Answer:
a) [tex]- ( g - \frac{q}{m} \frac{\sigma }{ 2 \epsilon_o} ) \frac{sin \theta}{R }[/tex] = [tex]\frac{d^2 \theta}{d t^2}[/tex]
b) f = 2π [tex]\sqrt{ \frac{R}{ g - \frac{q}{m} \frac{\sigma }{2 \epsilon_o} } }[/tex]
Explanation:
a) To have the equations of motion, let's use Newton's second law.
Let's set a reference system where the x-axis is parallel to the path and the y-axis is in the direction of tension of the rope.
For this reference system the tension is in the direction of the y axis, we must decompose the weight and the electrical force.
Let's use trigonometry for the weight that is in the vertical direction down
sin θ = Wₓ / W
cos θ = W_y / w
Wₓ = W sin θ
W_y = W cos θ
we repeat for the electric force that is vertical upwards
F_{ex} = F_e sin θ
F_{ey} = F_e cos θ
the electric force is
F_e = q E
where the field created by an infinite plate is
E = [tex]\frac{ \sigma}{2 \epsilon_o}[/tex]
let's write Newton's second law
Y axis
T - W_y = 0
T = W cos θ
X axis
F_{ex} - Wₓ = m a (1)
we use that the acceleration is related to the position
a = dv / dt
v = dx / dt
where x is the displacement in the arc of the curve
substituting
a = d² x /dt²
we substitute in 1
q E sin θ - mg sin θ = m [tex]\frac{d^2 x}{dt^2}[/tex]
we have angular (tea) and linear (x) variables, if we remember that angles must be measured in radians
θ = x / R
x = R θ
we substitute
sin θ (q E - mg) = m \frac{d^2 R \ theta}{dt^2}
[tex]- ( g - \frac{q}{m} \frac{\sigma }{ 2 \epsilon_o} ) \frac{sin \theta}{R }[/tex] = [tex]\frac{d^2 \theta}{d t^2}[/tex]
this is the equation of motion of the system
b) for small oscillations
sin θ = θ
therefore the solution is simple harmonic
θ = θ₀ cos (wt + Ф)
if derived twice, we substitute
- ( g - \frac{q}{m} \frac{\sigma }{ 2 \epsilon_o} ) \frac{\theta}{R } θ₀ cos (wt + Ф) = -w² θ₀ cos (wt + Ф)
w² = [tex]\frac{g}{R}[/tex] - [tex]\frac{q}{m} \frac{ \sigma }{2 \epsilon_o} \frac{1}{R}[/tex]
angular velocity is related to frequency
w = 2π f
f = 2π / w
f = 2π/w
f = 2π [tex]\sqrt{ \frac{R}{ g - \frac{q}{m} \frac{\sigma }{2 \epsilon_o} } }[/tex]
6xy from -12xy
please give me a answer this question
6 floors down from 12 floors underground = 18 floors underground.
6 degrees colder than 12 degrees below zero = 18 degrees below zero
6 brown cows taken away from -12 brown cows = -18 brown cows
6 cars sold from a dealer that 12 cars were stolen from = 18 cars gone
6xy taken away from -12xy = -18xy
1. What is matter?
2. What are the three phases of matter?
3. Describe how gas particles move.
4. What is temperature?
5. The slower the particles, the ______________ the temperature.
6. A change in temperature causes what?
7. What is the difference between boiling and evaporation?
8. What is sublimation?
9. Name the three ways thermal energy is transferred.
10. Sunburn is an example of what?
11. Give an example of convection.
12. What is conduction?
13. What is the difference between conductors and insulators?
Answer:
1.matter is any substance that has mass and takes up space by having volume.
2.The three fundamental phases of matter are solid, liquid, and gas (vapour),
3.In gases the particles move rapidly in all directions, frequently colliding with each other and the side of the container. With an increase in temperature, the particles gain kinetic energy and move faster. ... In liquids, particles are quite close together and move with random motion throughout the container.
3.In gases the particles move rapidly in all directions, frequently colliding with each other and the side of the container. With an increase in temperature, the particles gain kinetic energy and move faster. ... In liquids, particles are quite close together and move with random motion throughout the container.
why type of volcano is built almost entirely from ejected lava fragments
Answer:
Shield volcanoes
Explanation:
Which image best illustrates diffraction?
Answer: A
Explanation:
Planets don't collide into
the sun because they
A. Are moving
B. Have too much mass
C. Have their own gravity
D. Are more attracted to each other
Which of the following is an example of kinetic mechanical energy?
Immersive Reader
(2 Points)
A. A bike rolling down a hill
B. An elevated wrecking ball
C. A compressed spring
D. A loaded gun
E. A set mouse trap
Answer:
A
Explanation:
Kinetic energy must be moving. Potential energy has the ability to move but is not doing so at the moment.
A is likely the answer. But there's lots involved in that kind of motion.
B If the ball is elevated, it implies it is not moving yet. It has potential energy.
C Again, the spring is compressed. It will push something when it moves, but it is not moving yet.
D The load gun's bullet is not moving. It's still potential energy.
E. The mouse trap is set, but it is not moving. When the mouse eats the bait then it's potential energy will transform into kinetic energy.
Joe has a mass of 110 kg. If Joe has to climb a 10 m ladder to get to the top of a chimney, how much work did do?
We intend to measure the open-loop gain (LaTeX: A_{open}A o p e n ) of an actual operational amplifier. The magnitude of LaTeX: A_{open}A o p e n is in the range of 106 V/V. However, the signal generator in measurement setup can supply minimal voltage of 1 mV, and the oscilloscope used at amplifier output can measure maximal voltage level of 10 V. Can you design a simple measurement setup using this signal generator and oscilloscope, and accurately measure the LaTeX: A_{open}A o p e n
Answer:
voltage divider, R₂ = 1000 R₁
measuring the output in the resistance R₁
Explanation:
Let's analyze the situation, in an op amp in open gain loop, the gain is maximum G = 10⁶ V / V
in this case the signal generator gives a minimum wave of 1 10⁻³ V, after passing through the amplified it becomes 10³ V which saturates the oscilloscope.
To solve this problem we must use a simple voltage divider, for this we use the fact that in a series circuit the voltage is the sum of the voltages of each element.
If we use two resistors whose relationship is
R₂ / R₁ = 10³
R₂ = 1000 R₁
When measuring the output in the resistance R₁ we have the desired divider, with a tolerance range, for the minimum output of the generator (1 10⁻³V) we have a reading of V = 1 V in the oscilloscope, for which we can use voltage up to 10V on the generator
4. When you are holding a book, energy is stored between the book and the Earth.
This type of energy is called
potential energy.
A. Elastic potential energy
B. Chemical potential energy
C. Gravitational potential energy
D. Kinetic energy
Answer:
gravitational potential energy
What is the chemical formula for magnesium sulfide?
Answer:
MgS
Explanation:
The following problem applies to questions 8 and 9: a glass window acquires a net negative charge on its surface after being cleaned. Particles of dust, which are usually charged positively, start accelerating toward the window. If a particle travels a distance of 1 meter before reaching the window, in a time duration of 10 sec, and if the mass of the particle is 1 micro-gram and the charge on the particle is 10-12 Coulomb, then the magnitude of the electric field intensity is Group of answer choices
Answer:
the magnitude of the electric field intensity is 20 N/C
Explanation:
Given the data in the question;
mass m = 1 micro gram = 1 × 10⁻⁹ kg
time duration t = 10 sec
distance s = 1 m
the charge on the particle q = 10⁻¹² Coulomb
force applied on a charged particle due to electric field E is;
F = Eq ------ equ 1
where q is the charge on the particle.
Also, force on a particle with mass m will be;
F = ma ------ equ
where a is acceleration
so F = ma = Eq
ma = Eq -------- equ 3
using kinetic equation
Distance = 1/2×at²
where a is acceleration and t is the time period
now lets consider that initial velocity is zero (0)
Here;
1 m = 1/2 × a × ( 10 s )²
1 m = a × 50 s²
a = 1 m / 50 s²
a = 0.02 m/s²
so, from equation 3
ma = Eq
E = ma / q
we substitute
E = (1 × 10⁻⁹ kg × 0.02) / 10⁻¹² Coulomb
E = 2 × 10⁻¹¹ / 10⁻¹²
E = 20 N/C
Therefore, the magnitude of the electric field intensity is 20 N/C
Which of the following is NOT a reason
why gravity is important?
A It holds the planets in
orbit around the sun
B. It causes the ocean tides
C. It guides the growth of plants
D. None of the above
Answer:
I'm gonna say d
Explanation:
bc they all seem very important
hope this helped
What is the unique geological feature found on Mercury surface?
Answer:
The surface of Mercury has landforms that indicate its crust may have contracted. They are long, sinuous cliffs called lobate scarps. These scarps appear to be the surface expression of thrust faults, where the crust is broken along an inclined plane and pushed upward.
Explanation:
I hope this helps a little bit.
in a class where the number of girls is 36% of the total number,there are 48 boys.how many students are there in the class?
Answer:
There are 75 people in the class. The number of boys is 48 and the number of girls is 27. The percentage of girls is 36% of 75.
Explanation:
Which of the following objects is accelerating?
Answer: A flower pot falling
Explanation:
The car on the curve (its direction is changing) and the falling flower pot (its speed is changing) are both undergoing acceleration.
a race car goes around a circular track of radius 150 m at speed of 10.0 m/s. How long does it take to complete one lap?
Answer:
94.25 seconds
Explanation:
Solve for period (T) using: v=(2*pi*r)/T
rearrange: vT=2*pi*r
rearrange: T=(2*pi*r)/v
Plug in values.
T=(2*pi*150)/10
T=94.25 seconds
If a race car goes around a circular track of a radius of 150 m at speed of 10.0 m/s ,then the time taken to complete the one lap would be 94.25 seconds.
What is speed?The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.
As given in the problem a race car goes around a circular track of radius 150 m at speed of 10.0 m/s.
vT = 2 × π × r
T = (2 × π × r)/ v
T = (2 × π× 150)/10
T = 94.25 seconds
Thus, the time taken to complete the one lap would be 94.25 seconds.
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You are driving your car on a very cold late Fall day. You clear a turn and see a couple of pedestrians standing at the cross walk. They are eager to cross the road and to get into the warmth of their apartment as soon as possible. You have two options: continue driving your car as you were without lowering your speed and drive right by the pedestrians OR slow down, stop right at the crosswalk, and yield to the pedestrians. Although by Virginia law the choice is clear, what about Physics laws? Which scenario (passing by or slowing down and stopping at the crosswalk to yield) will minimize the time the pedestrians are out in the cold freezing before they can cross the road?
Make the following assumptions in your argument. Before you noticed the pedestrians, you are moving with a constant velocity v=22 miles/hour. The distance at which you noticed the pedestrians is D=23 meters. Write down a symbolic expression for the amount of time, tpass , the pedestrians will have to wait till they cross the road if you simply drive by without slowing down or speeding up.
Write down a symbolic expression for the amount of time, tstop, the pedestrians will have to wait till they cross the road if you slow down, come to a complete stop at the crosswalk and yield to the pedestrians.
Answer:
t_pass = 2.34 m
t_stop = 4.68 s
Thus, for the car passing at constant speed the pedestrian will have to wait less.
Explanation:
If the car is moving with constant speed, then the time taken by it will be given as:
[tex]t_{pass} = \frac{D}{v}[/tex]
where,
t_pass = time taken = ?
D = Distance covered = 23 m
v = constant speed = (22 mi/h)(1609.34 m/1 mi)(1 h/3600 s) = 9.84 m/s
Therefore,
[tex]t_{pass} = \frac{23\ m}{9.84\ m/s} \\[/tex]
t_pass = 2.34 m
Now, for the time to stop the car, we will use third equation of motion to get the acceleration first:
[tex]2as = v_{f}^{2} - v_{i}^2\\a = \frac{v_{f}^{2} - v_{i}^2}{2D}\\\\a = \frac{(0\ m/s)^{2}-(9.84\ m/s)^2}{(2)(23\ m)}\\\\a = -2.1\ m/s^2[/tex]
Now, for the passing time we use first equation of motion:
[tex]v_{f} = v_{i} + at_{stop}\\t_{stop} = \frac{v_{f}-v_{i}}{a}\\\\t_{stop} = \frac{0\ m/s - 9.84\ m/s}{-2.1\ m/s^2}[/tex]
t_stop = 4.68 s
Constant velocity is the velocity which covers the same distance for each interval of the time.
The time required to pass is 2.34 seconds and the time to stop is 4.68 seconds.
What is constant velocity?Constant velocity is the velocity which covers the same distance for each interval of the time.
It can be given as,
[tex]v=\dfrac{x}{t}[/tex]
As the distance covered by the car is 23 meters and the constant velocity of the car is 22 miles per second.
Convert the unit of velocity in m/s the value obtained will be 9.84 m/s.
Thus amount of time, [tex]t_{pass}[/tex] is,
[tex]9.84=\dfrac{23}{t_{pass} } \\t_{pass} =\dfrac{23}{9.84} \\t_{pass} =2.34[/tex]
As the distance covered by the car is 23 meters and the constant velocity of the car is 22 miles per second.
Convert the unit of velocity in m/s the value obtained will be 9.84 m/s.
Thus amount of time, [tex]t_{pass}[/tex] is,
[tex]9.84=\dfrac{23}{t_{pass} } \\t_{pass} =\dfrac{23}{9.84} \\t_{pass} =2.34[/tex]
According to the third equation of the motion acceleration can be given as,
[tex]v^2-u^2=2ax\\a=\dfrac{v^2-u^2}{2x}\\a=\dfrac{0^2-9.84^2}{2\times 23}\\a=-2.1 \rm \; m/s^2[/tex]
Now, use the first equation of motion, to get the required time,
[tex]v=u+at\\0=9.84+(-2.1)t\\t=4.68\rm \; s[/tex]
Therefore, the time required to pass is 2.34 seconds and the time to stop is 4.68 seconds.
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what dose current equal?
A 50 kg mass is sitting on a frictionless surface. An unknown constant force called force A pushes the mass for 2 seconds until the mass reaches a velocity of 3 m/s. If the 50 kg mass is now pushed by an unknown force B and reaches the velocity of 3 m/s in 4 seconds, compare the impulse delivered to the mass when acted upon by force A with the impulse delivered to the mass when acted on by force B? *
A) The impulse delivered to the mass when acted upon by force A is greater
B) The impulse delivered to the mass when acted upon by force B is greater
C) The impulse is the same in each case
D) We need to know the value of force A and force B in order to determine this
Answer:
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
how many electrons can occupy each sublevel?
A wave with a frequency of 5Hz travels a distance of 40mm in 2 seconds.What is the speed of the wave
Answer:
20mm per second
Explanation:
Take 100 PONTS!!!!!! PLEASE I NEED HELP FAST. Just look The picture.
Answer:
i THINK it’s false. You don’t have to give me points ;-;
Explanation:
Answer:
i think false and true is spelt wrong lol
Explanation:
What is the average kinetic energy of particles in a gas at a temperature of 245 Kelvins?
Answer:
2)
Explanation:
If a 15 N box is lifted a distance of 3 m, how much work is done?
0 J
45 J
5 J
5 N
Answer:
W=45J
Explanation:
W=Fd
W=15(3)=45
W=45J
A 1000 kg truck moving at 2.0 m/s runs into a concrete wall. It takes 0.5 s for the truck to completely stop. What is the magnitude of force exerted on the truck during the collision?
Answer:
Momentum is given by
p
=
m
v
. Impulse is the change of momentum,
I
=
Δ
p
and is also equal to force times time:
I
=
F
t
. Rearranging,
F
=
I
t
=
Δ
p
t
=
0
−
20
,
000
5
=
−
4000
N
.
Explanation:
Momentum before the collision is
p
=
m
v
=
2000
⋅
10
=
20
,
000
k
g
m
s
−
1
.
Assuming the truck comes to a complete halt, the momentum after the collision is
0
k
g
m
s
−
1
.
The change in momentum,
Δ
p
, is initial minus final
→
0
−
20
,
000
=
−
20
,
000
This is called the impulse:
I
=
Δ
p
. Impulse is also equal (check the units) to force times time:
I
=
F
t
.
We can rearrange this expression to make
F
the subject:
F
=
I
t
=
Δ
p
t
=
−
20
,
000
5
=
−
4000
N
The negative sign just means the force acting is in the opposite direction to the initial momentum.
(This will be the average force acting during the collision: collisions are chaotic so the force is unlikely to be constant.)
HELP me please cause I don't understand it.
Answer:
Force = 0.49 N (Approx)
Explanation:
Given:
Mass = 50 grams = 0.05 Kg
Acceleration = 9.81 m/s²
Find:
Force
Computation:
Force = Mass x Acceleration
Force = 0.05 x 9.81
Force = 0.4905
Force = 0.49 N (Approx)
Which statement about oceans is incorrect?
A Evaporation occurs when water is warmed by the sun.
B Most evaporation and precipitation occur over the ocean.
C 97 percent of Earth's water is fresh water from the ocean.
D Water leaves the ocean by the process of evaporation.
Each vertical line on the graph is 1 millisecond (0.001 s) of time. What is the period and
frequency of the sound waves?
Explanation:
Given that,
Each vertical line on the graph is 1 millisecond (0.001 s) of time.
We need to find the period and the frequency of the sound wave. The period of a wave is equal to the each vertical line on graph i.e. 0.001 s.
Let f be the frequency of the sound wave. So,
f = 1/T
i.e.
[tex]f=\dfrac{1}{0.001 }\\\\f=1000\ Hz[/tex]
So, the period and the frequency of the sound waves is 1 milliseond and 1000 Hz respectively.
One of the smallest planes ever flown was the Bumble Bee II, which had a mass of 180 kg. If the pilot’s mass was 70 kg, what was the velocity of both plane and pilot if their momentum was 20,800 kg∙m/s to the west?
Answer:
83.2 m/s to the West
Explanation:
From the question given above, the following data were obtained:
Mass of plane = 180 Kg
Mass of pilot = 70 Kg
Momentum = 20800 Kg∙m/s West
Velocity =?
Next, we shall determine the total mass. This can be obtained as follow:
Mass of plane = 180 Kg
Mass of pilot = 70 Kg
Total mass =?
Total mass = Mass of plane + Mass of pilot
Total mass = 180 + 70
Total mass = 250 Kg
Finally, we shall determine the velocity. This can be obtained as follow:
Total mass = 250 Kg
Momentum = 20800 Kg∙m/s West
Velocity =?
Momentum = mass × Velocity
20800 = 250 × Velocity
Divide both side by 250
Velocity = 20800 / 250
Velocity = 83.2 m/s West
Thus, the velocity of both plane and pilot is 83.2 m/s to the West
The local church is hosting a carnival which includes a bumper car ride. Bumper car A and its driver have a mass of 300 kg; bumper car B and its driver have a mass of 200 kg. Bumper car A has a velocity to the right of 2 m/s and bumper car B is at rest. At t = 0 s, bumper car A and B are separated by 10 m. Bumper car A accelerates at 1 m/s2 to a velocity of 4 m/s and continues at this constant speed until colliding with bumper car B.
Calculate the time required for bumper car A to travel the 10 m to collide with bumper car B.
Calculate the speed of bumper car A following the collision with bumper car B, which now has a velocity to the right of 3 m/s.
Is the direction of motion for bumper car A following the collision with bumper car B to the right, to the left, or is bumper car A at rest?
Is the collision elastic? Justify your answer.
Answer:
a. 20 s
b. 0 m/s
c. right
d.no its inelastic because when the car b was at rest and a was coming in at it, since b had no force what so ever car a swept it away with it moving to the right
Explanation:
im not sure though
By applying conservation of linear momentum, the answers are:
1. Time = 2 s
2. 3 m/s
3. same direction
4. Inelastic collision
COLLISIONThere are for types of collision. They are;
Elastic CollisionPerfectly elastic collisionInelastic collisionPerfectly Inelastic collisionGiven that a local church is hosting a carnival which includes a bumper car ride. Bumper car A and its driver have a mass of 300 kg; bumper car B and its driver have a mass of 200 kg. Bumper car A has a velocity to the right of 2 m/s and bumper car B is at rest. At t = 0 s, bumper car A and B are separated by 10 m. Bumper car A accelerates at 1 m/s2 to a velocity of 4 m/s and continues at this constant speed until colliding with bumper car B.
1. The time required for bumper car A to travel the 10 m to collide with bumper car B can be calculated by using first equation of linear motion.
V = U + at
Where
V = 4 m/s
U = 2 m/s
a = 1 m/[tex]s^{2}[/tex]
Substitute all the parameters into the formula
4 = 2 + t
t = 4 - 2
t = 2s
2. To calculate the speed of bumper car A following the collision with bumper car B, which now has a velocity to the right of 3 m/s, we will apply conservation of linear momentum
[tex]m_{1}u_{1}[/tex] = [tex]m_{1}v_{1}[/tex] + [tex]m_{2}v_{2}[/tex]
300 x 4 = 300V + 200 x 3
1200 = 300V + 300
300V = 1200 - 300
300V = 900
V = 900/300
V = 3 m/s
3. Since the final velocity of car A is positive, the direction of motion for bumper car A follows the collision with bumper car B to the right.
4. Since the both move at the same velocity, the collision inelastic.
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