1. The amount of heat required to melt the ice is 334.4 J.
2. The temperature of the soda after the ice melts is 0°C.
3. The total change in entropy of the glass of cold soda is approximately 1.224 J/K, which is positive.
Determine what is the amount of heat required?1. The amount of heat required to melt the ice is 334.4 J.
To calculate the heat required to melt the ice, we can use the formula:
Q = m × ΔHf
Where Q is the heat required, m is the mass of the ice, and ΔHf is the heat of fusion for ice.
Given that the mass of the ice is 10 g and the heat of fusion for ice is 334 J/g, we can substitute these values into the formula:
Q = 10 g × 334 J/g = 3340 J = 334.4 J
Therefore, the amount of heat required to melt the ice is 334.4 J.
Determine what is the temperature of the soda?2. The temperature of the soda after the ice melts is 0°C.
When the ice melts, it absorbs heat from the soda. Assuming all the heat required to melt the ice flowed from the soda and neglecting any heat exchange with the surroundings, the soda would lose an equal amount of heat as the heat required to melt the ice.
Since the specific heat of soda is the same as that of water, we can use the formula:
Q = m × c × ΔT
Where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Given that the mass of the soda is 250 g and assuming no change in temperature, ΔT = 0, we can rearrange the formula to solve for the final temperature:
Q = m × c × ΔT
c × ΔT = Q / m
ΔT = Q / (m × c)
ΔT = 334.4 J / (250 g × 4.18 J/g°C)
ΔT ≈ 0.32°C
Therefore, the temperature of the soda after the ice melts is approximately 0°C.
Determine what is the total change in entropy?3. The total change in entropy of the glass of cold soda after it comes to thermal equilibrium with the room is positive.
Entropy is a measure of the disorder or randomness in a system. When the glass of cold soda comes to thermal equilibrium with the room, heat will flow from the soda to the surroundings, increasing the entropy of the system.
The change in entropy, ΔS, can be calculated using the formula:
ΔS = Q / T
Where ΔS is the change in entropy, Q is the heat transfer, and T is the temperature in Kelvin.
In this case, the heat transfer, Q, is the same as the amount of heat required to melt the ice, which is 334.4 J. The temperature of the soda after the ice melts is 0°C, which is 273.15 K.
ΔS = 334.4 J / 273.15 K ≈ 1.224 J/K
Therefore, the total change in entropy of the glass of cold soda after it comes to thermal equilibrium with the room is approximately 1.224 J/K, which is positive, indicating an increase in disorder or randomness.
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A pot containing 630 g of water is placed on the stove and is slowly heated from 21°C to 81°C. Calculate the change of entropy of the water in J/K.
A pot containing 630 g of water is placed on the stove and is slowly heated from 21°C to 81°C, then the change in entropy of the water is 7200 J/K.
To calculate the change in entropy (ΔS) of water, we can use the formula:
ΔS = mcΔT / T
Where:
m is the mass of the water,
c is the specific heat capacity of water,
ΔT is the change in temperature, and
T is the initial temperature.
First, we need to find the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g°C.
Mass of water (m) = 630 g
Change in temperature (ΔT) = (81°C - 21°C) = 60°C
Initial temperature (T) = 21°C
Substituting these values into the formula, we get:
ΔS = (630 g) * (4.18 J/g°C) * (60°C) / (21°C)
Simplifying the equation:
ΔS = (630 g) * (4.18 J/g°C) * (60°C) / (21°C)
= 630 * 4.18 * 60 / 21
= 7200 J/K
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Can anyone help me with this question please .
I’ll mark as brainliest
No links
Answer:
A
Explanation:
The wavelength is the spatial time of an occasional wave, the distance over which the wave's shape rehashes.
Hope this helped!!
Answer:
wavelength
Explanation:
A conveyer belt carries a load of mass 180kg n lift it up in 1
Answer:
Cool.
Explanation:
What's the question..? :|
Can someone help with this please
The graph that correctly gives the variation of the electric field as a function of r is the third graph.
How to explain the informationThe electric field inside a conducting shell is zero. This is because the charges on the shell distribute themselves so that the electric field is zero everywhere inside the shell.
The electric field outside a conducting shell is radial and directed away from the center of the shell. The magnitude of the electric field is inversely proportional to the square of the distance from the center of the shell.
Therefore, the graph of the electric field as a function of r is a horizontal line at zero for r < a, a vertical line at r = a, and a decreasing curve for r > a.
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f. write two reasons why it is better to obtain the moment of inertia through a linear fit than by solving for i in the equation and plugging in the value of ωmax and θ0 for one or two points.
Two reasons why it is better to obtain the moment of inertia through a linear fit rather than by solving for I using specific points (ωmax and θ0) are:
Increased Precision: A linear fit allows for the consideration of a larger set of data points, which can provide a more accurate determination of the moment of inertia. By analyzing the relationship between θ and ω over a range of values, the linear fit captures the overall trend and minimizes the potential errors associated with individual data points. This leads to a more precise estimation of the moment of inertia compared to relying on only one or two specific points. Account for Nonlinearities: In some cases, the relationship between θ and ω may not follow a simple linear pattern. If nonlinearity exists, using a linear fit provides a more flexible approach to capture the overall trend. By fitting a line to the data, even if the relationship is not strictly linear, we can still obtain a reasonable approximation of the moment of inertia by considering the best-fit line that represents the general behavior of the system. This method accounts for potential nonlinearities and provides a more reliable estimate of the moment of inertia compared to a limited number of specific points.
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if 104 w/m2 corresponds to 160 db, what is the sound intensity level, in decibels, of ultrasound with intensity 10^5 w/m2, used to pulverize tissue during surgery?
β= ___ dB
The sound intensity level of the ultrasound used to pulverize tissue during surgery is approximately 29.83 dB.
To determine the sound intensity level (β) in decibels (dB) for ultrasound with an intensity of ([tex]10^{5}[/tex] W/[tex]m^{2}[/tex]), we can use the formula for sound intensity level
β = 10 * log10(I/I₀)
Where:
β is the sound intensity level in decibels,
I is the sound intensity of the ultrasound,
I₀ is the reference sound intensity.
In this case, the reference sound intensity corresponds to 104 W/[tex]m^{2}[/tex], which corresponds to 160 dB. Therefore, we have:
β = 10 * log10(I / 104)
Plugging in the given intensity of ultrasound ([tex]10^{5}[/tex] W/[tex]m^{2}[/tex]), we have:
β = 10 * log10([tex]10^{5}[/tex] / 104)
β = 10 * log10(961.54)
β = 10 * 2.983
β = 29.83 dB
Therefore, the sound intensity level of the ultrasound used to pulverize tissue during surgery is approximately 29.83 dB.
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A 3.0-kg ball with an initial velocity of (4i +3j) m/s collides with a wall and rebounds with avelocity of (-4i + 3j) m/s.What is the impulse exerted on the ball by the wall?
Question 2 answers
a. +24i N s
b. -24i N s
c. +18j N s
d. -18j N s
e. +8.0i N s
The impulse exerted on the ball by the wall is -24i N s, the answer is option b.
The impulse exerted on the ball by the wall can be determined using the impulse-momentum theorem.
Impulse is equal to the change in momentum.
That is,
J = Δp
Since momentum is a vector,
p = mv
Substituting the values,
p(initial) = mv(initial) = 3.0 kg × (4i + 3j) m/s
p(initial) = 12i + 9j N s
p(final) = mv(final) = 3.0 kg × (-4i + 3j) m/s
p(final) = -12i + 9j N s
Change in momentum,
(Δp) = p(final) - p(initial)
= (-12i + 9j) N s - (12i + 9j) N s
= (-12 - 12)i + (9 - 9)j N s
= -24i N s
Thus, the impulse exerted on the ball by the wall is -24i N s, which means that the answer is option b.
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6. calculate the power of the eye when viewing an object 3.00 m away.
The power of the eye when viewing an object 3.00 m away is 58.82 diopters (D).
What is power of the eye?
The power of the eye refers to its ability to refract light and focus it onto the retina, enabling clear vision at different distances. The power of the eye is measured in diopters (D).
In the case of the human eye, it is generally assumed to have an equivalent focal length of approximately 17 mm, which is equivalent to 0.017 m. This value represents the average refractive power of the eye.
To calculate the power of the eye when viewing an object 3.00 m away, we can use the following formula:
P = 1 / f
P = 1 / 0.017
P = 58.82 D
Therefore, the power of the eye when viewing an object 3.00 m away is approximately 58.82 diopters (D).
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A wedge with a mechanical advantage of 0.78 is used to raise a house corner from its foundation. If the output force is 7500 N, what is the input force?
Therefore, the input force is 9615.38N
Input force calculation.
T0 determine the input force needed 0.78 to raise a house corner from its foundation we need to use the formula for mechanical advantage.
Mechanical advantage = output force/ input force
Given the output force to be 7500N and the mechanical advantage 0.78.
We can rearrange the the formula
IF = 7500/0.78
IF = 9615.38N
Therefore, the input force is 9615.38N
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at a temperature of __________ °c, 0.444 mol of co gas occupies 11.8 l at 889 torr.
A)73 °C
B)379 °C
C)32 °C
D)14 °C
E)106 °C
The ideal gas law can be used to solve the problem. The relationship between pressure, temperature, volume, and the number of moles of gas is given by the ideal gas law. PV = nRT is the formula for the ideal gas law, Where:P = pressure in atm, V = volume in Litersn = a number of moles, R = gas constant, T = temperature in Kelvin.
The temperature at which 0.444 mol of CO gas occupies 11.8 L at 889 torr can be calculated as follows ;
First, we must convert the pressure from torr to atm: 889 torr × 1 atm/760 torr = 1.17 atm.
Using the ideal gas law formula: PV = nRT.
We can solve for T.T = PV/nR where, P = 1.17 atmV = 11.8 Ln = 0.444 molR = 0.08206 L•atm/mol•K.
Substitute the given values,T = (1.17 atm × 11.8 L)/(0.444 mol × 0.08206 L•atm/mol•K)T = 379 K.
Convert Kelvin to Celsius by subtracting 273.15 from the value,379 K - 273.15 = 105.85°C ≈ 106°C.
Therefore, the temperature at which 0.444 mol of CO gas occupies 11.8 L at 889 torr is approximately 106°C. Hence, the correct option is E)106 °C.
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a 600-w tv receiver is turned on for 4 hours with nobody watching it. if electricity costs 10 cents/kwh, how much money is wasted? the wasted money is cents.
A 600-w TV receiver is turned on for 4 hours with nobody watching it. If electricity costs 10 cents/kWh, the amount of money wasted is cents. Therefore, the amount of money wasted in this case is 24 cents.
There are different steps to calculate the money wasted in this case. Here is the step-by-step solution to this problem:
First, we need to calculate the energy consumed in kWh:
Energy consumed = Power × Time Power = 600 W Time = 4 hours
Energy consumed = Power × Time Energy consumed = 600 W × 4 hours
Energy consumed = 2400 Wh.
To convert Wh into kWh, we need to divide the energy consumed by 1000:
Energy consumed = 2400 Wh = 2.4 kWh.
Now, we can calculate the amount of money wasted:
Cost of 1 kWh = 10 cents Cost of 2.4 kWh = 2.4 kWh × 10 cents/kWh
Cost of 2.4 kWh = 24 cents.
A 600-w TV receiver is turned on for 4 hours with nobody watching it. If electricity costs 10 cents/kWh, the amount of money wasted is cents. The energy consumed by the TV receiver can be calculated by multiplying the power rating by the time it is used. In this case, the power rating is 600 W, and the time is 4 hours.
Therefore, the energy consumed is 600 W × 4 hours = 2400 Wh.
To convert the energy consumed into kWh, we need to divide it by 1000. So, 2400 Wh = 2.4 kWh. The cost of electricity is 10 cents per kWh.
Therefore, the cost of 2.4 kWh is 2.4 kWh × 10 cents/kWh = 24 cents.
This is the amount of money wasted by keeping the TV receiver turned on for 4 hours without anyone watching it. It is important to turn off electrical appliances when they are not in use to save electricity and reduce the electricity bill.
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a long, thin solenoid has 900 turns per meter and radius 2.50 cm. the current in the solenoid is increasing at a uniform rate of 48.0 a/s. What is the magnitude of the induced electric field at a
point near the center of the solenoid and (a) 0.500 cm from the axis of the solenoid; (b) 1.00 cm
from the axis of the solenoid?
The magnitude of the induced electric field at a point near the center of the solenoid and 0.500 cm from the axis of the solenoid is 1.07 × 10⁻⁴ V/m,
The magnitude of the induced electric field at a point near the center of the solenoid and 1.00 cm from the axis of the solenoid is 4.284 × 10⁻⁴ V/m.
Total no. of turns on the solenoid = 900 turns/m
Radius of solenoid = 2.50 cm = 0.025m
Rate of increase in current = 48.0 A/s
The magnetic field inside the solenoid,
B = μ₀nI
Where,
n = no. of turns per unit length
n = 900 turns/m
I = current flowing through the solenoid= 0 + 48t= 48t
T = 0s → I = 0
T = ∞ → I = 48
T = t
B = 4π × 10⁻⁷ × 900 × 48t
B = 1.363 T
The induced electric field at a point near the center of the solenoid.
(a) 0.500 cm from the axis of the solenoid
Area of the loop,
A = πr²
= π(0.005)²
A = 7.85 × 10⁻⁵m²
Enclosed current,
I = nA × I
= 900 × 7.85 × 10⁻⁵ × 48tI
= 0.3396t
Magnetic flux,
Φ = BA = 1.363 × 7.85 × 10⁻⁵
Φ = 1.070 × 10⁻⁴ Wb
Induced electric field
E = - (dΦ/dt)
E = -d/dt (1.070 × 10⁻⁴)
E = - (-1.070 × 10⁻⁴)/dt
E = 1.07 × 10⁻⁴V/m(
b) 1.00 cm from the axis of the solenoid
Area of the loop,
A = πr² = π(0.01)²
A = 3.14 × 10⁻⁴m²
Enclosed current
I = nA × I
= 900 × 3.14 × 10⁻⁴ × 48t
I = 1.36224t
Magnetic flux,
Φ = BA = 1.363 × 3.14 × 10⁻⁴
Φ = 4.284 × 10⁻⁴ Wb
Induced electric field,
E = - (dΦ/dt)
E = -d/dt (4.284 × 10⁻⁴)
E = - (-4.284 × 10⁻⁴)/dt
E = 4.284 × 10⁻⁴V/m
Hence,
the magnitude of the induced electric field at a point near the center of the solenoid and 0.500 cm from the axis of the solenoid is 1.07 × 10⁻⁴ V/m,
and
the magnitude of the induced electric field at a point near the center of the solenoid and 1.00 cm from the axis of the solenoid is 4.284 × 10⁻⁴ V/m.
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Show that liquid pressure is directly
proportional to height of liquid in a vessel.
Answer:
P=F/A where F is the weight of the water and A is the area on which it is resting. The weight of the water is mg. The mass of the water is dv where d is the density and v is the volume. Finally, the volume of the water in a vessel is equal to the area of the base of the vessel times the height of the vessel. (v=Ah)
Plugging everything in we get:
P = dAhg/A
So
P=dhg
So we have shown that liquid pressure is directly proportional to height of liquid in a vessel.
Define Eukaryote cells and Prokaryote cells
Answer:
Ekaryote cells
an organism consisting of a cell or cells in which the genetic material is DNA in the form of chromosomes contained within a distinct nucleus. Eukaryotes include all living organisms other than the eubacteria and archaea.
prokaryote cells
microscopic single-celled organism which has neither a distinct nucleus with a membrane nor other specialized organelles, including the bacteria and cyanobacteria
Question 16 (1 point)
Light travels through a material at a speed of 4.3 x 108 m/s. What is the index of
refraction for the material?
Your Answer:
Answer
units
Answer:
η = 0.7
Explanation:
The refractive index of the material can be calculated by using the following formula:
[tex]\eta = \frac{c}{v}\\[/tex]
where,
η = refractive index of the material = ?
c = speedof light in vaccuum = 3 x 10⁸ m/s
v = speed of light in this material = 4.3 x 10⁸ m/s
Therefore,
[tex]\eta = \frac{3\ x\ 10^8\ m/s}{4.3\ x\ 10^8\ m/s}[/tex]
η = 0.7
In the subset number duplication example at the bottom of page 231, if the last record (2) was replaced with 1805, the Number Frequency Factor would _______.
Group of answer choices
- increase
- decrease
- remain the same
In the subset number duplication example at the bottom of page 231, if the last record (2) was replaced with 1805, the Number Frequency Factor would remain the same.
The subset number duplication example is an example of the identification of the degree of duplication in a given group of data sets. It consists of records of numbers and their duplicates which are listed in order, the frequency with which each number is repeated, and the percentage of total numbers that each number represents.The given example contains a series of numerical values that represent the degree of duplication within a given group of data sets. By substituting the last record with the number 1805, the Number Frequency Factor would remain unchanged, as there is no instance of this number in the dataset. Hence, the number frequency factor would remain the same even after substituting the last record with 1805.
The units of the pre-outstanding variable An are indistinguishable from those of the rate consistent and will change contingent upon the request for the response. It has units of s1 for a reaction of first order. As a result, it is frequently referred to as the frequency factor.
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Two point charges of magnitude 5.0 nC and -3.0 nC are separated by
35.0 cm. What is the potential difference between a point infinitely far
away and a point midway between the charges?
Answer:
V = 411.43 V
Explanation:
The two forces as a result of each of the 2 charges are;
F1 = kq1•q/r
F2 = kq2.q/r
Where r = r/2 since we are dealing with potential difference at a point midway between the charges.
q1 = 5 nC = 5 × 10^(-9) C
q2 = 3 nC = 3 × 10^(-9) C
k = 9 × 10^(9) N.m²/C²
r = 35 cm = 0.35m
r/2 = 0.35/2
Thus;
F1 = (9 × 10^(9) × 5 × 10^(-9) × q)/(0.35/2)²
F1 = 1469.39q
F2 = (9 × 10^(9) × 3 × 10^(-9) × q)/(0.35/2)²
F2 = 881.63q
Net force acting midway is;
F_net = F1 + F2
F_net = 1469.39q + 881.63q
F_net = 2351.02q
Now, we know that formula for electric potential is;
V = kq/r
Thus ;
V = Fr/q derived from the earlier equation for force we used.
Where F is F_net.
V = 2351.02q × r/q
V = 2351.02r
Recall that we are dealing with midpoint and r = r/2
Thus;
V = 2351.02 × 0.35/2
V = 411.43 V
When copper combines with oxygen to form copper(II) oxide, the charge of the copper ion is
a large, flat, horizontal sheet of charge has a charge per unit area of 5.40 µc/m2. find the electric field just above the middle of the sheet. magnitude kn/c direction ---select---
The magnitude of the electric field just above the middle of the sheet is approximately 3.05 x 10⁶ N/C.
To find the electric field just above the middle of a large, flat, horizontal sheet of charge, we can use Gauss's law.
Gauss's law states that the electric field (E) due to a flat sheet of charge is directly proportional to the charge density (σ) and perpendicular to the sheet.
The charge density is given as 5.40 µC/m², which represents the charge per unit area of the sheet.
The electric field just above the middle of the sheet is the same as the electric field just below the sheet. This is because the sheet is infinitely large and uniformly charged, creating a symmetric electric field.
The formula to calculate the electric field just above the middle of the sheet is:
E = σ / (2ε₀)
Where σ is the charge density and ε₀ is the permittivity of free space, which is approximately 8.85 x 10⁻¹² C²/(N·m²).
Substituting the given values, we have:
E = (5.40 x 10⁻⁶ C/m²) / (2 x 8.85 x 10⁻¹² C²/(N·m²))
Simplifying, we get:
E = 3.05 x 10⁶ N/C
The direction of the electric field is perpendicular to the sheet and points away from it.
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26. A solid wheel accelerates at 3.25 rad/s2 when a
force of 4.5 N exerts a torque on it. If the wheel
is replaced by a wheel which has all of its mass
on the rim, the moment of inertia is given by
1 = mr? What force should be exerted on the
strap to give the same angular velocity?
Answer:
9.0 N
Explanation:
The location of the mass of the wheel on the wheel = Evenly distributed
The acceleration of the solid wheel, α = 3.25 rad/s²
The applied force on the wheel = 4.5 N
The location mass of the replacement wheel = All on (around) the rim
The moment of inertia of the new wheel, I = m·r² (From an online source)
We have;
The moment of inertia for a solid wheel = 1/2·m·r²
The torque, τ = Moment of inertia, I × Acceleration, α
For the solid wheel, we have;
τ = 1/2·m·r² × 3.25 rad/s²
τ = r × F = r × m × a
For the replacement wheel, we have;
τ = m·r² × 3.25 rad/s² = 2 × 1/2·m·r² × 3.25 rad/s²
∴ τ = 2 × r × F
Given that the radius remains the same, the force applied on the replacement wheel needs to be doubled
The force that should be exerted on the strap to give the same angular velocity, F' = 2 × F
The required force, F' = 2 × 4.5 N = 9.0 N.
A car travels 140 miles in 3 hours. What is its velocity?
Answer:
46.67 miles/s
Explanation:
...........
Why is a spherical bob preferred to bobs of other shapes for use in simple pendulum experiments
Answer
A spherical bob creates more control for the simple pendulum experiment. An irregular bob like a large piece of paper for instance, will create too much air resistance for a basic classical experiment to yield predictable results within the academic lab.
PLEASE HELP ME I AM TIMED!
Answer: B
Explanation: I can tell the block weights more since the water went down
ANSWER ASAPPP
What type of mountain would form from vertical movements along fault lines?
A) volcano
B) dome
C) fault-block
D) folded
C) fault-block mountain
) A spring with a spring constant of 2.1N/m is stretched 0.2m. What force is produced by
the spring?
Answer:
Force = 0.42 Newton
Explanation:
Given the following data;
Spring constant, k = 2.1
Extension, e = 0.2m
To find the force, we would use the formula below;
Force = spring constant * extension
Force = 2.1 * 0.2
Force = 0.42 Newton
How much work w must be done on a particle with a mass of m to a\ccelerate it from rest to a speed of 0.902 c ? express your answer as a multiple of mc2 to three significant figures.
We can utilize Einstein's mass-energy equivalence equation, E = mc², where E represents the energy. The work done on the particle is equal to the change in energy.
When the particle is at rest, its energy is solely its rest energy, which is given by E = mc². As the particle is accelerated to a speed of 0.902 c, its total energy increases. The change in energy (ΔE) is the difference between the final energy and the initial rest energy.
The final energy of the particle when it reaches a speed of 0.902 c is given by E = γmc², where γ is the Lorentz factor. The Lorentz factor is defined as γ = 1/√(1 - (v/c)²), where v is the velocity of the particle.
By substituting the given values into the Lorentz factor equation, we can calculate the Lorentz factor for the particle. With the Lorentz factor known, we can determine the final energy of the particle.
The work done on the particle is equal to the change in energy, so the work can be calculated as ΔE = (γ - 1)mc². By substituting the values into the equation and expressing the answer as a multiple of mc², we can determine the work required to accelerate the particle to the given speed.
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Find the density of a 2 cm x 2 cm x 2 cm cube with a mass of 64 g.
Answer:
8 g/cm³
Explanation:
density=mass/volume
volume=2*2*2=8 cm³
mass=64 g
density=64/8=8 g/cm³
The density of a 2 cm x 2 cm x 2 cm cube with a mass of 64 g is equal to 8 g/cm³.
What is the density?Density can be defined as the material mass per unit of volume. The symbol commonly used to represent density ρ and the letter 'D' can also be used.
The mathematical equation of the density can be represented as written below:
Density = Mass /Volume
or, ρ = m/V
The density of a material varies with pressure and temperature. There is a small variation for solids and liquids of any material but much larger for gases. Increasing the pressure of material decreases the volume and thus increases its density.
Given the volume of the cube = 2 cm x 2 cm x 2 cm
V = 8 cm³
The mass of the cube, m = 64 g
The density of the cube can be calculated from the above-mentioned formula:
Density = Mass of cube/volume
D = 64/8
D = 8 g/cm³
Therefore, the density of the cube is 8 g/cm³.
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use a parametrization to find the flux across the portion of the sphere in the first octant
The flux across the portion of the sphere is a³/ 16.
To find the flux across the portion of the sphere in the first octant, we need to use a parametrization of the surface. The sphere can be parametrized as:
r(θ, φ) = (a sin φ cos θ, a sin φ sin θ, a cos φ)
where 0 ≤ θ ≤ π/2 and 0 ≤ φ ≤ π/2.
The normal vector to the surface is:
n = r_θ × r_φ
where r_θ and r_φ are the partial derivatives of r with respect to θ and φ, respectively.
We have:
r_θ = (-a sin φ sin θ, a sin φ cos θ, 0)
r_φ = (a cos φ cos θ, a cos φ sin θ, -a sin φ)
So:
n = (-a² sin² φ cos θ, -a² sin² φ sin θ, -a² sin φ cos φ)
The flux of F across S is given by:
∫∫S F ⋅ n dS
where F is the vector field and dS is the surface area element. In this case,
F = (0, 0, z)
dS = |r_θ × r_φ| dθ dφ
So we have:
∫∫S F ⋅ n dS = ∫∫D F(r(θ, φ)) ⋅ (r_θ × r_φ) dθ dφ
= ∫0(0[tex]^{\pi } /2[/tex] )∫0[tex]^{\pi } /2[/tex] (a cos φ) (-a² sin² φ cos θ i - a² sin² φ sin θ j - a² sin φ cos φ k) ⋅ (-a² sin φ i - a² sin φ j - a² cos φ k) dθ dφ
= ∫0^(π/2) ∫0[tex]^{\pi } /2[/tex] a³ sin³ φ cos²φ dθ dφ
= (a³ / 4) ∫0[tex]^{\pi } /2[/tex] (sin 4φ / 4) dφ
= (a³ / 16) [1 - 0]
= a³/ 16
To know more about vector field
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Why do baseball pitchers throw the ball at an angle that is slightly above the horizontal if they want the ball to reach at approximately the same height as it was thrown when it gets to the batter?
Answer:
The angle above the horizontal at which the pitcher throws the ball determines the distance the ball travels before returning to the height at which it was thrown
Explanation:
The baseball is thrown as a projectile and the range, 'R', of the baseball which is the distance the baseball travels before the height above the ground returns to the initial height is given given as follows;
[tex]R = \dfrac{u^2 \cdot sin(2\cdot \theta )}{g}[/tex]
Where;
R = The range of the baseball = The horizontal distance away from the pitcher the ball reaches
u = The initial velocity with which the baseball was thrown
θ = The angle above horizontal a baseball pitcher throws the ball
g = The acceleration due to gravity ≈ 9.81 m/s²
From the the equation, when θ = 0, sin(θ) = sin(0) = 0 and the ball does not cover any horizontal distance before going lower than the height at which it was thrown, therefore, for the ball to travel further, the angle of launch, θ has to be larger than 0.
When it is winter in the Northern Hemisphere, it is summer in the Southern Hemisphere. Which statement best explains the reason for this situation?
Group of answer choices
A) When the Northern Hemisphere is closer to the sun than the Southern Hemisphere is, the Southern Hemisphere is relatively far from the sun.
B) When the Northern Hemisphere is tilted toward the sun, the Southern Hemisphere is tilted away from the sun.
C) When the Northern Hemisphere is farther from the sun than then Southern Hemisphere is, the Southern Hemisphere is relatively close to the sun.
D) When the Northern Hemisphere is tilted away from the sun, the Southern Hemisphere is tilted toward the sun.
Explanation::i dont know the answer ,but pls then also mark me as brainlist
Answer:
When the N. Hemisphere is tilted away from the sun, the S. Hemisphere is tilted toward the sun
Explanation:
Unlike the idiot down there that just wanted point here you go