A. [tex]\( \iint_{S_2} F \cdot dS = 128 \)[/tex]
B. [tex]\( \iint_{S_2} F \cdot dS = 128 \)[/tex]
(A) If the magnitude of (F) is inversely proportional to the square of the distance from the origin:
We know that the flux integral over [tex]\( S_1 \)[/tex] is [tex]\( \iint_{S_1} F \cdot dS = 8 \)[/tex].
Since ( F ) is a radial force field, (F) and (dS) are parallel, and the dot product simplifies to [tex]\( |F| \cdot |dS| \)[/tex].
The surface area of a sphere is [tex]\( 4\pi r^2 \)[/tex], so the magnitude of [tex]\( dS \)[/tex] on [tex]\( S_1 \)[/tex] is [tex]\( |dS| = 16\pi \)[/tex].
Therefore, [tex]\( |F| \cdot |dS| = 8 \implies |F| \cdot 16\pi = 8 \)[/tex], which gives [tex]\( |F| = \frac{1}{2\pi} \)[/tex].
For [tex]\( S_2 \)[/tex], with radius 16, [tex]\( |dS| = 256\pi \)[/tex].
So, [tex]\( \iint_{S_2} F \cdot dS = |F| \cdot 256\pi = \frac{1}{2\pi} \cdot 256\pi = 128 \)[/tex].
(B) If the magnitude of (F) is inversely proportional to the cube of the distance from the origin:
For [tex]\( S_1 \)[/tex], [tex]\( |dS| = 16\pi \)[/tex] as before. So, [tex]\( |F| \cdot |dS| = 8 \implies |F| = \frac{1}{2} \)[/tex].
For [tex]\( S_2 \)[/tex], [tex]\( |dS| = 256\pi \)[/tex] as before.
So, [tex]\( \iint_{S_2} F \cdot dS = |F| \cdot 256\pi = \frac{1}{2} \cdot 256\pi = 128 \)[/tex].
Explain in detail why it may take longer for you to fight off the flu virus the first time this season than it would if you caught the same strain a second time.
Answer:
"when an infection has cleared, a small number of B and T cells are present in the blood with memory of the virus, allowing them to activate and destroy viruses more quick and fast next time when they enter the body."which is known as immune system."
Explanation:
Our immune system is not only designed to destroy disease-causing codes but remembers codes it's encountered so they are able to fight against them with when they return. when we all come across these types of invaders our layer of protection stops it from entering our body. When body senses a virus or other infections, like bacteria, the body tends to try and destroy the foreign invaders. The first step is the macrophages is activated. Macrophages destroy the foreign invaders. If the viruses penetrates deep into the body it result into infection. Where the T cells and B cells are activated to fight against these viruses.T & B cells contains antibodies that attach to the virus and label it as foreign for other cells to destroy.
A 100 kg box is hanging from two strings. String #1 pulls up and left, making an angle of 80o with the horizontal on the left, and string #2 pulls up and to the right, making an angle of 65o with the horizontal on the right. FInd the tension in string #2 (on the right side)
Answer:296.76 N
Explanation:
Given
mass of box [tex]m=100 kg[/tex]
Let [tex]T_1[/tex] be the Tension in left side and [tex]T_2[/tex] be the Tension in the right side
From diagram
[tex]T_1\cos 80=T_2\cos 65[/tex]
[tex]T_1=T_2\cdot \frac{\cos 65}{\cos 80}[/tex]
and
[tex]T_1\sin 80+T_2\sin 65=100\cdot g[/tex]
[tex]T_2\left [ \tan 80\cdot \cos 65+\sin 65\right ]=100\cdot g[/tex]
[tex]T_2=\frac{100\cdot g}{\left [ \tan 80\cdot \cos 65+\sin 65\right ]}[/tex]
[tex]T_2=\frac{980}{3.3023}=296.76 N[/tex]
After coming down a steep hill at a constant speed of 43 m/s, a car travels along the circumference of a vertical circle of radius 618 m until it begins to climb another hill. r x What is the magnitude of the net force on the 34 kg driver of the car at the lowest point on this circular path? Answer in units of kN.
Answer:
F=0.101 kN
Explanation:
Newton's 2nd law, F = ma, but this is circular path, the acceleration (a) is the centripetal acceleration.
a = (v²) / r
F = (m×v²) /r
F=(34 kg)×(43 m/s)² / 618 m
F=101.72 N
To convert Newtons into kilo-Newtons divide it 1000.
F=0.101 kN
A concrete pump of 120-cy/hr max. output is used to place 250 cy of concrete. It is supplied by 8 cy transit-mix trucks arriving to the site every 15 mins. Barring interruptions how many hours will the operation require, considering 80% efficiency factor.
Answer:
Completing the operation will require 9.765625 hours.
Explanation:
First, let's check which of the stages will be the process limitation:
Regarding the pump, it can perform up to 120 cy/h. The trucks will deliver 8 cy every 15 min, i.e., 32 cy/h, then this is the smaller capacity within the whole process.
Now, let's establish a simple relation:
Placement speed x Efficiency = Placed quantity / time,
solving for time. we have
[tex]t = \frac{q}{\epsilon s} = \frac{250 cy}{0.8\times 32\frac{cy}{h}} = \mathbf{9.765625 h}.[/tex]
The operation will require approximately 2.6 hours, taking into account the efficiency factor.
Explanation:To determine how many hours the operation will require, we need to calculate the total time it takes for all the trucks to arrive at the site and unload the concrete. Since each truck delivers 8 cy of concrete every 15 mins, we can calculate the time it takes for all the trucks to deliver 250 cy of concrete: 250 cy / (8 cy/truck * 15 mins/truck) = 250 cy / (120 mins) = 2.08 hours.
However, we need to account for the 80% efficiency factor, which means the pump is only operating at 80% of its maximum output. Therefore, the total time required would be 2.08 hours / 0.8 = 2.6 hours.
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Starting from rest, your friend dives from a high cliff into a deep lake below, yelling in excitement at the thrill of free-fall on her way down. You watch her, as you stand on the lake shore, and at a certain instant your keen hearing recognizes that the usual frequency of her yell, which is 919 Hz, is shifted by 55.9 Hz. How long has your friend been in the air when she emits the yell whose frequency shift you hear? Take 342 m/s for the speed of sound in air and 9.80 m/s2 for the acceleration due to gravity.
Answer:
2 seconds
Explanation:
f = Frequency of yell = 919 Hz
[tex]\Delta f[/tex] = Shifted frequency = 55.9 Hz
v = Speed of sound in air = 342 m/s
[tex]v_r[/tex] = Velocity of friend
a = Acceleration due to gravity = 9.81 m/s²
From the Doppler shift formula we have
[tex]\dfrac{f+\Delta f}{f}=\dfrac{v}{v-v_r}\\\Rightarrow v_r=v-\dfrac{vf}{f+\Delta f}\\\Rightarrow v_r=342-\dfrac{342\times 919}{919+55.9}\\\Rightarrow v_r=19.61\ m/s[/tex]
The velocity of the my friend is 19.61 m/s
[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{19.61-0}{9.8}\\\Rightarrow t=2\ s[/tex]
The time my friend is in the air is 2 seconds
Near the top of the Citigroup Bank building in New York City, there is a 4.00 105 kg mass on springs having adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven — the driving force is transferred to the mass, which oscillates instead of the building.
(a) What effective force constant should the springs have to make the mass oscillate with a period of 3.00 s? N/m
(b) What energy is stored in the springs for a 2.00 m displacement from equilibrium?
Answer:
(a) k = 1.76× 10⁶ N/m
(b) E = 3.52 × 10⁶ J
Explanation:
(a)
The period (T) of a spring = 2π√(m/k)
where m = mass of the spring in kg, k = spring constant.
T = 2π√(m/k)..................... equation 1
making k the subject of the equation,
k = 4π²(m)/T².............................. equation 2
Where m = 4.00 × 10⁵ kg, T = 3.00 s, π = 3.143
Substituting these values into equation 2
k = 4(3.143)²(4.0×10⁵)/3²
k = (1.58 × 10⁷)/9
k = 1.76× 10⁶ N/m
(b)
The energy stored(E) in a spring = 1/2ke²
Where k = spring constant, e = extension.
E = 1/2ke²
k = 1.76× 10⁶ N/m, e= 2.00 m
∴E = 1/2(1.76× 10⁶)(2)²
E = 2 × 1.76 × 10⁶
E = 3.52 × 10⁶ J
There was an accident at a uranium processing plant in Tokai, Japan, on September 30, 1999. Using your favorite search engine, find out what happened and compare this accident with the ones at Chernobyl and Three Mile Island. How could these accidents have been avoided? Do these incidents prove that nuclear power plants should be phased out? Why or why not?
For the three accidents mentioned there were human factors that caused the destabilization of the reactors and generated catastrophies.
In the case of Tokai, there was an excess of Uranium due to the fact that workers (Not qualified, since such work did not merit it) added to the containers, which generated an excess in the filling generating an emulsion of radiation to all the personnel.
In the case of Chernobyl, it was the experimentation through a series of tests to reduce the power, during which a series of imbalances occurred in the reactor 4 of this nuclear power plant, which led to the uncontrolled overheating of the reactor core nuclear-
In the case of Three Mile Island it was a design error in which the water level was underestimated, believing that the required level was available but in the end it was noted that said water level was not sufficient which caused the melting of a water dipstick.
All this leaves us with reflections on the security protocols followed for the construction or management of these nuclear power plants, and calls into question the human capacity to react to one of these catastrophes. Today, these plants not only put human health at risk but also generate waste that pollutes the planet. Alternatives such as renewable and clean energy already become more popular every day and are about to leave nuclear energy in the past to give rise to a new human stage.
A seaside cliff is 30 m above the ocean surface, and Sam is standing at the edge of the cliff. Sam has three identical stones. The first stone he throws off the cliff at 30° above the horizontal. The second stone he throws vertically downward into the ocean. The third stone he drops into the ocean.
1. In terms of magnitude, which stone has the largest change in its velocity over a one second time interval after its release? (Sam’s throwing speed is 10 m/s.)
Answer:
In terms of magnitude, the stones 2 and 3 have the largest change in its velocity over a one second time interval after their release.
Explanation:
Stone 1:
vi = 10 m/s
vix = vi*Cos ∅ = (10 m/s)*Cos 30° = 8.66 m/s = vx
viy = vi*Sin ∅ = (10 m/s)*Sin 30° = 5 m/s
vy = viy - g*t = (5 m/s) - (9.8m/s²)*(1 s) = -4.8
then
v = √(vx²+vy²) = √((8.66)²+(-4.8)²) = 9.90 m/s
Δv = v - vi = 9.902 m/s - 10 m/s
⇒ Δv = -0.098 m/s
Stone 2:
vi = 10 m/s
v = vi + g*t = (10 m/s) + (9.8m/s²)*(1 s) = 19.8 m/s
Δv = v - vi = (19.8 m/s) - (10 m/s)
⇒ Δv = 9.8 m/s
Stone 3:
vi = 0 m/s
v = g*t = (9.8m/s²)*(1 s) = 9.8 m/s
Δv = v - vi = (9.8 m/s) - (0 m/s)
⇒ Δv = 9.8 m/s
Finally, in terms of magnitude, the stones 2 and 3 have the largest change in its velocity over a one second time interval after their release.
While skiing in Jackson, Wyoming, your friend Ben (of mass 69.8 kg) started his descent down the bunny run, 16.8 m above the bottom of the run. If he started at rest and converted all of his gravitational potential energy into kinetic energy, what is Ben’s kinetic energy at the bottom of the bunny run? Use g = 9.8 m/s 2 Answer in units of J.
Answer:
11484.18 J
Explanation:
Applying conservation of energy we get
potential energy = kinetic energy
mgh = 0.5mv^2
gh= 0.5v^2
[tex]v= \sqrt{2gh}[/tex]
h= 16.8 m
g= 9.8 m/s^2
[tex]v= \sqrt{2\times16.8\times9.8}[/tex]
v=18.14 m/s at the bottom of the bunny run
therefore, Kinetic energy at the bottom of the bunny run
K= [tex]\frac{1}{2} mv^2=\frac{1}{2}69.8\times18.14^2[/tex]
therefore K= 11484.18 J
= 11.48 KJ
Answer: What is his final velocity?
Answer in units of m/s.
Explanation: i need help
At high noon, the sun delivers 1 000 W to each square meter of a blacktop road.
What is the equilibrium temperature of the hot asphalt, assuming its emissivity e = 1? (σ = 5.67 × 10−8W/m2⋅K4) .
a. 75°Cb. 84°Cc. 91°Cd. 99°C
Answer:
The correct answer is c, T = 91.3°C
Explanation:
For this exercise let's use Stefan's equation on the emission of a black body
P = σ A e T⁴
Where σ is the Stefan-Boltzmann constant, A the area, and 'e' emissivity and T the absolute temperature
In this case give the absorbed power is 1000W per square meter, let's clear the temperature equation
T⁴ = (P / A) 1/σ e
Let's calculate
T⁴ = 1000 1 / (5.67 10⁻⁸ 1)
T⁴ = 176.37 10⁸
T =[tex]\sqrt[4]{176.37 10^8}[/tex]
T = 3.6442 10² K
Let's reduce to degrees Celsius
T = 364.42 -273.15
T = 91.3 ° C
The correct answer is c
The equilibrium temperature of the hot asphalt, assuming it behaves as a perfect blackbody with emissivity of 1, can be calculated using the Stefan-Boltzmann law, resulting in approximately 91°C, making choice (c) the correct answer.
To determine the equilibrium temperature of the hot asphalt, we can use the concept of blackbody radiation.
Since the emissivity (e) is 1, the asphalt behaves as a perfect blackbody, which means it absorbs and emits radiation efficiently.
The power per unit area absorbed by the asphalt is:
P = 1000 W/m²According to the Stefan-Boltzmann law, the power radiated per unit area by a blackbody is given by:
P = σeT⁴where
σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴), and T is the equilibrium temperature in KelvinGiven that e = 1 for a perfect blackbody, we can set the absorbed power equal to the emitted power:
1000 = 5.67 × 10⁻⁸ T⁴Solving for T:
T⁴ = 1000 / 5.67 × 10⁻⁸T⁴ ≈ 1.76 × 10¹⁰T ≈ (1.76 x 10¹⁰)∧1/4T ≈ 278.8 KConverting to Celsius:
T ≈ 278.8 K - 273.15 ≈ 5.65°CThis result does not match any answer choices, which suggests a potential issue. The correct calculations should yield a higher temperature due to an error in an earlier assumption or value misunderstanding. Revisiting the calculations correctly:
Solving again for higher accuracy:
T ≈ (1000 / 5.67 x 10⁻⁸)∧1/4 ≈ 364 K ≈ 91°CTherefore, the correct equilibrium temperature is 91°C, making the correct choice: (c) 91°C
The deflection of air masses to the right or left (depending on latitude) as they move from one latitude to another is called the:
a. Coriolis effect.
b. Hadley cell.
c. Saffir-Simpson scale.
d. Cyclonic effect.
e. Ekman spiral.
The coriolis effect is the force produced by the rotation of the Earth in space, which tends to deflect the trajectory of objects that move on the surface of the earth; to the right in the northern hemisphere and to the left, in the south. Said 'object' for this particular case is the mass of air. Therefore the correct answer is A: Coriolis effect.
Interactive Solution 9.37 presents a method for modeling this problem. Multiple-Concept Example 10 offers useful background for problems like this one. A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.130 m, an angular speed of 78.0 rad/s, and a moment of inertia of 1.25 kg·m2. A brake shoe presses against the surface of the cylinder and applies a tangential frictional force to it. The frictional force reduces the angular speed of the cylinder by a factor of 6 during a time of 3.00 s. (a) Find the magnitude of the angular deceleration of the cylinder. (b) Find the magnitude of the force of friction applied by the brake shoe.
Answer:
21.67 rad/s²
208.36538 N
Explanation:
[tex]\omega_f[/tex] = Final angular velocity = [tex]\dfrac{1}{6}78=13\ rad/s[/tex]
[tex]\omega_i[/tex] = Initial angular velocity = 78 rad/s
[tex]\alpha[/tex] = Angular acceleration
[tex]\theta[/tex] = Angle of rotation
t = Time taken
r = Radius = 0.13
I = Moment of inertia = 1.25 kgm²
From equation of rotational motion
[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{13-78}{3}\\\Rightarrow \alpha=-21.67\ rad/s^2[/tex]
The magnitude of the angular deceleration of the cylinder is 21.67 rad/s²
Torque is given by
[tex]\tau=I\alpha\\\Rightarrow \tau=1.25\times -21.67\\\Rightarrow \tau=-27.0875[/tex]
Frictional force is given by
[tex]F=\dfrac{\tau}{r}\\\Rightarrow F=\dfrac{-27.0875}{0.13}\\\Rightarrow F=-208.36538\ N[/tex]
The magnitude of the force of friction applied by the brake shoe is 208.36538 N
The angular deceleration of the cylinder is 46.0 rad/s².
The force of friction applied by the brake shoe is 1180 N.
Here's how we can approach it:
(a) Angular Deceleration:
Initial Angular Speed (ω₀): 92.0 rad/s
Final Angular Speed (ωf): ω₀/2 = 92.0 rad/s / 2 = 46.0 rad/s
Time (Δt): 4.00 s
We can use the following equation to find the angular deceleration (α):
α = (ωf - ω₀) / Δt
Substituting the values:
α = (46.0 rad/s - 92.0 rad/s) / 4.00 s
α = -46.0 rad/s² (negative sign indicates deceleration)
Therefore, the magnitude of the angular deceleration of the cylinder is 46.0 rad/s².
(b) Force of Friction:
Moment of Inertia (I): 1.36 kg·m²
Angular Deceleration (α): 46.0 rad/s²
The net torque (τ) acting on the cylinder is equal to the product of its moment of inertia and angular deceleration:
τ = I * α
The frictional force (F) applied by the brake shoe creates a torque that opposes the cylinder's rotation. This torque is equal to the force multiplied by the radius of the cylinder (r):
τ = F * r
Since the net torque is caused solely by the frictional force, we can equate the two torque equations:
I * α = F * r
Solving for the force of friction:
F = I * α / r
Substituting the values:
F = 1.36 kg·m² * 46.0 rad/s² / 0.0530 m
F = 1180 N
Therefore, the magnitude of the force of friction applied by the brake shoe is 1180 N.
1. A 70-kg swimmer dives horizontally off a 500-kg raft. The diver's speed immediately after leaving the raft is 6.0 m/s. A micro-sensor system attached to the edge of the raft measures the time interval during which the diver applies an impulse to the raft just prior to leaving the raft surface. If the time interval is read as 0.25 s, what is the magnitude of the average horizontal force by diver on the raft?
To solve this problem it is necessary to apply the concepts related to momentum theorem.
The equation for impulse is given as
[tex]I = Ft[/tex]
Where
I = Force
t = Time
At the same time we have the equation for momentum is given as
[tex]p = mv[/tex]
The impulse momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. Therefore
I = p
Ft = mv
Solving to find the force
[tex]F = \frac{mv}{t}[/tex]
[tex]F = \frac{(70)(6)}{0.25}[/tex]
[tex]F = 1680N[/tex]
Therefore the magnitude of the average horizontal force by diver on the raft is 1680N
The magnitude of the average horizontal force exerted by the diver on the raft is 1680 N.
Explanation:To find the magnitude of the average horizontal force exerted by the diver on the raft, we need to start by calculating the change in momentum of the diver. The momentum of an object is given by the equation p = mv, where p is the momentum, m is the mass, and v is the velocity. The change in momentum is equal to the impulse, which is given by the equation J = Δp = mΔv.
Since the swimmer dives horizontally, the change in velocity is equal to the initial velocity of the swimmer. Therefore, Δv = 6.0 m/s. Substituting the values, we get J = (70 kg)(6.0 m/s) = 420 kg·m/s.
The impulse is equal to the average force multiplied by the time interval, so we can rearrange the equation to solve for the average force. F = J / Δt = 420 kg·m/s / 0.25 s = 1680 N.
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How many calories are equal to one BTU? (One calorie = 4.186 J, one BTU = 1 054 J.)
a. 0.252b. 3.97c. 252d. 397
Explanation:
We need to find how many calories is 1 BTU.
Given
1 BTU = 1054 J
1 calorie = 4.186 J
So we have
1 BTU = 4.186 x 251.79 J
1 BTU =251.79 calorie
1 BTU = 252 calorie.
Option C is the correct answer.
Acetylene torches are used for welding. These torches use a mixture of acetylene gas, C2H2, and oxygen gas, O2 to produce the following combustion reaction: 2C2H2(g)+5O2(g)→4CO2(g)+2H2O(g) Imagine that you have a 6.50 L gas tank and a 4.00 L gas tank. You need to fill one tank with oxygen and the other with acetylene to use in conjunction with your welding torch. If you fill the larger tank with oxygen to a pressure of 115 atm , to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time? Assume ideal behavior for all gases.
Answer:
Pressure in acetylene gas tank will be 74.8atm
Explanation:
Step 1: Using the ideal gas equation, determine the number of moles of oxygen
[tex]n=\frac{PV}{RT}[/tex]
[tex]P_O=115atm[/tex]
[tex]V_O=6.50L[/tex]
[tex]n_O=\frac{P_OV_O}{RT}[/tex]
[tex]n_O=\frac{115*6.50}{RT}[/tex]
[tex]n_O=\frac{747.5}{RT}[/tex]
As temperature is unknown and assumed to be the same for both gases, and the ideal gas constant will be the same for both cases, these values are left as constants 'T' and 'R'.
Step 2: Determine the proportionate number of moles of acetylene required based on the chemical equation
2 moles of acetylene require 5 moles of oxygen for complete combustion
Thus, 0.4 moles of acetylene are required per mole of oxygen
[tex]n_A=0.4n_O[/tex]
[tex]n_A=0.4*\frac{747.5}{RT}[/tex]
[tex]n_A=\frac{299}{RT}[/tex]
Step 3: Determine the pressure of acetylene tank required in 4.00L tank
[tex]n_A=\frac{P_AV_A}{RT}[/tex]
[tex]\frac{299}{RT}=\frac{P_A*4.00}{RT}[/tex]
[tex]P_A=\frac{299}{4.00}[/tex]
[tex]P_A=74.75 atm[/tex]
Assumptions:
Temperature is the same for both gases and constant
The ideal gas constant is the same for both gases
The combustion reaction is complete and there are no limiting factors
This question relates to the practicality of searching for intelligent life in other solar systems by detecting their radio broadcasts (or aliens find us from ours). The closest stars are 4 light years away from us. How far away must you be from a 781 kHz radio station with power 50.0 kW for there to be only one photon per second per square meter? Assume that the photons spread out spherically. The area of a sphere is 4????????2.
Answer:
[tex]2.77287\times 10^{15}\ m[/tex]
Explanation:
P = Power = 50 kW
n = Number of photons per second
h = Planck's constant = [tex]6.626\times 10^{-34}\ m^2kg/s[/tex]
[tex]\nu[/tex] = Frequency = 781 kHz
r = Distance at which the photon intensity is i = 1 photon/m²
Power is given by
[tex]P=nh\nu\\\Rightarrow n=\dfrac{P}{h\nu}\\\Rightarrow n=\dfrac{50000}{6.626\times 10^{-34}\times 781000}\\\Rightarrow n=9.66201\times 10^{31}\ photons/s[/tex]
Photon intensity is given by
[tex]i=\dfrac{n}{4\pi r^2}\\\Rightarrow 1=\dfrac{9.66201\times 10^{31}}{4\pi r^2}\\\Rightarrow r=\sqrt{\dfrac{9.66201\times 10^{31}}{4\pi}}\\\Rightarrow r=2.77287\times 10^{15}\ m[/tex]
The distance is [tex]2.77287\times 10^{15}\ m[/tex]
You must stay at a distance of [tex]2.77287*10^1^5m[/tex]
How can we arrive at this result?First, we have to find the number of protons per second. This will be done using the equation: [tex]n= \frac{P}{h*v}[/tex]In this equation, the "h" represents Planck's constant and will take on the value of [tex]6.626*10^-^3^4m^2\frac{Kg}{s}[/tex]
The "r" will be equal to 1 photon/m² and the "P' will be equal to 50 kW.
Therefore, we will solve the equation as follows:
[tex]n= \frac{50000}{(6.626*10^-^3^4*781000)}= 9.66201*10^3^1 \frac{protons}{s}[/tex]
From this value, we can calculate the appropriate distance for you to position yourself. For this, we will use the equation:[tex]r^2=\frac{n}{4*\pi} \\r= \sqrt{\frac{9.6621*10^3^1}{4*\pi } } = 2.77287*10^1^5m[/tex]
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There is a skier at the top of a ski slope. The skier has potential energy. What gives the skier his potential energy? A. his speed B. friction C. gravity D. his efficiency
Answer:C
Explanation:
Skier at the top of a ski has Potential Energy due to gravity.
Potential Energy is the Energy Possessed by an object when it attains a height concerning some zero level Position.
During the process of attaining the height, some work has to be done against gravity and this energy stored within the object after attaining some height w.r.t relative zero position.
The answer is C: gravity
the crankshaft of an engine increases its spin from 1,000 to 2,000 rpm in 0.50 s what is its angular acceleration
Answer:
angular acceleration = 209.44 [rad/s^2]
Explanation:
First we have to convert the velocities which are in revolutions per minute to radians on second.
where:
[tex]w_{0} = 1000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 104.7[\frac{rad}{s} ]\\w = 2000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 209.4[\frac{rad}{s} ][/tex]
Now we can find the angular acceleration:
[tex]w=w_{0} + \alpha *t\\\alpha =\frac{w-w_{0} }{t} \\\alpha =\frac{209.43-104.71}{\0.5 } \\\alpha = 209.44[\frac{rad}{s^{2} } ][/tex]
The angular acceleration of the crankshaft is [tex]\(209.44 \, \text{rad/s}^2\)[/tex].
To find the angular acceleration, we can use the following formula:
[tex]\[ \alpha = \frac{\Delta \omega}{\Delta t} \][/tex]
where:
[tex]\(\alpha\)[/tex] is the angular acceleration
[tex]\(\Delta \omega\)[/tex] is the change in angular velocity
[tex]\(\Delta t\)[/tex] is the change in time
First, we need to convert the angular velocities from revolutions per minute (rpm) to radians per second (rad/s).
1. Initial angular velocity [tex](\(\omega_i\))[/tex]:
[tex]\[ \omega_i = 1000 \, \text{rpm} \][/tex]
2. Final angular velocity [tex](\(\omega_f\))[/tex]:
[tex]\[ \omega_f = 2000 \, \text{rpm} \][/tex]
To convert rpm to rad/s:
[tex]\[ \omega (\text{rad/s}) = \omega (\text{rpm}) \times \frac{2\pi \, \text{rad}}{60 \, \text{s}} \][/tex]
[tex]\[ \omega_i = 1000 \times \frac{2\pi}{60} \, \text{rad/s} = \frac{2000\pi}{60} \, \text{rad/s} \approx 104.72 \, \text{rad/s} \][/tex]
[tex]\[ \omega_f = 2000 \times \frac{2\pi}{60} \, \text{rad/s} = \frac{4000\pi}{60} \, \text{rad/s} \approx 209.44 \, \text{rad/s} \][/tex]
Now, we can find the change in angular velocity:
[tex]\[ \Delta \omega = \omega_f - \omega_i \][/tex]
[tex]\[ \Delta \omega = 209.44 \, \text{rad/s} - 104.72 \, \text{rad/s} = 104.72 \, \text{rad/s} \][/tex]
Given that the change in time [tex](\(\Delta t\))[/tex] is 0.50 s:
[tex]\[ \alpha = \frac{104.72 \, \text{rad/s}}{0.50 \, \text{s}} \][/tex]
[tex]\[ \alpha = 209.44 \, \text{rad/s}^2 \][/tex]
what consistent physiological pattern is more common in men's' teeth? A. Men have more room in their mouths for their molars. B. Men generally have stronger enamel. C. Men have more teeth. D. Men generally have larger teeth.
Answer:
B.
Explanation:
Men generally have stronger enamel than the women.
An inventor develops a stationary cycling device by which an individual, while pedaling, can convert all of the energy expended into heat for warming water.
How much mechanical energy is required to increase the temperature of 300 g of water (enough for 1 cup of coffee) from 20°C to 95°C?
(1 cal = 4.186 J, the specific heat of water is 4 186 J/kg⋅°C)
a. 94 000 J
b. 22 000 J
c. 5 400 J
d. 14 J
Answer:
[tex]Q=94185\ J[/tex]
Explanation:
Given:
mass of water, [tex]m=0.3\ kg[/tex]initial temperature of water, [tex]T_i=20^{\circ}C[/tex]final temperature of water, [tex]T_f=95^{\circ}C[/tex]specific heat of water, [tex]c=4186\ J.kg^{-1}.K^{-1}[/tex]Now the amount of heat energy required:
[tex]Q=m.c.\Delta T[/tex]
[tex]Q=0.3\times 4186\times (95-20)[/tex]
[tex]Q=94185\ J[/tex]
Since all of the mechanical energy is being converted into heat, therefore the same amount of mechanical energy is required.
A damped harmonic oscillator consists of a block of mass 2.5 kg attached to a spring with spring constant 10 N/m to which is applied a damping force (in Newtons) of the form F = –0.1v, with v the velocity in m/s. The spring is stretched a distance xm and released. After four complete oscillations, what fraction of the mechanical energy is retained by the system?
Answer:
0.5% per oscillation
Explanation:
The term 'damped oscillation' means an oscillation that fades away with time. For Example; a swinging pendulum.
Kinetic energy, KE= 1/2×mv^2-------------------------------------------------------------------------------------------------------------(1).
Where m= Mass, v= velocity.
Also, Elastic potential energy,PE=1/2×kX^2----------------------------------------------------------------------------------------------------------------------(2).
Where k= force constant, X= displacement.
Mechanical energy= potential energy (when a damped oscillator reaches maximum displacement).
Therefore, we use equation (3) to get the resonance frequency,
W^2= k/m--------------------------------------------------------------------------------------(3)
Slotting values into equation (3).
= 10/2.5.
= ✓4.
= 2 s^-1.
Recall that, F= -kX
F^2= (-0.1)^2
Potential energy,PE= 1/2 ×0.01
Potential energy= 0.05 ×100
= 0.5% per oscillation.
In a damped harmonic oscillator, the fraction of mechanical energy retained by the system after multiple oscillations can be calculated by comparing the initial and final potential energies. The fraction of mechanical energy retained is equal to the ratio of the final amplitude squared to the initial amplitude squared.
Explanation:In a damped harmonic oscillator, the mechanical energy is gradually lost due to the damping force. The fraction of mechanical energy retained by the system after four complete oscillations can be determined by comparing the initial mechanical energy to the final mechanical energy. The initial mechanical energy is the sum of the potential energy and kinetic energy, while the final mechanical energy is only the potential energy.
Using the equation for the potential energy of a spring, U = ½kx², we can calculate the initial and final potential energies. The initial potential energy can be calculated using the initial amplitude, A, and the spring constant, k. The final potential energy can be calculated using the final amplitude, A', and the same spring constant, k.
The fraction of mechanical energy retained by the system is equal to the ratio of the final potential energy to the initial potential energy. This can be calculated using the equation: fraction of mechanical energy retained = (A'/A)².
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A row of five 1.2 N wooden blocks is being pushed across a tabletop at a constant speed by a toy tractor that exerts a force of 1.7 N on the row. What is the coefficient of kinetic friction between the wooden blocks and the tabletop?
To solve this problem we will apply the concepts related to the Kinetic Friction Force for which we define as
[tex]F = \mu_k N[/tex]
Where,
N = Normal Force (Mass for gravity)
[tex]\mu_k =[/tex] Kinetic frictional coefficient
The total force applied is 1.7N and the Force from the (normal) weight is equivalent to five times 1.2N, therefore:
[tex]F = 5(N)\mu_k[/tex]
[tex]1.7 = 5(1.2)(\mu_k)[/tex]
[tex]\mu_k = \frac{1.7}{5*1.2}[/tex]
[tex]\mu_k =0.283[/tex]
Therefore the coefficient of kinetic friction between the wooden blocks and the tabletop is 0.283
A slice of bread contains about 100 kcal. If specific heat of a person were 1.00 kcal/kg·°C, by how many °C would the temperature of a 70.0-kg person increase if all the energy in the bread were converted to heat?a. 2.25°Cb. 1.86°Cc. 1.43°Cd. 1.00°C
Answer:
(c) 1.43°C
Explanation:
If the energy in the bread are converted to heat.
Then, The heat transferred from the bread to person = 100 kcal.
From specific heat capacity,
Q = cmΔT............................ equation 1
Where Q = quantity of heat, m = mass of the person, c = specific heat capacity of the person, Δ = increase in temperature.
Making ΔT the subject the equation 1,
ΔT = Q/cm........................ equation 2
Where Q = 100 kcal, c= 1.00 kcal/kg.°C, m = 70.0 kg
Substituting these values into equation 2,
ΔT = 100/(1×70)
ΔT = 100/70
ΔT = 1.428
ΔT ≈ 1.43°C
The increase in temperature of the body is = 1.43°C
The right option is (c) 1.43°C
A refrigerator is being pulled up a ramp with a horizontal force P, which acts at the top corner. The refrigerator has a mass of 75 kg, acting through point G. The ramp is inclined at 20º, and the coefficient of static friction is 0.3 between the refrigerator and the ramp.
(a) Find the force P required to move the refrigerator.
(b) Does the refrigerator tip or slide?
Answer:
(a) P = 459.055 N.
(b) the refrigerator tips.
Explanation:
Given, the angle of ramp is 20°.
When the weight of refrigerator is resolved in directions parallel and perpendicular to ramp, 75×g×sin(20°) and 75×g×cos(20°).
⇒ normal contact force is 75×g×cos(20°).
⇒ frictional force is 0.3×75×g×cos(20°) = 207.414 N
so, total opposite force is 207.414 + 75×g×sin(20°) = 459.055 N.
so, the force needed is P = 459.055 N
And as the moment due to both opposite force and P force are in same direction the refrigerator tips rather than just sliding.
An inductor with an inductance of 3.50 H and a resistance of 8.00 Ω is connected to the terminals of a battery with an emf of 4.00 V and negligible internal resistance.a)
Just after the circuit is completed, at what rate is the battery supplying electrical energy to the circuit?Express your answer with the appropriate units.b)When the current has reached its final steady-state value, how much energy is stored in the inductor?Express your answer with the appropriate units.c)What is the rate at which electrical energy is being dissipated in the resistance of the inductor?Express your answer with the appropriate units.d)What is the rate at which the battery is supplying electrical energy to the circuit?
Answer:
a. 0 W
b. 0.4375 J
c. 2 W
d. 2 W
Explanation:
a.
Recall that the power is directly proportional to the current in the circuit. (P=I*V) First, determine the current at t=0. Note that inductor prevents an instantaneous build-up of current. Therefore, initial power is 0 W.
P initial = 0 W
b.
given on the APPC equation sheet (last equation bottom right):
U = (1/2)*L*(I^2)
we know I = V/R
U = (1/2)*3.5*(4/8)^2
U = .4375 J
c.
P = R*I^2
I=V/R
P = 8*(4/8)^2
P=2 W
d. (same as part c.)
P = R*I^2
I=V/R
P = 8*(4/8)^2
P=2 W
a) The battery supplies electrical energy at a certain rate just after the circuit is completed. b) When the current has reached its steady-state value, the energy stored in the inductor can be calculated. c) The rate at which electrical energy is being dissipated in the resistance of the inductor can be found using the power dissipated formula. d) The rate at which the battery is supplying electrical energy to the circuit is the same as the power delivered by it.
Explanation:a) Just after the circuit is completed, at what rate is the battery supplying electrical energy to the circuit?
To determine the rate at which the battery is supplying electrical energy, we need to calculate the power delivered by the battery. Power is given by the formula P = IV, where P is power in watts, I is current in amperes, and V is voltage in volts. Since we know the voltage (4.00 V) and the resistance (8.00 Ω), we can use Ohm's Law (V = IR) to find the current. Once we have the current, we can calculate the power delivered by the battery.
b) When the current has reached its final steady-state value, how much energy is stored in the inductor?
When the current reaches its final steady-state value, the inductor acts like a short circuit and has no effect on the circuit. Therefore, all the energy stored in the inductor is dissipated as heat due to the resistance. Since we know the inductance (3.50 H) and the resistance (8.00 Ω), we can calculate the energy stored in the inductor using the formula E = 0.5LI^2, where E is energy in joules, L is inductance in henries, and I is current in amperes.
c) What is the rate at which electrical energy is being dissipated in the resistance of the inductor?
The rate at which electrical energy is being dissipated in the resistance of the inductor is equal to the power dissipated. Power dissipated is given by the formula P = I^2R, where P is power in watts, I is current in amperes, and R is resistance in ohms. Since we know the resistance (8.00 Ω) and the current, we can calculate the power.
d) What is the rate at which the battery is supplying electrical energy to the circuit?
The rate at which the battery is supplying electrical energy to the circuit is the same as the power delivered by the battery, which we calculated in part a using the formula P = IV.
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What is absolute zero? What is the temperature of absolute zero on the Kelvin and Celsius scales?
Answer:
Absolute zero = 0 K or - 273°C
Explanation:
Absolute zero :
When the entropy and enthalpy of the ideal system reach at the minimum value then the temperature at that condition is known as absolute zero condition.
Absolute temperature is the minimum temperature in the temperature scale.The value of absolute zero is 0 K.
We know that
[tex]\dfrac{C-0}{100}=\dfrac{K-273}{100}=\dfrac{F-32}{180}[/tex]
F=Temperature in Fahrenheit scale
K=Temperature in Kelvin scale
C=Temperature in degree Celsius scale
When K = 0
[tex]\dfrac{C-0}{100}=\dfrac{K-273}{100}[/tex]
[tex]\dfrac{C-0}{100}=\dfrac{0-273}{100}[/tex]
C= - 273°C
Absolute zero = 0 K or - 273°C
Absolute zero is the lowest possible temperature, defined as 0 K on the Kelvin scale and -273.15°C on the Celsius scale. At this temperature, particles have minimal vibrational motion.
Explanation:Absolute zero is the lowest possible temperature where nothing could be colder and no heat energy remains in a substance. It is the point at which the fundamental particles of nature have minimal vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion.
On the Kelvin scale, absolute zero is defined as 0 K. This is not stated in degrees, as it is an absolute measure. On the Celsius scale, absolute zero is equivalent to -273.15°C.
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A hypodermic needle can be thought of as a large area pipe leading to a small pipe that opens into the vein. The diameter of the plunger is 1.2 cm and the needle diameter is 0.15 cm. If the gauge pressure in the vein is 25 mmHg, what minimum is needed on the plunger in order for a fluid flow into the vein to occur
According to the statement and the data presented, it is presumed that the variable to look for is force. To solve this problem it is necessary to apply the concepts related to the Force according to the pressure and the Area.
Mathematically the Force can be expressed as
[tex]F = PA[/tex]
Where,
P = Pressure (At this case, the plunger pressure)
A = Cross-sectional Area ( At this case the plunger area), defined for a circle.
Our values are given as,
[tex]r = 0.006m[/tex]
[tex]P = 25mmHg[/tex]
Replacing we have that
[tex]F = (25mmHg \big [\frac{133N/m^2}{1mm\cdot Hg} \big ])(\pi 0.006^2)[/tex]
[tex]F = 0.376N[/tex]
Therefore the minimum force needed on the plunger inorder for a fluid flow into the vein to occur is 0.376
Our favorite program runs in 10 seconds on computer A, which has a 4 GHz. clock. We are trying to help a computer designer build a new machine B, that will run this program in 6 seconds. The designer can use new (or perhaps more expensive) technology to substantially increase the clock rate, but has informed us that this increase will affect the rest of the CPU design, causing machine B to require 1.2 times as many clock cycles as machine A for the same program. What clock rate should we tell the designer to target?
Answer:
The rate clock is about
F = 8 GHz
Explanation:
f₁ = 4 G Hz , t₁ = 10 s , t₂ = 6s , f₂ = 1.2 f₁
Can organize to find the rate clock the designer build to the target so
X / 4 Ghz = 10 s , 1.2 X / Y = 6 s
X * Y = 10 s ⇒ F = 10 s
1.2 * 4 G Hz = 6 s
F = 10 * ( 1.2 * 4 G Hz ) / 6
F = 10 * ( 1.2 * 4 x 10 ⁹ Hz ) / 6
F = 8 x 10 ⁹ Hz
F = 8 GHz
Final answer:
To run a program in 6 seconds on Machine B, which needs 1.2 times as many clock cycles as Machine A, the target clock rate should be 8 GHz.
Explanation:
The student asked for the target clock rate needed for computer B to run a program in 6 seconds, given that computer A runs it in 10 seconds with a 4 GHz clock and that machine B needs 1.2 times as many clock cycles as machine A for the same program. To solve this, we know that time (T) is equal to the number of cycles (N) divided by the clock rate (C), or T = N / C. For machine A, TA = NA / CA and for machine B, TB = (1.2 * NA) / CB. If machine A completes the program in 10 seconds, the number of cycles it uses is CA * TA, which is 4 GHz * 10 s, yielding 40 billion cycles.
Machine B needs to run these 40 billion cycles in 6 seconds. Also, machine B requires 1.2 times the number of cycles of machine A; thus we have (1.2 * 40 billion) / 6 s to find CB, the clock rate for machine B. This simplifies to 8 GHz. Thus, for machine B to run the program in 6 seconds, the target clock rate should be 8 GHz.
Which one of the following statements is not a characteristic of a plane mirror?
A) The image is the same size as the object.
B) The image is always upright.
C) The image is real.
D) The image is reversed left to right compared to the object.
E) The image is the same distance behind the mirror as the object is in front of the mirror.
Answer:
C) false. The image is formed by the prolongation of the rays, so it is VIRTUAL
Explanation:
Let's review each of the statements
A) True. The image is the same size as the object in a flat mirror, m = 1
B) True. The rays are not inverted, so the right images
C) false. The image is formed by the prolongation of the rays, so it is VIRTUAL
D) True. Flat mirrors reverse left and right
E) True. When using trigonometry the angles are equal, therefore two triangles formed have the same leg, and the distance to the object and the image are equal
Answer:
The image is real is not a characteristics of a plane mirror.
Explanation:
A plane mirror is a reflector with a flat reflective covering. For light beams hitting a plane mirror, the angle of reflection matches the angle of incidence. The angle of the incidence is the angle within the incident beam and the surface normal flat mirror.
Reason for Image is not real in the plane mirror:
A real image is that picture that is created when the light beams originating from an object meet each other after reflection or refraction.A real image can be captured on the screen. The real image is constantly inverted. A common example of a real image is the image formed on the cinema screen.Thus we can say, real image is not a characteristic of a plane mirror.
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In the experiment to measure specific heat of a metal, you get the following data. What is the specific heat of the metal in J/kg.C?
(answer within +-3% will considered correct) MASSES: water= 259 g, metal=159 g, calorimeter=97 g INITIAL TEMPERATURES: water+calorimeter=21ºC, metal=98ºC Final equilibrium temp=31ºC Calorimeter is made of aluminum.
Answer:
c = 1,100 J/kgºC
Explanation:
Assuming that all materials involved, finally arrive to a final state of thermal equilibrium, and neglecting any heat exchange through the walls of the calorimeter, the heat gained by the system "water+calorimeter" must be equal to the one lost by the unknown metal.
The equation that states how much heat is needed to change the temperature of a body in contact with another one, is as follows:
Q = c * m* Δt
where m is the mass of the body, Δt is the change in temperature due to the external heat, and c is a proportionality constant, different for each material, called specific heat.
In our case, we can write the following equality:
(cAl * mal * Δtal) + (cH₂₀*mw* Δtw) = (cₓ*mₓ*Δtₓ)
Replacing by the givens , and taking cAl = 0.9 J/gºC, we have:
Qg= 0.9 J/gºC*97g*10ºC + 4.186 J/gºC*259g*10ºC = 11,715 J(1)
Ql = cₓ*159g*67ºC (2)
Based on all the previous assumptions, we have:
Qg = Ql
So, we can solve for cx, as follows:
cx = 11,715 J / 159g*67ºC = 1.1 J/gºC (3)
Expressing (3) in J/kgºC:
1.1 J/gºC * (1,000g/1 kg) = 1,100 J/kgºC