If you apply a greater force the spring constant will remain the same, since it is a constant.
What is Hooke's law?This law states that the force applied to an elastic material is directly proportional to the extension of the material.
That is as the force applied to an elastic material increases the extension of the elastic material increases provided the elastic limit of the material is not exceeded.
Mathematically, this law can be written as;
F = kx
where;
F is the applied forcek is the spring constx is the extension of the materialSo when the force applied is increased, the extension of the material increases as well.
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Draw the following vectors: (answer key, just need them drawn)
The diagram representing the vectors, A, B, R, and C for each of the questions is in the image attached.
What is the direction of the vectors?The direction of any vectors shows the angle of the vector taken from the positive x-axis.
The direction of the given vectors is determined as;
4. Vector A = 10 cm/s at 15⁰
Vector B = 7 cm/s at 300⁰ = 7 cm/s at 30⁰
Vector R = 13.61 cm/s at 345.23⁰ = 13.61 cm/s at 75.23⁰
5. Vector A = 6 miles at 180⁰
Vector B = 8 miles at 230⁰
Vector R = 12.71 miles at 208⁰
6. Vector A = 14 N at 155⁰
Vector B = 22 N at 168⁰
Vector C = 18 N at 100⁰
Vector R = 46.8 N at 142.9⁰
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A gasoline engine has a power output of 210 kW (about 282 hp ). Its thermal efficiency is 28.5%.
a) How much heat must be supplied to the engine per second? Express your answer in joules.
b) How much heat is discarded by the engine per second? Express your answer in joules.
The heat supplied the engine per second is 736 kJ and the heat discarded by the engine per second is 526 kJ.
A gasoline engine has a power output of 210kW and the effciency of engine is 28.5%. The Work done of the engine in time 1s is,
Work done = power × time
= 210 × 1
= 210 kJ
The work done of the engine is,W = 210 kW.
The efficiency of the engine,η = Work / (Qh)
Qh is the heat suppllied to the engine, η is the efficiency and is equal to 28.5 %
Qh = 210kW / (0.285)
= 736.8 kW
The heat discarded by the engine,
(Qc) = Qh - W'
= 736.8 - 210
=526.8 kW
The heat discarded by the engine, (Qc) = 526.8 kW
The heat supplied to the engine, (Qh) = 736.8 kW.
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1. Two waves approach each other on the same string. Which statement best describes the process of events that will happen?
a. The waves will approach, interfere with each other, then pass through each other having been altered by the interference process
b. The waves will approach, interfere with each other, then pass through each other after interfering, unchanged
c. The waves will approach, then they will bounce off each other and move away from each other as normal
d. The waves will approach, interfere with each other, then this interference will cancel them both out
2. Which of the following interferences would produce the largest amplitude resultant wave?
a. Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m)
b. Crest of wave 1 (8 m) combines with crest of wave 2 (1.1 m)
c. Crest of wave 1 (9.5 m) combines with the trough of wave 2 (3.5 m)
d. Trough of wave 1 (3.2 m) combines with the trough of wave 2 (2.8 m)
1. a. The waves will approach, interfere with each other, then pass through each other having been altered by the interference process.
2. a. Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m).
Two waves approach each other on the same string, undergo the process of interference, and then the output wave gets altered. Thus, option A is correct.
What is interference?Interference is the process of superimposing two waves. The phenomenon of two coherent waves is combined by adding their intensities, and displacements with respect to the phase change.
Interference is of two types: Constructive Interference and Destructive Interference. When the crests/trough of wave 1 is merged with the crests/trough of wave 2 gives Constructive interference and the output waves are larger in intensity and amplitude.
When the crest/trough of wave 1 is merged with the trough/crest of wave 2 results in Destructive Interference and there is no output waveform as the waves cancel each other.
From the given, two waves approach each other on the same string, interfere with each other, then pass through each other having been altered by the interference process. The crest of wave 1 (5m) is combined with crest of wave2 (11.8m).
Thus, the ideal solutions for statements 1 and 2 are Option A and Option A.
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What is the magnetic field at the position of the dot in (Figure 1)? Give your answer as the components of a vector.
Answer:
200000000000 x 10^-7
Explanation:
The Biot Savart Law defines fundamental quantitative relationship between an electric current and the magnetic field it produces, based on the experiments in 1820 of the French scientists Jean-Baptiste Biot and Félix Savart.
The Biot-Savart law is applied in a specific case by adding up the contributions to the magnetic field at a given point from the whole series of short current segments that constitute a specific conductor of whatever shape
A dog starts from point A and moves 15m toward the east, then turns 90 degrees south and moves 3m. His displacement is
The displacement of the dog is 15.3 meters at a bearing of 339.4 degrees (or about 20.6 degrees west of due north).
Displacement is a vector quantity that measures the change in position of an object from its initial position to its final position. It is the straight-line distance and direction between these two points.
To calculate the displacement, we need to find the straight-line distance and direction between the starting point A and the final point where the dog ends up.
The dog first moves 15m toward the east. This means that its position changes in the x-direction by 15m. We can represent this as a vector:
d1 = 15i
where i is the unit vector in the x-direction.
Next, the dog turns 90 degrees south and moves 3m. This means that its position changes in the y-direction by -3m (since south is in the negative y-direction). We can represent this as another vector:
d2 = -3j
where j is the unit vector in the y-direction.
To find the displacement, we can add these two vectors:
d = d1 + d2
= 15i - 3j
The magnitude of this vector is:
|d| = sqrt(15^2 + (-3)^2)
= sqrt(234)
≈ 15.3
So the dog's displacement is approximately 15.3 meters. To find the direction, we can calculate the angle that this vector makes with the positive x-axis:
theta = arctan(-3/15)
≈ -0.197
Since the angle is negative, we know that the vector points in the fourth quadrant. To express the direction as a compass bearing, we can add 360 degrees to the angle and convert to degrees:
theta_degrees = (-0.197 + 2*pi) * 180/pi
≈ 339.4
Hence, the dog's displacement is approximately 15.3 meters at a bearing of 339.4 degrees (or about 20.6 degrees west of due north).
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HELP! Photo attached worth 60+ points
The period of the wave from the calculation can be seen to be 10 s
What is the period of a wave?When we talk about the period of the wave what we mean is the inverse of the frequency of the wave. Thus the period and the the frequency of the wave are actually the opposites of each other as we know in physics.
Given f = 0.10 Hz
T = 1/f = 1/0.10
T = 10 seconds
In the study of wave motion, the period of a wave is a crucial variable that is employed in many fields, such as optics, seismology, and communication systems.
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lectric Charges
The glass is attracting the pieces of paper. What does
this tell you about the charges on the glass and the
paper?
The glass and the paper have the same charge.
O The glass and the paper have different charges.
ONeither the glass nor the paper has a charge.
Consider an elastic collision between two pucks on an air-hockey table (no friction). The first
puck has a mass of 0.500 kg and is travelling at 4.00 m/s along the x-axis. The second puck
has a mass of 0.300 kg and is at rest. After the collision, the first puck has a velocity of 2.00 m/s
in an unknown direction, O, and the second puck travels at an unknown velocity v2₂ and an
unknown direction of O₂. Determine the 3 missing values.
(6 marks)
Physic question help
The good conductors of heat and electricity are Penny, and An aluminum soda can.
option A and B.
What are good conductors of electricity?Good conductors of electricity are those materials that allow easy passage of electric current through them.
All metals are good conductors of electricity, and some of their examples include;
Aluminum
Copper
Silver
Zinc, etc
Poor conductors on the other hand do not allow easy passage of electric current through them.
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100 points + Brainliest
A block (mass = m) is lifted upward with the help of a wheel barrow by making an angle . Draw the FBD and write equations by showing all possible forces.
According to these equations, the normal force equals the weight component in the y direction, and the tension force equals the weight component in the x direction.
How to determine possible forces?Here is a description of the forces acting on the block:
Weight force (mg): The force due to gravity acting on the block and directed downwards.
Normal force (N): The force exerted by the wheelbarrow on the block and perpendicular to the surface of contact.
Tension force (T): The force exerted by the rope on the block and directed upwards at an angle .
Here is a free body diagram (FBD) of the forces acting on the block:
mg
↓
┌───┐
T ← ┤ ├── N
└───┘
Write the equations for the forces in the x and y directions:
In the y direction:
N - mg cosθ = 0
N = mg cosθ
In the x direction:
T - mg sinθ = 0
T = mg sinθ
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A battery has 2 cells .Each of the potential difference 1.2v.If the cells are connected in parallel and the total current flowing through is 4.0A.Draw a circuit diagram to show the circuit arrangement
The connection of the circuit is shown in the image attached here.
What is a parallel?
When we heat that a connection is done in parallel our minds would have to go to a connection that is made to common junction. The implication of this is that there are wires that would come out from each of the cells and that the wires would be joined at a common point.
Many different applications, including electric automobiles where many batteries may be connected in parallel to enhance the range and power output of the vehicle, can benefit from the parallel connection of cells.
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why does liquid candle wax flow but solid candle wax does not?
Answer:
Because the matter in solid objects doesn't move
Explanation:
Logic
put the different features into the appropriate box, either Mars or Venus.
Venus is the 2nd planet of the solar system whereas the Mars is the fourth planet in the solar system. They are different from each other.
These two planets are terrestial planet and similar to earth. Venus is very close to the Sun and the Mars are away from the Sun with certain distance. These planets are the brightest of the others.
These planets have certain similarities like the presence of volcanoes, weathered surfaces and and atmosphere. Mars has two moons and the venus has no moon.
Mars and Venus also different from each other. Like Earth, these planets do not have the ability to produce magnetic field and hence they get affected by the solar winds. The atmosphere of Venus is thick and dense and the atmosphere of Mars is light and teneous.
The mars has ice and liquid water on its surface whereas in Venus, there is lack of water. The gravity of venus is twice that of mars. The rotational speed of the venus is lesser than that of mars. Venus is very hot as it present near to the Sun and mars is the comparatively cold.
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What is one fitness resource that outside of the school that is available to high school students
Answer:
high school students toward fitness and sports activities taught in physical education, and the perceived effectiveness of their physical education curriculum for improving their fitness and skill levels
Explanation:
A 80.7 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.57 rad/s. A monkey drops a 9.57 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.1 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.91 m.
Angular velocity of the platform with its load is 0.94 rad/s.
Since, there is no external torque acting on the system, the momentum is conserved.
So, Initial momentum, L₁ = Final momentum, L₂
I₀ω₁ = (I₀ + m₁r₁² + m₂r₂²)ω₂
I₀ω₁ = [1/2 x 80.7 x (1.91)²] (1.57)
I₀ω₁ = 147.2 x 1.57 = 231.1 kgm²/s
So,
231.1 = [147.2 + 9.57(4/5 x 1.91)² + 21.1(1.91)²]ω₂
Therefore, the final angular velocity,
ω₂ = 231.1/246.5
ω₂ = 0.94 rad/s
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1. In order to generate a current from a magnet, which of the following would generate a current?
a. Spinning a magnet near a wire
b. Placing the north end of a magnet near a wire
c. Place the south end of a magnet near a wire
2. In order for a circuit to function, which of the following must be true?
a. The circuit cannot have more than 3 bulbs attached
b. The circuit must have an switch placed in the circuit in the open position
c. The circuit must make a complete loop and must have all parts connected to that loop
Spinning a magnet near a wire would generate a current.
The circuit must make a complete loop and must have all parts connected to that loop.
What is the spinning magnet?When a magnet approaches a conductor, such as a wire, the magnetic field changes, causing the wire to conduct electricity. Electromagnetic induction is a process that underlies the operation of electric motors and generators.
Electromagnetic induction and is the basis for how generators and electric motors work and it explains the fact that current is generated by a spinning a magnet near a wire.
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Help! Photo Attached!!! WORTH: 60+ POINTS! Difficulty: Medium
The wavelength of the given wave is 4 meters and the amplitude of the wave is 2 meters.
Wavelength of the wave is the distance between two crests or two troughs and the amplitude is the maximum height of the wave.
From the given figure,
the distance between two crests or two trough,
wavelength = 4 × 1 meter
λ = 4 meter.
The maximum distance of the crest or trough,
Amplitude (a) = 2×1 meter
a = 2 meter
Hence, the wavelength of the wave is 4 meter and the amplitude of the wave is 2 meter.
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An object that is 1.14 cm tall is placed 15.0 cm in front of a diverging lens of focal length 23.0 cm. How tall is the image (in centimeters, to three significant figures)?
The height of the image would be 9.64 cm.
We can use the thin lens equation to determine the position of the image:
1/f = 1/do - 1/di
where f is the focal length of the lens, do is the distance from the object to the lens, and di is the distance from the image to the lens. Rearranging this equation, we get:
1/di = 1/f - 1/d₀
Substituting the given values, we get:
1/di = 1/23 - 1/15
1/di = -0.007971
di = -125.3 cm
The negative sign for di indicates that the image is virtual (i.e., it appears on the same side of the lens as the object).
Now, we can use the magnification equation to determine the height of the image:
m = -di/d₀
where m is the magnification. Substituting the given values, we get:
m = -(-125.3 cm)/(15.0 cm)
m = 8.353
The negative sign for the magnification indicates that the image is inverted with respect to the object. The absolute value of the magnification tells us that the image is larger than the object by a factor of 8.353.
Therefore, the height of the image is:
hi = mho
hi = 8.3531.14 cm
hi = 9.64 cm
Rounding to three significant figures, the height of the image is 9.64 cm.
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A 1500, kg space probe is orbiting the Earth at a distance of 25 000. km from
the Earth's centre. The probe is hit head-on by a 2000. kg meteor moving at
1000, kph in the opposite direction. (see class example 2 for diagram). After the
completely inelastic collision, the meteorite and crumpled probe will fall
together into a lower orbit. Find the (average) radius of this new stable orbit.
(13 500 km-1.35x107 m)
The radius of the new stable orbit is around 13,500 kilometers.
How to calculate raduis of orbit?First, find the velocity of the meteor relative to the Earth, which is:
V = 1000 km/h = 1000/3600 km/s = 0.2778 km/s
Since the probe is in orbit, it has a velocity of:
Vp = √(GMe/Re)
Where G = gravitational constant,
Me = mass of the Earth, and
Re = distance from the center of the Earth to the probe's original orbit.
Plugging in the values:
Vp = √((6.6743 × 10⁻¹¹ m³/(kg s²)) x (5.972 × 10²⁴ kg) / (25000 km + 6371 km)) = 7.785 km/s
The total momentum of the system is conserved, so:
(meteor × V) + (probe × Vp) = (meteor + probe) × Vf
Where Vf = velocity of the combined mass after the collision.
Solving for Vf:
Vf = [(meteor × V) + (probe × Vp)] / (meteor + probe) = (2000 kg x 0.2778 km/s + 1500 kg x 7.785 km/s) / (2000 kg + 1500 kg) = 6.083 km/s
Now find the radius of the new orbit using:
Vf = √(GMe/Rnew)
Solving for Rnew:
Rnew = (GMe)/(Vf²) = (6.6743 × 10⁻¹¹ m³/(kg s₂)) x (5.972 × 10²⁴ kg) / (6.083 km/s)² = 1.35 × 10⁷ m = 13,500 km
Therefore, the new stable orbit has a radius of approximately 13,500 km.
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1. The wave speed of a wave through a medium is equal to the frequency times the wavelength. When the frequency changes, the wavelength must change to compensate. Why can't the velocity of the wave change?
a. The velocity of a mechanical wave is dependent on the medium
b. The wavelength is separate from the velocity, so it can change while the wavelength cannot
c. The velocity of the wave cannot change because it is set by the force that starts the oscillation
2. If a water wave has a velocity of 4.5 m/s and has a frequency of 25 Hz, what is the wavelength of the wave?
a. 0.80 m
b. 5.6 m
c. 0.18 m
Only answer if you know the right answer pls :)
1. The correct statement is "The velocity of a mechanical wave is dependent on the medium", and 2. The wavelength of the water wave is 0.18 m. The correct option for Question 1. is A and for Question 2 is C.
A mechanical wave is a type of wave that requires a medium to travel through, such as a solid, liquid, or gas. These waves propagate by transferring energy from one particle of the medium to the next. Examples of mechanical waves include sound waves, water waves, and seismic waves.
1. A. The velocity of a mechanical wave is dependent on the medium through which it travels. The speed of sound waves, for example, is different in air than it is in water. The velocity of a wave is not determined by its frequency or wavelength alone.
2. The formula relating wave speed, frequency, and wavelength is:
Wave speed = frequency x wavelength
Rearranging this formula to solve for wavelength, we get:
Wavelength = wave speed/frequency
Substituting the given values, we get:
Wavelength = 4.5 m/s / 25 Hz
Wavelength = 0.18 m
So, the wavelength of the water wave is 0.18 m.
Hence, The correct option for Question 1 is A. And for Question 2 is C.
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What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when the power
output of the trumpet is 0.20 W? Assume that the sound waves are spherical.
CAN SOMEONE HELP I REALLY NEED IT THANK YOU SO MUCH
The intensity of the sound wave produced by the trumpet at a distance of 3.2 m is 1.56×10⁻³ W/m²
How do i determine the intensity of the sound wave?From the question given above, the following data were obtained:
Distance from source (r) = 3.2 mPower output (P) = 0.20 WPi (π) = 3.14Intensity of sound wave (I) =?The intensity of the sound wave can be obtained as illustrated below:
Intensity (I) = P / 4πr²
Inputting the various parameters, we have:
I = 0.2 / (4 × 3.14 × 3.2²)
I = 0.2 / 128.6144
I = 1.56×10⁻³ W/m²
Thus, we can conclude from the above calculation that the intensity of the sound wave is 1.56×10⁻³ W/m²
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The centrifuge at NASA Ames Research Center has a radius of 8.8 m and can produce forces on its payload of 20 gs or 20 times the force of gravity on Earth. (a) What is the angular momentum of a 20-kg payload that experiences 10 gs in the centrifuge? (b) If the driver motor was turned off in (a) and the payload lost 10 kg, what would be its new spin rate, taking into account there are no frictional forces present?
(a) The angular momentum of a 20-kg payload experiencing 10 gs in a centrifuge with a radius of 8.8 m is 5,483 kg m^2/s. (b) If the payload loses 10 kg, the new spin rate taking into account no frictional forces present is 7.54 rad/s.
(a) The angular momentum of a rotating object is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
The moment of inertia for a point mass rotating in a circle is given by:
I = mr^2
where m is the mass of the object and r is the radius of the circle.
To calculate the angular momentum of the 20-kg payload that experiences 10 gs in the centrifuge, we first need to calculate the angular velocity of the payload. The force on the payload is 10 times the force of gravity on Earth, so the net force on the payload is:
F = ma
F = (10 × 9.8 m/s^2) × 20 kg
F = 1960 N
The net force on the payload is the centripetal force, which is given by:
F = mv^2/r
where v is the velocity of the payload.
Rearranging this equation to solve for v:
v = sqrt(Fr/m)
v = sqrt((1960 N) × (8.8 m) / (20 kg))
v = 33.2 m/s
The angular velocity of the payload is:
ω = v/r
ω = 33.2 m/s / 8.8 m
ω = 3.77 rad/s
Finally, we can calculate the angular momentum of the payload:
L = Iω
L = (mr^2)ω
L = (20 kg) × (8.8 m)^2 × 3.77 rad/s
L = 5,483 kg m^2/s
(b) When the payload loses 10 kg, its new moment of inertia becomes:
I' = m'r^2
I' = (10 kg) × (8.8 m)^2
I' = 774.4 kg m^2
Conservation of angular momentum tells us that:
L = Iω = I'ω'
where ω' is the new angular velocity of the payload.
Solving for ω':
ω' = (I/I')ω
ω' = ((20 kg) × (8.8 m)^2 × 3.77 rad/s) / ((10 kg) × (8.8 m)^2)
ω' = 7.54 rad/s
So, the new spin rate of the payload is 7.54 rad/s.
Therefore,(a) For a 20-kg payload experiencing 10 gs in a centrifuge with an 8.8 m radius, the angular momentum is 5,483 kg m^2/s. (b) If the payload's mass reduces by 10 kg without any frictional forces present, the new spin rate is 7.54 rad/s.
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A student is investigating what happens when a neutral metal sphere sitting on an insulated stand is touched by negatively charged rod. the set up for the students investigation as shown in the diagram. what will happen to the excess electrons when the negatively charged rod touches the medal sphere 
The sphere will become negatively charged.
What happens?When a neutral metal sphere comes into touch with a negatively charged rod, some of the excess electrons from the rod move to the sphere, making it negatively charged.
The extra electrons that are delivered to the sphere will disperse uniformly across its surface, rejecting one another and maintaining the surface by means of electrostatic forces.
Until the negative charge is discharged or somehow neutralized, the sphere will remain negatively charged.
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13. A solid has a mass of 200 g in air and when partly immersed in a certain liquid it has a mass of 160 g. Given that the relative density of the liquid is 0.80, calculate the volume of the solid immersed in the liquid.
The volume of the solid immersed in the liquid is 5 x 10⁻⁵ m³.
What is the volume of the solid?The volume of the solid is calculated as follows;
V = (Ws - Wa) / (ρg)
where;
Ws is the weight of the solid in airWa is the weight of the solid in liquidρ is the density of the solidg is gravityWs = 0.2 kg x 9.8 m/s²
Ws = 1.96 N
Wa = 0.16 kg x 9.8 m/s²
Wa = 1.568 N
ρ = 0.8 x 1000 g/km³ = 800 kg/m³
The volume is calculated as;
V = (1.96 - 1.568 )/(800 x 9.8)
V = 5 x 10⁻⁵ m³
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What is true about the requirements of your academic career plan
Academic career planning mainly needs, coordination of your educational requirements with your job ambitions.
ACP, or academic career planning, is a student-driven, adult-supported process whereby students develop their own distinct, knowledge-based visions for success after high school through self-exploration and career-reflection as well as the acquisition of career management and planning skills.
It requires the understanding of your abilities, values, and interests relate to potential occupations or jobs matching your abilities, matching your financial needs and career ambitions, etc.
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A gas expands from I to F in the figure. The
energy added to the gas by heat is 430 J when
the gas goes from I to F along the diagonal
path.
1): What is the change in internal energy of the
gas?
Answer in units of J.
2): How much energy must be added to the gas
by heat for the indirect path IAF to give the
same change in internal energy?
Answer in units of J.
The change in internal energy of the gas is -5570 J, and 860 J of energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy.
1. The change in internal energy of the gas is equal to the work done on the gas plus the heat added to the gas. From the diagram, we can see that the work done on the gas when it expands from I to F along the diagonal path is negative. This is because the gas expands against a constant external pressure, and its volume increases, so the work done by the gas is positive, and the work done on the gas is negative. The work done on the gas can be calculated as:
W = -PΔV = -1.5 × 10^5 Pa × 0.04 m^3 = -6000 J
The change in internal energy is then:
ΔU = Q + W = 430 J - 6000 J = -5570 J
Therefore, the change in internal energy of the gas is -5570 J.
2. For the indirect path IAF, we can break it down into two steps: I to H along the horizontal path, and H to F along the vertical path. For the first step, the work done on the gas is zero, since the volume does not change. So, the heat added to the gas is equal to the change in internal energy:
Q1 = ΔU = -5570 J
For the second step, the work done on the gas can be calculated as:
W2 = -PΔV = -1.5 × 10^5 Pa × 0.08 m^3 = -12000 J
The heat added to the gas for this step must be equal to the change in internal energy minus the work done on the gas:
Q2 = ΔU - W2 = -5570 J - (-12000 J) = 6430 J
The total heat added to the gas for the indirect path IAF is then:
Q = Q1 + Q2 = -5570 J + 6430 J = 860 J
So, 860 J of energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy.
Hence, The gas's internal energy changes by -5570 J, while the indirect path IAF requires that 860 J of energy be given to the gas via heat in order to produce the same internal energy change.
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In a 'keep-fit' exercise, a student of mass 45 kg steps 40 times on and off a box of height 0.50 m. How much work does the student do to raise her body each time she steps on the box
Answer:Calculate the work done using:
work done (in joules) = force (in newtons) x distance moved (in metres)
To practice calculations involving force, distance and work done.
Explanation: I hope this helps srry if I'm wrong
How would the calculation change if a typical comet in the Oort cloud is only 1 km in diameter?
When a typical comet in the Oort cloud is only 1 km in diameter, then the mass of the Oort cloud is changes to 4.18×10⁹ kg.
The mass of each comet int he Oort cloud is,
mass = density × Volume
volume of sphere = 4/3(π×r²) where, r = radius of the sphere
From the given,
diameter = 1 km
radius = Diameter / 2 = 1/2(D)
Volume of the comet = 4/3 (π×r²) = 4/3 (π× (1/2 (10)³)²)
= 4/3×(π) ×(1/8×10⁶)
Mass = density × volume, where density = 1000 kg/m³
= 1000 × 4/3×(π) ×(1/8×10⁶)
= 4.18 ×10⁹ kg
When the typical comet in the Oort cloud is only 12 km in diameter the mass of Oort cloud is 4.18×10⁹ kg.
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Why is DNA a useful evolutionary clock?
V2 Problem 2.4 In the turbine of a gas turbine unit the gases flow through the turbine at 17kg/s and the power developed by the turbine is 14 000kW. The specific enthalpies of the gases at inlet and outlet are 1200 kJ/kg and 360 kJ/kg respectively, and the velocities of the gases at inlet and outlet are 60 m/s and 150 m/s respectively. Calculate the rate at which heat is rejected from the turbine. Find also the area of the inlet pipe given that the specific volume of the gases at inlet is 0.5m³/kg. Solution
The rate at which heat is rejected from the turbine is 14,000kW and the area of the inlet is 0.1417m²
Solution to Thermodynamic ProblemTo find the heat rejected from the turbine, we apply the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
Mathematically,
ΔU = Q - W
where
ΔU = change in internal energy,
Q = heat added to the system,
W = work done by the system.
Assuming the gas turbine unit operates under steady-state conditions, the change in internal energy of the gases passing through the turbine is negligible. With that we can say, the heat rejected by the turbine is equal to the work done by the turbine:
Q = W = 14,000 kW
Therefore, the rate at which heat is rejected from the turbine is 14,000 kW.
To find the area of the inlet pipe, we can use the continuity equation:
m = ρ * A * V
but we are given:
m = mass flow rate = 17kg/s
V= velocity = 60m/s
v = specific volume = 0.5m³/kg
ρ = density = 1/v = 1/0.5 = 2kg/m
By making A the subject of the formula we have,
A = m / (ρ * V)
A = 17 / (2 * 60)
A = 0.1417 m²
Therefore, the area of the inlet pipe is approximately 0.1417 m².
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