Answers
For the three-point charges fixed in a right triangle, we have:
1. The magnitude of the electric force on the +1.00 μC charge is 1.79 N.
2. The force does an angle of 21.68° with the x-axis.
1. Magnitude of the electric forceFirst, let's denote the charges as is shown in the picture below:
q₁: is the charge 1 = +0.800 μC = +0.800x10⁻⁶ Cq₂: is the charge 2 = +1.00 μC = +1.00x10⁻⁶ Cq₃: is the charge 3 = -0.600 μC = -0.600x10⁻⁶ C
The magnitude of the electric force on the charge 2 (+1.00 μC) is given by:
[tex]|F_{net}| = \sqrt{(\Sigma\vec{F}_{x})^{2} + (\Sigma\vec{F}_{y})^{2}}[/tex] (1)
Where:
[tex]\Sigma\vec{F}_{x}[/tex]: is the sum of the forces acting on the x-axis[tex]\Sigma\vec{F}_{y}[/tex]: is the sum of the forces acting on the y-axisWe can calculate the electrical forces with Coulomb's law:
[tex]\vec{F} = \frac{Kq_{1}q_{2}}{d^{2}}[/tex]
Where:
K is the Coulomb's constant = 9.00x10⁹ Nm²/C² q₁ and q₂ are the chargesd is the distance between the charges
Forces in the x-axis ([tex]\Sigma\vec{F}_{x}[/tex])
The forces in the x-component are given by:
[tex]\Sigma\vec{F}_{x} = \vec{F}_{21}_{x} + \vec{F}_{23}_{x}[/tex]
[tex]\Sigma\vec{F}_{x} = \vec{F}_{21}_{x}cos(\theta) + \vec{F}_{23}_{x}[/tex]
[tex]\Sigma\vec{F}_{x} = \frac{Kq_{1}q_{2}}{d_{12}^{2}}cos(\theta) + \frac{Kq_{2}q_{3}}{d_{23}^{2}}[/tex] (2)
Where:
θ: is the angle of the force F₂₁ with the x-axisd₁₂ = z = 9.60 cm = 0.0960 m d₂₃ = xWe can calculate the angle θ with the following trigonometric function:
[tex]sin(\theta) = \frac{y}{z}[/tex]
[tex]\theta = sin^{-1}(\frac{y}{z}) = sin^{-1}(\frac{8.10 cm}{9.60 cm}) = 57.5 ^\circ[/tex]
To find the distance x (d₂₃), we need to use Pythagoras:
[tex]x = \sqrt{z^{2} - y^{2}} = \sqrt{(0.0960 m)^{2} - (0.0810 m)^{2}} = 0.051 m[/tex]
After entering θ and x (d₂₃) into equation 2, we have:
[tex]\Sigma\vec{F}_{x} = \frac{9.00\cdot 10^{9} Nm^{2}C^{-2}(0.800 \cdot 10^{-6} C)(1.00 \cdot 10^{-6} C)}{(0.0960 m)^{2}}cos(57.5) + \frac{9.00 \cdot 10^{9}Nm^{2}C^{-2}(1.00 \cdot 10^{-6} C)(-0.600 \cdot 10^{-6} C)}{(0.051 m)^{2}}[/tex]
[tex]\Sigma\vec{F}_{x} = [0.78*cos(57.5) + (-2.08) N] = -1.66 N[/tex]
Hence, the x-component of the force is -1.66 N.
Forces in the y-axis ([tex]\Sigma\vec{F}_{y}[/tex])
The only force acting on the y-axis is the y-component of the force F₂₁, so:
[tex]\Sigma\vec{F}_{y} = -\vec{F}_{21}_{y} = -\vec{F}_{21}sin(\theta)[/tex]
The minus sign is because the vector is pointing in the negative y-direction (see the picture below).
[tex]\Sigma \vec{F}_{y} = -\frac{9.00\cdot 10^{9} Nm^{2}C^{-2}(0.800 \cdot 10^{-6} C)(1.00 \cdot 10^{-6} C)}{(0.0960 m)^{2}}sin(57.5) = -0.66 N[/tex]
Hence, the y-component of the force is -0.66 N.
Finally, the magnitude of the electric force on the charge +1.00 μC is (eq 1):
[tex]|F_{net}| = \sqrt{(-1.66 N)^{2} + (-0.66 N)^{2}} = 1.79 N[/tex]
Therefore, the magnitude of the electric force on the +1.00 μC charge is 1.79 N.
2. Direction of the force with the x-axisAccording to the picture below, the angle of the force with respect to the x-axis is given by:
[tex]tan(\beta) = \frac{\Sigma\vec{F}_{y}}{\Sigma\vec{F}_{x}}[/tex]
[tex]\beta = tan^{-1}(\frac{-0.66 N}{-1.66 N}) = 21.68 ^\circ[/tex]
Therefore, the force does an angle of 21.68° with the x-axis.
Find more about Coulomb's law here:
brainly.com/question/506926
I hope it helps you!
Related Questions
ELE Review questions
POSSIBLE POINTS: 3
Match the energy transformation sequence with the device it describes:
A hair dryer plugged into the wall
a
A hand crank generator emergency radio
A battery operated fan
11 CE to ELE
+ ELE to KE
:: KE to ELE
h
1
2
A Review
Answers
Answer:
1. ELE to KE = Electrical energy conversion to kinetic energy.
2. KE to ELE = kinetic energy conversion to electrical energy.
3. CE to ELE = chemical energy conversion to electrical energy.
Explanation:
The Law of Conservation of Energy states that energy cannot be destroyed but can only be transformed or converted from one form to another.
Some examples of energy are chemical energy, electrical energy, kinetic energy, sound energy, potential energy, light energy, etc.
The transformation of energy from one form to another are described below;
1. A hair dryer plugged into the wall: it involves the conversion of electrical energy to kinetic energy. The energy type present in the wall socket is electrical energy which powers the hair dryer to have kinetic energy i.e the energy possessed due to motion of hair dryer.
2. A hand crank generator emergency radio: it illustrates the conversion of kinetic energy to electrical energy. The hand crank generator possess kinetic energy as it is being wounded before it is then converted into electrical energy which powers the radio.
3. A battery operated fan: it illustrates the conversion of chemical energy to electrical energy. The cells present in battery possess chemical energy that is being converted into electrical energy to power the fan.
Suppose a meteor of mass 2.50 x 1013 kg is moving at 33.0 km/s relative to the center of the Earth and strikes the Earth. Suppose the meteor creates the maximum possible decrease in the angular speed of the Earth by moving toward the west and striking a point on the equator tangentially. What is the change in the angular speed of the Earth due to this collision
Answers
Answer:
change is imperceptible
w_f = 7.272 10⁻⁵ rad / s
Explanation:
For this exercise we can use the conservation of angular momentum.
Initial. Before the crash
L₀ = I w₀
final. After the crash
L_f = I w_f + p r
where the moment is
p = mv
As the system is formed by the two bodies, the forces during the impact are internal, therefore the angular momentum is conserved
L₀ = L_f
I w₀ = I w_f + m v r
w_f = w₀ - [tex]m \frac{ v \ r }{I}[/tex]
We can approximate the Earth to a sphere, so its angular momentum is
I = 2/5 M r²
we substitute
w_f = w₀ - [tex]\frac{5 \ m \ v}{2 \ M \ r}[/tex]
We can find the angular velocity of the Earth with the duration of a spin which is the period of one day
w₀ = 2π / T
T = 24 h (3600 s / 1h) = 86 400 s
w₀ = 2π / 86400
w₀ = 7.272 10⁻⁵ rad / s
let's calculate
w_f = 7.27 10⁻⁵ - [tex]\frac{5 \ 250 \ 10^{13} \ 33.0 \ 10^{3} }{ 2 \ 5.98 \ 10^{24} \ 6.37 10^{6} }[/tex]
w_f = 7.272 10⁻⁵ - 1.0829 10⁻¹³
w_f = 7.27199999 10⁻⁵
this change is imperceptible
w_f = 7.272 10⁻⁵ rad / s
A Drive to the BeachMary drove from her home to the beach that is 30 mi from her house. The first 15 mi she drove at 60 mph, and the next 15 mi she drove at 30 mph. Would the trip take more, less, or the same time if she traveled the entire 30 mi at a steady 45 mph
Answers
Answer:
Explanation:
Let us calculate the average velocity .
Average velocity = total distance / total time
Time taken to drive first 15 mi
= 15 / 60 = .25 h
Time taken to drive next 15 mi
= 15 / 30 = .5 h
Total time = .25 + .5 = .75 h
Total distance = 30 mi
average speed = 30 / .75
= 40 mi / h
So average speed is 40 mph which is less than given velocity of 45 mph .
Hence if she travels at 45 mph , she will take less time .
a water tank holds water to the depth of the 80cm what is the pressure of the water of the tank
Answers
Answer:
7976 Pascals significant figure= 7.9*10^3
Explanation:
formula of hpg = height*density*gravitational energy
.80*10*997=7976 pascals
Which factors affect the gravitational force between two objects?
-
distance and velocity
O mass and distance
O mass and weight
acceleration and weight
TELE
Answers
Mass and distance
Explanation:
According to Newton’s law, “objects with greater mass have a stronger force of gravity between them.” And “objects that are closer together have a stronger force of gravity between them.” Both of them mean mass and distance. Therefore, the correct answer is mass and distance.
Answer:
mass and distance
Explanation:
mass, and distance. The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them.
Friction produces heat because it causes molecules to move faster and
have more energy.
True or false.
Answers
Answer:
True
Explanation:
Friction occurs because no surface is perfectly smooth. Even surfaces that look smooth to the unaided eye make look rough or bumpy when viewed under a microscope. You know that friction produces heat. That’s why rubbing your hands together makes them warmer. But do you know why? Friction causes the molecules on rubbing surfaces to move faster, so they have more energy. This gives them a higher temperature, and they feel warmer. Heat from friction can be useful. It not only warms your hands.
A physicist attempts to use Newton's laws of motion to predict the behavior of a molecule of water, but the laws fail to give accurate predictions. What is the most likely reason?
A) Liquids do not follow the laws of motion.
B) The molecule is small enough so that quantum effects are important.
C) Newton’s laws apply to atoms, but not to molecules.
D) The molecule was likely traveling at a near-light speed.
Answers
Answer:
B) The molecule is small enough so that quantum effects are important.
Explanation:
The molecules of water behave like wave and their motion cannot be accurately predicted by classical physics laws but can be properly predicted by quantum theory.
Classical physics describes matter that behave like solid particles while quantum effect describes matter that behaves like waves.
Therefore, the correct option is B.
Suppose you have a cylinder filled with diatomic oxygen (O2) and it is running low. The cylinder is shown above, is made of steel, and has a fixed volume of 10 L.
You are asked to determine the number of O2 molecules that are left in the cylinder, so you take a measurement of the temperature to be 20℃. You then note that the pressure gauge reads 100 psi, which you checked at sea level in Bellingham, where the local pressure is one atm (14.7 psi). Calculate the number of O2 molecules left in the container.
Answers
Answer:
The number of O₂ molecules that are left in the cylinder is 1.70x10²⁴.
Explanation:
The number of oxygen molecules can be found using the Ideal Gas law:
[tex] PV = nRT [/tex]
Where:
P: is the pressure = 100 psi
V: is the volume = 10 L
n: is the number of moles =?
T: is the temperature = 20 °C = 293 K
R: is the gas constant = 0.082 L*atm/(K*mol)
Hence, the number of moles is:
[tex]n = \frac{PV}{RT} = \frac{100 psi*\frac{1 atm}{14.7 psi}*10 L}{0.082 L*atm/(K*mol)*293 K} = 2.83 moles[/tex]
Now, the number of molecules can be found with Avogadro's number:
[tex]n_{m} = \frac{6.022 \cdot 10^{23}\: molecules}{1\: mol}*2.83 moles = 1.70 \cdot 10^{24} \: molecules[/tex]
Therefore, the number of O₂ molecules that are left in the cylinder is 1.70x10²⁴.
I hope it helps you!
How much time will it take for a bug to travel 2 meters across the floor if it is traveling at 0.5 m/s?
Answers
What happens to ar object in free fall?
Answers
Which statement can be supported by using a position-time grap
O A negative slope results when an individual is moving away
O A horizontal line on the graph means the individual is moving
O A positive slope results when an individual is moving away fr
O The speed of an individual cannot be determined from this ty
Answers
Answer:
A negative slope results when an individual is moving away
Explanation:
When one person shouts at a football game, the sound intensity level at the center of the field is 69.6 dB. When all the people shout together, the intensity level increases to 103 dB. Assuming that each person generates the same sound intensity at the center of the field, how many people are at the game
Answers
Answer:
there are 2188 people at the game
Explanation:
Given the data in the question;
we know that decibel is defined as; dB = 10log(l/l₀)
so if one produces an intensity l₁, it results in 69.6 dB
69.6 = 10log(l₁/l₀) ---- equ1
also. if x number of people produces this intensity, it result to 103 dB
103 = 10log(xl₁/l₀)
103 = 10( log(l₁/l₀) + log(x) )
103 = 10log(l₁/l₀) + 10log(x) ----- equ2
input equation 1 into to equation 2
103 = 69.6 + 10log(x)
10log(x) = 103 - 69.6
10log(x) = 33.4
divide both side by 10
log(x) = 3.34
x = [tex]10^{3.34}[/tex]
x = 2187.76 ≈ 2188
Therefore, there are 2188 people at the game
Calculate the amount of potential difference in a capacitor of 0.9 MF , If the amount of charge is 1.4x10^-4 C .(Show all the work)
Answers
Answer:
Potential difference [tex]V=1.6\times 10^{-10}\ V[/tex]
Explanation:
Capacitance of capacitor, C = 0.9 MF
Charge, [tex]Q=1.4\times 10^{-4}\ C[/tex]
We need to find the amount of potential difference. We know that,
[tex]Q=CV[/tex]
V is potential difference
So,
[tex]V=\dfrac{Q}{C}\\\\V=\dfrac{1.4\times 10^{-4}}{0.9\times 10^6}\\\\V=1.6\times 10^{-10}\ V[/tex]
So, the required potential difference is [tex]1.6\times 10^{-10}\ V[/tex].
I need help with this, I can't figure it out.
Here is the link:
https://platform.breakoutedu.com/game/play/fun-in-the-sun-140559-XMWCQF1LPL
Answers
Answer:
Star, Triangle, Circle, Rhombus, Square.Left, Down, Right, Down, Up.2,3,2,4.L,O,O,K,I,N,G,F,L,Y.Explanation: You're welcome ✓
What attitudes and actions can group leaders take in trying to establish trust within a group during the initial stage of group development? How is each attitude and action important in the process of initiating trust?
Answers
Answer:
i dont know!
Explanation:
So Fn = dº* p*g What would happen to the force (FN) if the size of each side of the cube were to double? d -> 2d
Answers
Answer:
Fn=m(a + g) :
Explanation:
nf=a(m +g)
an=f(g+m)
A stone is dropped off of a 123 meter cliff and falls to the ground below. How long does it take for the stone to hit the ground
Answers
25.10 or 24.6m/s both answers are correct
Explanation:
firstly , divide the multiply with 2 and divide the result by acceleration due to gravity which is 9.8m/s or 10m/s
123*2=246
246/9.8 or 10
= 25.10 or 24.6m/s
if a=8i+j-2k and b=5i-3j+k what is the value of b X a
Answers
Distribute the product:
a×b = (8i + j - 2k) × (5i - 3j + k)
a×b = 8i × (5i - 3j + k) + j × (5i - 3j + k) - 2k × (5i - 3j + k)
a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))
… … … + (5 (j×i) - 3 (j×j) + k×j)
… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))
Recall the definition of the cross product:
i×i = j×j = k×k = 0 (the zero vector)
i×j = k
j×k = i
k×i = j
and for any two vectors x and y, we have x×y = -(y×x).
So we have some cancellation and rewriting:
a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))
… … … + (5 (j×i) - 3 (j×j) + j×k)
… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))
a×b = (-24k - 8j) + (-5k + i) + (-10j - 6i)
a×b = -5i - 18j - 29k
Then
b×a = -(a×b) = 5i + 18j + 29k
Convert the arc length of 6.86 radians into cycles.
Plz convert this for me people have been putting random comments
Answers
Answer:
1.092 cycles
Explanation:
We need to convert the arc length of 6.86 radians into cycles.
We know that,
1 radian = 0.1592 cycles
To convert 6.86 radians to cycles, we use unitary method.
6.86 radian = (0.1592 × 6.86) cycles
= 1.092 cycles
Hence, there are 1.092 cycles in 6.86 radians. Hence, this is the required solution.
Select all the correct locations on the image.
Which hot spots identify features in the image that can help lower the effects of urbanization?
Answers
Answer:
its the top 3 can confirm on plato
Explanation:
Answer:
plato
Explanation:
A cube of wood with a side length of 1 meter is place in the water. It half of the wood sank under the water, find the mass of the wood. (density of water 1.0 × 103kg/m3)
Answers
Answer:
Volume of cube is equal to two times the weight of replaced water [tex]1000[/tex] Kg
Explanation:
Length of one side of cube is [tex]1[/tex] meter
Volume of cube [tex]= 1* 1* 1 = 1[/tex] cubic meter
Half of the wood sank
Hence, the volume of water replaced will be equal to half the volume of cube
Volume of water replaced [tex]= \frac{1}{2} = 0.5[/tex] cubic meter
Density of water [tex]1 * 10^3[/tex] kg/m3
Weight of water replaced
[tex]= 1 * 10^3 * 0.5\\= 500[/tex]Kg
Volume of cube is equal to two times the weight of replaced water
[tex]= 2* 500 = 1000[/tex] Kg
Which is the MOST likely reason scientists are trying to find ways to get energy from more renewable
resources?
А
Renewable resources cost less to produce than
energy from nonrenewable resources
B
Renewable resources are easier to replace than
nonrenewable resources
C
Renewable resources create more power than
nonrenewable resources
D
Renewable resources put more pollution in the air than nonrenewable resources
Answers
A capacitor and an electric source are both connected to a light bulb. If the power source is momentarily disconnected from the circuit, what will happen to the light bulb?
Group of answer choices
It will get brighter because the capacitor is providing more power than the electrical source.
It will no light because the electric source is the only thing required to power the bulb.
It will stay momentarily lit because the capacitor is supplying a voltage.
It will flash on and off because of the unstable power.
Answers
Answer:
It will no light because the electric source is the only thing required to power the bulb.
Explanation:
Atoms of which pair of elements will form ionic bonds in a compound?
A.
Ti and Ni
B.
Ti and O
C.
Cl and Br
D.
P and Cl
Answers
Answer:
Ti and O
Explanation:
It is what it is.
Answer:
B. Ti and O
Explanation:
A.P.E.X
se the following graph describing a motorcycle's motion to answer the question below.
Answers
Could a sea breeze occur at night? Explain why or why not.
Answers
Hope this helps ✌️
.What is the relationship between the solar radius and the brightness of stars?
Answers
Answer:
Its radius is thought to be around 1400 times than of our sun, and its luminosity 270,000 greater than our sun. Also, if a star has the same radius as the sun but a higher surface temperature, the hotter star exceeds the sun in luminosity
Explanation:
As the solar radius of the star increases, the brightness of the star also increases.
What is meant by luminosity ?Luminosity is defined as the measure of brightness of a celestial object or the relative quantity of light.
Here,
Solar radius is a unit of distance, which is used to determine the size of the stars relative to the sun.
The size of the star and the luminous intensity are directly proportional. As the size of the star increases, the luminosity of the star also increases. Therefore, larger stars shine more brighter than the smaller ones.
The brightness of a star is directly proportional to the square of its solar radius. Therefore, the luminosity increases with increase in solar radius.
Hence,
As the solar radius of the star increases, the brightness of the star also increases.
To learn more about luminosity, click:
https://brainly.com/question/13912549
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A spacecraft drifts through space at a constant velocity. Suddenly, a gas leak in the side of the spacecraft gives it a constant acceleration in a direction perpendicular to the initial velocity. The orientation of the spacecraft does not change, so the acceleration remains perpendicular to the original direction of the velocity. What is the shape of the path followed by the spacecraft in this situation
Answers
Answer: The path will be a parabola.
Explanation: The path is a parabola because the motion described is a projectile motion, in which an object thrown or projected is subjected only to the acceleration.
In this motion, velocity must be constant and horizontal and acceleration is perpendicular compared to the direction of the velocity. In these conditions, the path is a parabola and the motion is a projectile.
9. What is the magnitude of the velocity of a 25 kilogram mass that is moving with a
momentum of 100 kilogram-meters per second? [Neglect friction] Round your
answer to the nearest tenths place.
Answers
Answer:
4
Explanation:
The momentum of the object is 100 kgm/s, therefore the magnitude of the velocity of the object is 4 meters per second.
What is Momentum?Momentum of an object is the product of its mass and velocity. Momentum is the quantity of motion which is made up of the amount of matter which is being moved and the velocity at which the object moves. When we walk, run, etc., then we have momentum.
p = m × v
where, p is the momentum of the object,
m is the mass of the object,
v is the velocity of the object
p = 100 kgm/s
m = 25 kg
p = m × v
v = p/m
v = 100/ 25
v = 4 m/s
Therefore, the magnitude of velocity of the object is 4 meters per second.
Learn more about Momentum here:
https://brainly.com/question/24030570
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A copper wire of length L and cross-sectional area A has resistance R. A second copper wire at the same temperature has a length of 2L and a cross-sectional area of A. What is the resistance of the second copper wire?
A. 2R
B. 4R
C. R
D. 1/2 R
Answers
Answer: 4R
Explanation:R=pL/A
R second wire=p2L/1/2A
=4R