The center of the Milky Way galaxy is located in the southern constellation Sagittarius which is only 26,000 light-years away from the milk way.
The name of the Milky Way comes from the fact that the goddess Hera in Greek mythology sprinkled the sky with milk. Our galaxy has a different name in other parts of the world. In China it is called the "Silver River" and in the Kalahari Desert in southern Africa it is called the "Night Spine". The Milky Way is made up of a lot of dark matter, with billions of stars, gas, and dust bound together by their mutual gravitational pull. Our galaxy is about 100,000 light-years across. The location of center of the Milkyway is near the Sagittarius galaxy.
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a spring has a natural length of 10 m. if the work done in stretching the spring from 10 m (its natural length) to 11 m is 5 2 joules, what is the force in newtons needed to stretch the spring from its natural length to a length of 20 m?
The force in newtons needed to stretch the spring from its natural length to a length of 20 m is 104 N
As the metal spring expands and contracts, it deviates from its equilibrium position. The result is a restoring force that tends to push the spring back to its original position. This force is called spring force.
Given;
Natural length=10m
Work done to stretch from 10m to 11m =5.2J
so change in length (x)=1m
Work done on spring(W) = 1/2 *k *x^2
5.2 =1/2*k*1^2
so, k=10.4N/m
Spring is stretch to 20m so new x=10m
Force needed to stretch the spring = kx = 10.4 *10= 104 N
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an earthquake near the fiji islands measured 4.6 on the richter scale. use the formula r=log(aa0) to determine approximately how many times stronger the wave amplitude a of the earthquake was than a0
The correct option regarding how many times stronger the wave amplitude A of the earthquake was than the standard wave Ao is given by:
A = 39,811 Ao.
How to obtain the ratio of A and Ao?
To find the ratio of A and Ao, which states how many times a earthquake measuring R in the Richter scale was stronger than the standard intensity Ao, we have to solve the following logarithmic function:
R = log(A/Ao)
The Richter scale of the earthquake in this problem is given as follows:
R = 4.6.
Hence the ratio of the measures is obtained as follows:
4.6 = log(A/Ao)
The power of 10 is the inverse function of the logarithm, hence if it is applied to both sides of the equation, then we can isolate the ratio A/Ao as follows:
A/Ao = 10^4.6
A/Ao = 39,811.
Applying cross multiplication, the ratio is given as follows:
A = 39,811 Ao.
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a 307 g ball is tied to a string. it is pulled to an angle of 6.8 ∘ and released to swing as a pendulum. a student with a stopwatch finds that 17 oscillations take 14 s.
The string is 16 cm long.
What is time period?
Period of simple is given by the equation
[tex]$T=2 \pi \sqrt{\frac{l}{g}}$[/tex]
It will not depend upon angle and mass of ball.
A student with a stopwatch finds that 17 oscillations take 14 s.
So we can find period for 1 oscillation
[tex]\text { Period, } \mathrm{T}=\frac{14}{17}=0.82 \mathrm{~s}[/tex]
Substituting in equation of period
[tex]\begin{aligned}& T=2 \pi \sqrt{\frac{l}{g}} \\& 0.82=2 \pi \sqrt{\frac{l}{9.81}} \\& l=\frac{0.82^2 \times 9.81}{4 \pi^2}\end{aligned}[/tex]
[tex]l=0.16m[/tex]
The string is 16 cm long.
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Part A Identify the highlighted structure. striations Submit Previous Answers Request Answer X Incorrect; Try Again Part A Identify the cartilage type in this field of view. Submit Request Answer Provide Feedback intentProblemiDa 195914571&attemptNo1&offsetnet 9 O RI EPC a Part A 1408 Identify the epithelium indicated by the arrows. simple columnar epithelial cells Submit Previous Answers Request Answer X Incorrect; Try Again Part A 12 Identify the highlighted structures. Submit Request Answer
First image:cardiac muscle cell.
Second image: elastic cartilage.
Third image: Pseudo-stratified Columnar Epithelium.
Fourth image: cilia.
What is cardiac muscle cell?Cardiac muscle, a kind of striated, involuntary muscle found solely in the heart, is what allows the heart to pump blood.
Cardiac muscle cells are found in the heart's walls, where they may be seen as being striped (or striated) and controlled by an involuntary process.
Cells in cardiac muscle tissue, or the myocardium, respond to electrical signals from the nervous system by contracting and expanding. Together, these cardiac cells create the wavelike, rhythmic contractions that make up the heartbeat.
Part A:
In the first image, the highlighted structure is cardiac muscle cell.
The cartilage type in the second image is elastic cartilage.
In the third image, the epithelium indicated by the arrows are pseudo-stratified Columnar Epithelium .
In the fourth image the highlighted structures are cilia.
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The complete question is as follows:
a scale reads 246 n when a piece of copper is hanging from it. what does it read (in n) when it is lowered so that the copper is submerged in water?
The read of a scale when a piece of brass is submerged in water (and its apparent weight) can be determined using the following formula: W App = 242N.
Can you put brass in the water?Brass weakens and lost its zinc component quite quickly when immersed in water, endangering the metal's structural integrity. Due of its incredible endurance, brass is a superb metal for various applications other than those in which it is submerged in water.
brass gets wet, what happens?Brass tarnishes when exposed to moisture, whether from being used in the bath or from perspiration on our bodies. This is a very normal occurrence. Jewelry made of brass metal occasionally develops a darker patina as it ages. A coating of the brass is covered in patina, which is a greenish tint.
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A biologist keeps a specimen of his favorite beetle embedded in a cube of polystyrene plastic. The hapless bug appears to be 2.0cm within the plastic. Part A What is the beetle's actual distance beneath the surface? Express your answer using two significant figures..
The actual distance beneath the surface of the beetle in the medium of polystyrene is 3.24cm.
What is polystyrene?Polystyrene is a synthetic polymer created from styrene, an aromatic hydrocarbon, as its monomers. Solid or foamed polystyrene are both available.
what is a refractive index?Refractive Index (Index of Refraction) is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density. The refractive index variable is most commonly symbolized by the letter n or n' in descriptive text and mathematical equations.
Briefing:The equation which shows the relationship between apparent depth and actual depth is
n= d(actua)/d(apparent)
where d (actual)= actual depth of object
d(apparent)= apparent depth of object
n= refractive index of the medium
d(actual)= n*d(apparent)
d(actual)=1.62*2
=3.24cm
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what is the closest you can be to speaker b and be at a point of perfectly destructive interference?
The closest you can be to speaker B and be at a point of perfectly destructive interference- 1.008m.
The wavelength of sound emitted by speakers
= velocity / frequency
= 344 / 172
= 2 m
For destructive interference , path difference is equal to odd multiple of half the wavelength .
path difference = 2 / 2 = 1 m
d₂ - d₁ = 1 m
d₂ = d₁ + 1 m
d₂ = .008 m + 1
d₂ = 1.008 m
So, the closest you can be to speaker B and be at a point of perfectly destructive interference- 1.008m.
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The complete question is:
Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 HzHz. You are 8.00 mm from speaker A. Take the speed of sound in air to be 344 m/sm/s. What is the closest you can be to speaker B and be at a point of perfectly destructive interference?
A lever is used to raise a heavy rock which that weighs 445N. If the lever has a mechanical advantage of 9.5, what must be the effort force in the lever?
The length of the effort arm of a lever divided by the length of the resistance arm represents the optimal mechanical advantage.
What must be the effort force in the lever?First Class I Lever Trial: de = dr The force of the effort (Fe) multiplied by the effort's distance from the fulcrum (de) in a class one lever equals the force of the resistance (Fr) multiplied by the resistance's distance from the fulcrum (dr).The ratio of the effort arm's length to the resistance arm's length is known as the ideal mechanical advantage.The IMA is typically calculated as the effort force, Fe, divided by the resistance force, Fr.In addition, IMA is determined by dividing the load's travel distance (dr) by the distance over which the effort is applied (de).effort force = 445/9.5
= 46.84
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the longest wavelengths on the electromagnetic spectrum are ________.
Radio waves have the electromagnetic spectrum's longest wavelengths. Radio waves have wavelengths that are longer than one millimeter.
What is wavelength ?A waveform signal that is propagated in space or along a wire has a wavelength, which is the separation between two identical points (adjacent crests) in the adjacent cycles.
What are radio waves ?The electromagnetic spectrum's longest wavelengths, which are found in radio waves, are normally found at frequencies of 300 gigahertz and below. The wavelength for 300 GHz is 1 mm, while the wavelength for 30 Hz is 10,000 kilometers.
So,
Radio waves have the electromagnetic spectrum's longest wavelengths. Radio waves have wavelengths that are longer than one millimeter.
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at which of the first five labeled stages is the star in energy balance?
The star is in energy balance when its core energy production matches the amount of energy it radiates into space. This is only true when the star is a main-sequence star with a hydrogen core fusion and when it is a helium core-fusion star. It is out of energy balance at all other times, which is why it is either contracting or expanding.
Stars can squeeze various types of atomic fuel together, and it's through this process that we get almost every element in the universe. Stars contain a lot of mass which has a lot of gravity. The gravity pulls inwards, which could cause a star to collapse in on itself. In a main sequence star, this inward pull is balanced by the outward gas pressure due to the nuclear fusion reactions deep in the star's core. This balance is called hydrostatic equilibrium and stops the main sequence stars from collapsing.
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why don't the air molecules in your room all spontaneously collect in one half of the room, leaving the other half of the room completely empty of air? newtons law
The answer is entropy here. It's quite unlikely that spontaneously air molecules moves exclusively to one half of your room. This can be explained by understanding the concept of entropy and second law of thermodynamics.
Why is the second law of thermodynamics true?Entropy is the measure of disturbance or disorder of universe.
The second law of thermodynamics states that entropy of an isolated system doesn't decrease over time.
The second law of thermodynamics is true because there are very few ways that particles can be concentrated in an area. In most situations, the particles are evenly distributed. Similarly, in a room, the particles are evenly distributed and as particles start moving, there is a nonzero probability of low entropy state, Most of the time the system will increase in entropy that is increase in disturbance evenly. Hence it is not possible that air molecules will collect in one part of the room and not on the other part.
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two people hear a tornado siren, but one listener is 49.5 times farther away from the source of the sound than the other. what is the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener
-35.39dB is the intensity level of the sound for the more distant listener relative to that for the nearer listener
By using the inverse square law,
As one listener is 49.5 times farther away from the source of the sound than the other.
Then Increasing the distance by 49.5 times reduces the intensity by
= 3453.8 times
The intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is:
= 10log(ratio of intensities)
= 10log(1/3453.8)
= 10log(0.000289)
=10 × -3.539
= -35.39dB (The negative sign represents the sound is less intense for the farther listener)
So, the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is -35.39dB
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13. two freight cars, each with a mass of 3.0105 kg, collide and stick together. one was initially moving at 2.2 m/s, and the other was at rest. what is their final speed?
The final speed of cars, when the collide and stick together, will be 1.1m/s
What is linear momentum and how it can be calculated?Linear momentum is the vector quantity and it happens when a particle moves with some velocity.
Thus, linear momentum = mass × velocity.
For an isolated system, the system's total momentum will remain unchanged.
Calculation:The expression for the initial momentum is given by
p1=mv1+mv2
here, p is the total initial momentum of the system
it is given that both cars stick together after the collision, so the final velocity of each car will be the same
The expression for the final momentum is given b
pf=mv+mv
So, equating total initial and final momentum
pi=pf
v1+mv2=mv+mv
v=v1+v2/2
Substitute,
v=2.2m/s+0/2
v=1.1m/s
Thus, the final speed of each car is 1.1.m/s
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what is the average flow rate in cm3/scm3/s of gasoline to the engine of a car traveling at 100 km/h if it averages 10.0 km/l?
The average flow-rate of gasoline in cm³/s is 2.78 cm³/s to start the engine while travelling at 100 km/h.
In order to decide the Flow Rate represented as Q, we have to outline each the quantity V and the factor in time it's far flowing beyond represented through t, or Q = V/t. Additionally Flow price and pace are associated through the equation Q = Av wherein A is the cross-sectional vicinity of glide and v is its common pace.
Flow is the quantity of fluid that passes in a unit of time. In water resources, glide is regularly measured in gadgets of cubic toes consistent with second (cfs), cubic meters consistent with second (cms), gallons consistent with minute (gpm), or different numerous gadgets.
From the question : Q = v/A'.................... Equation 1
Where Q = Average flow rate, A' = inverse of Area, v = velocity of the car.
Given: v = 100 km/h, A' = 10 km/L
Substitute this value into equation 1
Q = 100/10
Q = 10 L/h.
Now, we convert L/h to cm³/s.
Since,
1 L = 1000 cm³, and
1 h = 3600 s
Therefore,
Q = 10(1000/3600) cm³/s
Q = 2.78 cm³/s
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You are running in a straight line. You ran 3km to the right and then you ran back for 1km.
How much distance you have covered and what is your displacement from the starting point.
(2pts)
3 km
1 km
Displacement (show your work) Don't forget units
Distance (show your work) Don't forget units
The amount of distance that was covered by this person is equal to 4 kilometers.
The displacement from the starting point is equal to 2 kilometers to the right.
What is distance?In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical body or object over a particular period of time and speed, irrespective of its direction, starting point or ending point.
In this scenario, the total distance covered in a straight line by this person can be calculated by adding the distance he ran towards the right direction to the distance he ran towards the left direction as follows:
Distance = xf + x₀
Distance = 3 + 1
Distance = 4 kilometers.
On the other hand (conversely), the displacement of this person would be calculated by subtracting the distance he covered when running back from the distance he covered when running towards the right direction as follows:
Displacement = xf - x₀
Displacement = 3 - 1
Displacement = 2 kilometers to the right.
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a 0.30-kg mass is suspended on a spring. in equilibrium the mass stretches the spring 2.0 cm downward. the mass is then pulled an additional distance of 1.0 cm down and released from rest. calculate the total energy of the system.
The general equation of simple harmonic motion is
y = a cos (? t )or y = a sin (? t )
but here y = a cos (? t )...because at t=0 amplitude is maximum
Here amplitude 'a '= 0.01 m
m = 0.3 kg
x = 0.02 m
Force constant k is given by,
k = mg / x = 0.3 x 9.8/ 0.02 = 147 N/m
The time period of oscillation is given by ,
T = 2 ? ?( m / k )
? = 2 ? / T = ? ( 147 / 0.3 )
? = 22.1
then y = (0.01m) cos (22.1 t )
In physics, a force is a power that can change the motion of an item. A force can purpose an object with mass to alternate its pace. Pressure also can be described intuitively as a push or a pull. A force has both value and path, making it a vector quantity.
A pressure is a push or a pull and it affects our each day lives because without force, people might not be capable of open and near stuff or lift up our arms or legs.
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a star's color tells us ... question 8 options: its rotational speed. how much energy a star produces. both how much energy it produces and its surface temperature. its surface temperature.
A star's color mostly indicates its surface temperature. However, it could also be used to estimate the age of the star.
There are several types of stars according to their colors which include the following;
O-class starsM-class starsB-class starsA-class starsF-class starsG-class starsThe O-class stars are often blue in color and they are the hottest while the M-class stars are red in color and their temperatures are very low compared to the others, making them the coldest type of stars.
The color of the star is not a major factor in the estimation of the age of the star though it could be used sometimes.
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One average force has a magnitude that is three times as large as that of
another average force . Both forces produce the same impulse of 3 N.m. The
average force acts for a time interval of 3.2 s. For what time interval does the
average force act?
The second average force act at a time interval of 1.1s(1dp)
What is impulse?Impulse of a force is defined as the product of the average force and the time interval for which the force acts on the body.
It is measured in Nm and it is a vector quantity.
impulse is given as force ×time
let F1 represent the first average force and F2 be the second average force.
the time interval for the first average force is 3.2 seconds, therefore the average time interval for the second force will be 3.2/3= 1.1s(1dp)
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With the knowledge of mathematics and with the use of formula, the time interval will be 1.07 s
What is Impulse ?Impulse can be defined as the product of force and time. Impulse is the same as change of momentum.
Given that one average force has a magnitude that is three times as large as that of another average force. That is,
F = 3f ....... (1)
If both forces produce the same impulse of 3 N.m. The average force acts for a time interval of 3.2 s. For what time interval does the other average force act?
Impulse = force × time
If both forces produce the same impulse of 3 Nm
For first average force F,
3 = F × T
F = 3/T
For second average force f
3 = f × t
f = 3/t
Substitute both F and f into equation 1
F = 3f
3/T = 3(3/t)
Given that t = 3.2 s
Then, 3/T = 9/3.2
Cross multiply
9T = 9.6
T = 9.6/9
T = 1.07 s
Therefore, the first average force will act for time interval of 1.07 s
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what is the upper block's acceleration if the coefficient of kinetic friction between the block and the table is 0.21?
Answer:
0.21 brokies
Explanation:
a hoop of mass 1.2 kg and radius 65 cm has a string wrapped around its circumference and lies flat on a horizontal frictionless table. the string is pulled with a constant force 7 n. how far does the center of the hoop travel in 4 s? answer in units of m. what is the angular velocity of the hoop about its center of mass after 4
1.57 rad/s is the angular velocity of the hoop about its center of mass.
Solution:
Given that
Weight of hoop m = 1.2 kg
radius of hoop R = 65 cm = 0.65 m
Force = 7 N
Torque on the hoop Τ = F×R →equation (1)
Where F is applied force on hoop
We also know that
Τ = Iα[tex]R^{2}[/tex]
Where α is the angular acceleration
I is the moment of inertia of hoop
For hoop I = m[tex]R^{2}[/tex]
T = (m[tex]R^{2}[/tex])α →equation (2)
From equation 1 and 2
FR = (m)α
F = mRα
α = F/mR
α = 7/1.2×0.65 = 3.79 rad/s×s
α= 3.79 rad/s×s
We have to calculate distance covered by center of hoop in 5 s
d = (1/2)at×t →equation(3)
Relation between linear acceleration and radius is
a = αR
a = 3.79×0.65
a = 2.46 m/s×s
now from equation (3)
d = 0.5×2.46×4×4
d = 19.68 m
so the distance covered by center of hoop in 4 s is 19.68 m.
Part(2)
angular velocity of hoop
angular momentum about the center of the hoop
w = v/R
ωt = 2×π
t is given 4 s
ωt = 6.28
ω×4= 6.28
ω = 1.57 rad/s
Hence, 1.57 rad/s is the angular velocity of the hoop about its center of mass.
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The SI units for position, velocity, and acceleration are, respectively: Question 11 options: m, m/s, m/s^2 kg, m/s, m^2/s m, m/s, m^2/s kg, m/s, m/s^2
Answer:
Explanation:
position: m
velocity: m/s
acceleration: m/s²
use voltage division to find the voltage across r3, positive at the top.
V1 = (1.2 A)(2 ) = 2.4 volts is the voltage across R1.V2 = (1.2 A)(3 ) = 3.6 volts is the voltage across R2.V3 = (1.2 A)(5 ) = 6.0 volts is the voltage across R3.
How can the voltage across be determined?We can use Ohm's Law (V = I x R) to determine actual voltage drops over each resistor once we have the amperage for such circuit (remember that the amperage doesn't really change inside a series circuit).
How can I calculate the voltage drop between two resistors?According to Ohm's Law, V=I*R, where V stands for voltage, I for current, and R for resistance.The power loss across each resistor in a series circuit will be inversely correlated with its size.The voltage drop over each resistor in a parallel connection will be equal to the voltage coming from the power source.
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how many times more powerful were the seismic waves of the nisqually earthquake than standard seismic waves?
The seismic waves of the Caracas earthquake were 3162277,66 times more powerful of the standard seismic waves.
What is seismic waves ?
An acoustic energy wave that moves through the Earth is known as a seismic wave. Large landslides, volcanic eruptions, magma movement, earthquakes, and man-made explosions that release a lot of low-frequency acoustic energy can all cause it.
By using formula given above, M= log(w/w_0), we can find
10^M= w/w_0, it means 10^M.w_0,= w
but M=6.5, so 10^6.5=3162277,66
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what is the equivalent capacitance for the circuit of the figure? (figure 1)
Answer:
The battery is connected to a series-parallel combinationof capacitors.The two rightmost paralle
Guidlines for replenishing fuel during endurance events include
A. consume 30 to 60 grams of carbohydrate per hr
B. use only one type of carbohydrate to avoid gastrointestinal upset
C. use a protein supplement every 30 mins
D. avoid fluid during exercise
Carbohydrates are the nutrition that matters most during endurance activity. Your muscles and liver both contain glycogen, which is the body's preferred form of energy storage. These stockpiles run low and exhaustion comes in when you exercise for more than 90 minutes.
What kinds of energy are required by endurance athletes?
For endurance sports, carbohydrates are frequently the preferred fuel source, so they take center stage in many athletes' nutrition programs. An additional source of carbohydrates is typically necessary to maintain peak performance because the body burns through its glycogen reserves, even at a pace below maximum
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two satellites are placed in geosynchronous orbits, orbits with a period of 24 hours, where each satellite hovers over a spot on the earth's equator. satellite b has three times the mass of satellite a. what is the relationship between the magnitudes of the gravitational forces of the earth on the two satellites?
Two satellites are placed in geosynchronous orbits, orbits with a period of 24 hours, where each satellite hovers over a spot on the earth's equator. satellite b has three times the mass of satellite a
F(b) = 3 F(a) is the relationship between the magnitudes of the gravitational forces of the earth on the two satellites.
What is satellite?A satellite is a body that orbits a planet, star, or moon. For instance, the fact that Earth circles the sun makes it a satellite. The moon is a satellite as well since it revolves around Earth. The term "satellite" often refers to a device that is sent into space and orbits the Earth or another celestial body.
Given that,
two satellites a and b are placed in geosynchronous orbits, orbits with a period of 24 hours.
Gravitational force is given by,
F = (G × M × m) / r²
Where, G = gravitational constant
M = Mass of the earth
m = mass of the satellite
r = distance between earth and satellite.
So, m(b) = 3 m(a) and r(a) = r(b)
Thus, F(a) = [(G × M × m(a)] / r(a)²
F(b) = [(G × M × m(b)] / r(b)²
or, F(b) = [(G × M × 3m(a)] / r(a)²
or, F(b) = 3[(G × M × m(a)] / r(a)²
or, F(b) = 3 F(a)
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Which of the following is not a type of radiation detector? (a) Geiger Muller (G.M.) counter (b) Proportional counter (c) Semiconductor radiation detector (d) Flame emission detector
Since it detects emissions from fires, the flame emission detector in the example is not a radioactive detector.
Which three main categories of radiation detectors are there?
Radiation detectors come in three primary categories. These include semiconductor detectors, gas ionization detectors, and detectors based on scintillation. The ionization chamber, proportional counter, and Geiger-Müller counter are gas ionization-based detectors.
Is Geiger radioactive in reverse?
A low pressure gas is kept in a copper cylinder in an early Geiger counter type while an electrical current passes through it. When a radioactive particle enters a cylinder, an electric current surge occurs, which is recorded on a counter.
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a 24.2-mw laser beam of diameter 1.97 mm is reflected at normal incidence by a perfectly reflecting mirror. calculate the radiation pressure on the mirror.
The Radiation Pressure on mirror is 15.944N/m² by normal incidence.
All of the light is reflected by a (perfect) mirror, which results in a twofold momentum transfer and twofold radiation pressure.
The spectral reflectance curve shows which frequencies are reflected and absorbed by various colored objects because different colored objects only reflect a portion of the light.
A completely reflective surface will reflect the photon back, changing its momentum twice as much as if it were to merely absorb it.
Because an absorbing surface warms up and then radiates, the situation becomes slightly more complicated. An isotropic radiation pattern results from perfect thermal transfer. So shape and materials are important for absorbers.
It would be possible to determine the radiation pressure using this, which would be somewhere between that of a perfectly black and perfectly mirrored object. In this case, you would additionally need to be familiar with the object's spectral energy distribution.
Radiation Pressure = Flux/c=24.2 x1.97/2.99
=15.944N/m²
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(a) the number of kilocalories in food is determined by calorimetry techniques in which the food is burned and the amount of heat transfer is measured. how many kilocalories per gram are there in a 5.00-g peanut if the energy from burning it is transferred to 0.500 kg of water held in a 0.100-kg aluminum cup, causing a temperature increase? (b) compare your answer to labeling information found on a package of peanuts and comment on whether the values are consistent.
a)The 5.00 of peanut has 5.73 Kcal/g of energy.
b)On comparing our answer to the label on package of peanut , it is found that the values are approximately same, the variation is due to the quality of peanuts.
a)
Given,
mass of peanut = 5.00 g
mass of water = 0.500 kg
mass of aluminium cup = 0.100 kg
temperature change = [tex]54.9 \textdegree C[/tex]
it is given that the heat from burning peanut is transferred to water and aluminium cup then,
the heat gained by water is [tex]Q_w=m_wC_w \Delta T[/tex]
Where,
[tex]m_w[/tex]= mass of water
[tex]C_w[/tex]= specific heat of water i.e.4184 J/kg°C
[tex]\Delta T[/tex]= change in temperature
[tex]Q_w[/tex][tex]=0.5*4184*54.9=1.15*10^5 J[/tex]
Now, the heat gained by aluminum cup is[tex]Q_{Al}=m_{Al}C_{Al} \Delta T[/tex]
Where,
[tex]m_{Al}[/tex]= mass of aluminium cup
[tex]C_w[/tex]= specific heat of water i.e.900J/kg°C
[tex]\Delta T[/tex]= change in temperature
[tex]Q_{Al}=0.1*900*54.9=4.94*10^3J[/tex]
then , the total heat gained by water and aluminium cup is
[tex]Q_T=(1.15*10^5)+(4.94*10^3)=1.20*10^5 J[/tex]
So,[tex]Q_T[/tex] is the heat transferred by burning of peanut to water and cup then the amount of heat for peanut will be same as [tex]Q_T[/tex],
[tex]Q_T=Q_{peanut}=1.20*10^5 J=\frac{1.20*10^5}{4184}=28.6 Kcal[/tex]
So, 5.00 g for peanut has 28.6 Kcal of energy then 1 g of peanut has [tex]\frac{28.6}{5}=5.73 Kcal.[/tex]
Hence, the 5.00 of peanuts have 5.73 Kcal/g of energy
b)
When we compare our answer to the label on the peanut package, we discover that the values are nearly identical; the difference is due to the quality of the peanuts.
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suppose you exert a force of 288 n tangential to a grindstone (a solid disk) with a radius of 0.275 m and a mass of 92.2 kg what is the resulting angular acceleration of the grindstone assuming negligible opposing friction?
The resulting angular acceleration of grindstone assuming negligible opposing friction is [tex]82.616 rad/s^{2}[/tex].
What is angular acceleration?Angular acceleration can be defined as the temporal rate at which angular velocity changes. The standard unit of measurement is radians per second square. It is also called rotational acceleration. It is a numerical representation of the variation in angular velocity over time.
A pseudoscalar, angular acceleration, exists. If the angular speed rises counterclockwise, the sign of angular acceleration is taken to be positive; if it grows clockwise, it is taken to be negative. Angular acceleration makes it easier to the motion of rotating objects.
The symbol for angular acceleration in SI units is alpha ([tex]\alpha[/tex]), and it is expressed as radians per second squared ([tex]rad/s^{2}[/tex]).
We know that,
Force on grindstone, F = 288 N
Radius of grindstone, r = 0.275 m
Mass of grindstone, m = 92.2 kg
The grindstone's angular acceleration must be determined. The relationship between torque and angular acceleration in rotational motion is given by:
τ = I x α
α = τ/I
I is the moment of Inertia of solid disk.
I =[tex]\frac{mr^{2}}{2}[/tex]
τ represents the torque exerted
τ = F x r
Thus
[tex]\alpha = \frac{Fr}{\frac{mr^{2}}{2}}[/tex]
[tex]\alpha = \frac{2Fr}{{mr^{2}}}[/tex]
[tex]\alpha = \frac{2(288) F}{(92.2 kg) (0.275^{2} m^{2} )}}[/tex]
[tex]\alpha = 82.616 rad/s^{2}[/tex]
Thus, we can conclude that the angular acceleration of the grindstone is 82.616 [tex]rad/s^{2}[/tex].
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