreases. Similarly, a decrease in foreign demand for U.S. exports could have negative short-term effects on the economy, but it may not necessarily lead to a long-term decline. In short, Keynesian economics emphasizes the importance of domestic demand management and stabilizing the economy through government intervention. While changes in foreign sector spending can have some impact on the economy, they are generally seen as unreliable and unpredictable, and therefore not a reliable tool for achieving economic stability in the long run.
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Which of the following equations defines the law of conservation of energy?
total energy = kinetic energy - potential energy
total energy = kinetic energy - potential energy
total energy = potential energy - kinetic energy
total energy = potential energy - kinetic energy
total energy = kinetic energy + potential energy
total energy = kinetic energy + potential energy
total energy = kinetic energy x potential energy
Answer:
Total energy =kinetic energy +potential energy.
Answer:
Kinetic Energy + Potential Energy = total energy
Explanation:
The conservation of mechanical energy can be written as “KE + PE = const”. Though energy cannot be created nor destroyed in an isolated system, it can be internally converted to any other form of energy.
Find the work done (in ft-lb) when a constant force F = 18 lb moves a chair from x = 0.6 to x = 1.4 ft.
Answer:
The work done is 14.4 lb-ft
Explanation:
Given;
constant force, F = 18 lb
initial position of the chair, x₁ = 0.6 ft
final position of the block, x₂ = 1.4 ft
Work is said to be done, when an applied force moves an object through a distance.
W = F x d
where;
F is the applied force
d is the distance moved by the object
Distance moved by the object, d = x₂ - x₁
d = 1.4ft - 0.6 ft
d = 0.8 ft
W = F x d
W = 18 lb x 0.8 ft
W = 14.4 lb-ft
Therefore, the work done is 14.4 lb-ft
1. Two forces act on a box as follows: F1 = 100 N at 01 = 170° and F2 = 75 N
at 02 = 30°. Find their resultant force on the box.
(a) the magnitude of vector sum Fi + F2
(b) the direction of of the vector sum Fi + F2
Answer:
a) F = 64.30 N, b) θ = 121.4º
Explanation:
Forces are vector quantities so one of the best methods to add them is to decompose each force and add the components
let's use trigonometry
Force F1
sin 170 = F_{1y} / F₁
cos 170 = F₁ₓ / F₁
F_{1y} = F₁ sin 170
F₁ₓ = F₁ cos 170
F_{1y} = 100 sin 170 = 17.36 N
F₁ₓ = 100 cos 170 = -98.48 N
Force F2
sin 30 = F_{2y} / F₂
cos 30 = F₂ₓ / F₂
F_{2y} = F₂ sin 30
F₂ₓ = F₂ cos 30
F_{2y} = 75 sin 30 = 37.5 N
F₂ₓ = 75 cos 30 = 64.95 N
the resultant force is
X axis
Fₓ = F₁ₓ + F₂ₓ
Fₓ = -98.48 +64.95
Fₓ = -33.53 N
Y axis
F_y = F_{1y} + F_{2y}
F_y = 17.36 + 37.5
F_y = 54.86 N
a) the magnitude of the resultant vector
let's use Pythagoras' theorem
F = Ra Fx ^ 2 + Fy²
F = Ra 33.53² + 54.86²
F = 64.30 N
b) the direction of the resultant
let's use trigonometry
tan θ’= F_y / Fₓ
θ'= \(tan^{-1} \frac{F_y}{F_x}\)
θ'= tan⁻¹ (54.86 / (33.53)
θ’= 58.6º
this angle is in the second quadrant
The angle measured from the positive side of the x-axis is
θ = 180 -θ'
θ = 180- 58.6
θ = 121.4º
A car starts from rest and accelerates at a constant rate in a straight line. In the first second the car moves a distance of 2.0 meters. How much additional distance will the car move during the second second of its motion?
Since the car is accelerating at a constant rate, the distance it travels during each second of its motion will be directly proportional to the time it has been accelerating.
In the first second, the car moved a distance of 2 meters, and in the second second, it will move twice the distance of the first second, so the car will move additional distance of 2*2 = 4 meters during the second second of its motion.
The distance traveled during the second second of its motion is 1/2 * 2 = 1 meters.
A car that accelerates at a constant rate will move a distance equal to the initial velocity multiplied by time plus 1/2 the acceleration multiplied by the square of time. Since the car starts from rest, the initial velocity is zero.
Therefore, the distance traveled during the second second is 1/2 * acceleration \(* (time)^2 = 1/2 * a * t^2 = 1/2 * a * 1^2 = 1/2 * a\) Since the car moved 2.0 meters in the first second, it means the acceleration is\(2m/s^2\), and the distance traveled during the second second is 1/2 * 2 = 1 meters.
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The magnetic flux that passes through one turn of a 8-turn coil of wire changes to 5.0 Wb from 8.0 Wb in a time of 0.098 s. The average induced current in the coil is 140 A. What is the resistance of the wire
Answer:
Resistance is 1.75 ohms
Explanation:
Magnetic flux:
\({ \phi{ = NBA}}\)
N is number of turns, N = 8
B is magnetic flux
A is area of projection.
From faradays law:
\(E = - \frac{ \triangle \phi}{t} \)
where E is the Electro motive force.
But E = IR
where I is current and R is resistance:
\(IR = \frac{( \phi_{1} - \phi _{2}) }{t} \\ \\ 140 \times R = \frac{8 \times (8 - 5)}{0.098} \\ \\ R = \frac{24}{0.098 \times 140} \\ \\ resistance = 1.75 \: ohms\)
Calculate the molar heat capacity at pressure and volume constant ( ) when knowing = = 1.4 and the gas density: 0 = 1.3 /3 .
(a) The molar heat capacity at pressure is 29.1 J/K.mol.
(b) The molar heat capacity at volume is 20.785 J/K.mol.
Molar heat capacity of gas at volumeMolar heat capacity of a gas at constant volume is defined as the quantity of heat required to raise the temperature of one mole of the gas by 1 degree Kelvin when its volume is constant.
Cv = R/(γ - 1)
where;
R is universal gas constant = 8.314 J/K.mol.γ is heat ratio = 1.4Cv = (8.314) / (1.4 - 1)
Cv = 20.785 J/K.mol
Molar heat capacity of gas at pressureMolar heat capacity of a gas at constant volume is defined as the quantity of heat required to raise the temperature of one mole of the gas by 1 degree Kelvin when its pressure is constant.
γ = Cp/Cv
Cp = γCv
Cp = 1.4 x 20.785
Cp = 29.1 J/K.mol
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The NEC states the resistance of 4/0 coated
copper conductors is 0.0626 ohms per 1000
feet. What would be the total resistance of the
three 4/0 conductors installed in parallel, if the
total length for each of the three conductors is
323 feet?
Answer:
The resistance of 4/0 coated copper conductors is given as 0.0626 ohms per 1000 feet. To find the total resistance of the three 4/0 conductors installed in parallel, we can use the formula for combining resistances in parallel.
Since the total length for each of the three conductors is 323 feet, the resistance of each conductor can be calculated as follows:
Resistance of one conductor = (0.0626 ohms / 1000 feet) * 323 feet
To find the total resistance when the conductors are in parallel, we use the formula:
1/Total Resistance = 1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3
Total Resistance = 1 / (1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3)
Substituting the values, we get:
Total Resistance = 1 / (1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet))
Simplifying the expression will give us the total resistance of the three 4/0 conductors installed in parallel.
How much energy is needed to change the temperature of 50g of water 15°c
Explanation:
This question is not feasible. There is no way to calculate the energy needed because the question is missing the final temperature
t: The toy car is given a push away from the origin and released. It continues to move with a constant velocity. Sketch the force g 0' after the car is released. A cart is moving toward the right and speeding up, as shown in the diagram below. Draw arrows above the cart representing the magnitudes and directions of the net (combined) forces you think are needed on the cart at t = 0 s, t = 1 s, etc., to maintain its motion with a steadily increasing velocity. Assume that the cart is already moving at t_1. Explain the reasons for your answers. If the positive direction is toward the right, what is the sign of the force at t = 2 s in Question
The car will move at a constant speed once it is unleashed, as is assumed. Hence, there is no acceleration. Newton's second law states that a straight line along zero will appear on the graph if F=ma=m(0)=0, F=0.
Acceleration is the rate at which an object changes its velocity. It is a vector quantity, which means it has both magnitude and direction. The standard unit of acceleration is meters per second squared (m/s²).
Acceleration can be caused by forces such as gravity, friction, and electromagnetism. When a force acts on an object, it causes a change in the object's motion, resulting in acceleration.
The relationship between acceleration, velocity, and time is described by the equation a = (v_f - v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is time.
The effects of acceleration can be seen in everyday experiences, such as feeling pushed back into your seat when a car accelerates or feeling weightless during freefall. Understanding acceleration is important in fields such as physics, engineering, and transportation.
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PLASES HELP ASAP
A baseball bat company is testing a new alloy that they claim will improve the power of its bats for very weak or low-power batters. Given the provided data of three bat compositions, swing force, and resulting ball travel distance, what conclusion can be made regarding their new alloy? A) There is no hypothesis provided. B) The hypothesis of the company is refuted. C) The hypothesis of the company is verified. D) The hypothesis was neither verified or refuted.
Answer:
B.
Explanation:
I'm not sure if it's the right answer but I think it is. I hope I helped out in some way.
The anomalous expansion characteristics of liquid water are crucial to many biological systems. Rather than an approximately constant value for the coefficient of volume expansion, the value for water changes drastically, as illustrated in the figure.
Below what temperature T
does water shrink when heated?
If the temperature of water at 30 ∘C
is raised by 1 ∘C
, the water will expand. At approximately what initial temperature T
will water expand by twice as much when raised by 1 ∘C
?
(A) The water will shrink when is heated above 4°C. (B).water at an initial temperature of 33.3°C will be expand by twice as much when it is raised by 1°C compared to water at 30°C.
The anomalous expansion of water refers to the fact that its volume increases upon cooling from 4°C to 0°C, and then contracts upon further cooling to 0°C, and continues to contract upon further cooling. Similarly, when water is heated, its volume first contracts until it reaches 4°C, and then expands upon further heating.
To determine at what temperature water shrinks when heated, we need to find the point at which the coefficient of volume expansion, β, becomes negative. The coefficient of volume expansion is defined as the fractional change in volume per degree Celsius change in temperature, i.e.,
β = (1/V) (dV/dT)
where V is the volume of the water and dV/dT is the rate of change of volume with respect to temperature.
At temperatures below 4°C, the coefficient of volume expansion is positive, indicating that water expands upon heating. However, at temperatures above 4°C, the coefficient of volume expansion becomes negative, indicating that water contracts upon heating.
Therefore, water will shrink when heated above 4°C.
To determine the initial temperature at which water will expand by twice as much when raised by 1°C, we can use the formula for the coefficient of volume expansion:
β = (1/V) (dV/dT)
We want to find the initial temperature T such that
(dV/dT)T = 2 (dV/dT)30
where (dV/dT)T is the rate of change of volume with respect to temperature at temperature T, and (dV/dT)30 is the rate of change of volume with respect to temperature at 30°C.
Using the coefficient of volume expansion for water, we have
β = 3α
where α is the coefficient of linear expansion, which is approximately constant for small temperature changes. Therefore, we can write
(dV/dT) = V × 3α
Substituting this into the equation above and simplifying, we get
T = 30 + 10/3 = 33.3°C
Therefore, water at an initial temperature of 33.3°C will expand by twice as much when raised by 1°C compared to water at 30°C.
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