A ball of mass m=10g, carrying a charge q =-20μe is suspended from a string of length L= 0.8m above a horizontal uniformly charged infinite plane sheet of charge density σ = 4μe/m^2. The ball is displaced from the vertical by an angle and allowed to swing from rest.
Required:
a. Obtain the equations of motion of the charged ball based on Newtonian laws of motion.
b. Assume the displaced angle θ is small and simplify the results obtained in part (a) to obtain the frequency of oscillations of the charged ball.
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]
What is the gravitational potential energy of an object that has a mass of 8 kg and is 11.2 meters above Earth? Round your answer the nearest whole number.
A. 878 J
B. 30 J
C. 680 J
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)
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:
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
Why does a person feel cooler under a rotating fan?
What a fan does is create a wind chill effect. ... By blowing air around, the fan makes it easier for the air to evaporate sweat from your skin, which is how you eliminate body heat. The more evaporation, the cooler you feel.
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?
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
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.
Which of these statements is true about the effect of a force exerted upon an object?
A. A large force always produces a large change in the object’s momentum.
B. A small force always produces a large change in the object’s momentum.
C. A small force applied over a long time interval can produce a large change in the object’s momentum.
D. A large force produces a large change in the object’s momentum only if the force is applied over a very short time interval.
Answer:
D. A large force produces a large change in the object’s momentum only if the force is applied over a very short time interval.
Explanation:
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
[tex] Momentum = mass * velocity [/tex]
Also, the impulse of an object is given by the formula;
[tex] Impulse = force * time [/tex]
In accordance with the impulse-momentum theorem, the statement which is true about the effect of a force exerted upon an object is that a large force produces a large change in the object’s momentum only if the force is applied over a very short time interval.
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.
For more details about equation of motion, refer to the link:
https://brainly.com/question/8898885
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.
how many electrons can occupy each sublevel?
what dose current equal?
What is the hottest planet in the milky way galaxy
Answer:
Venus
Explanation:
An inclined plane consists of a 25 m length that raises an object 5 m above the ground. When pushing a 4500 N crate to the top of the ramp you exert 1000 N. What is the ideal Mechanical Advantage of this machine?
The IDEAL mechanical advantage of this ramp is (25m / 5m) = 5 .
But it's only giving you a real MA of (4500N/1000N) = 4.5 .
The friction between the crate and the surface of the ramp is robbing some of the work you do as you slide the crate up the ramp, which degrades the mechanical advantage.
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.)
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
Which of the following types of models could be used to represent a cell?
a.
idea model
b.
physical model
c.
computer model
d.
all of the above
Answer:
d. all of the above
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.
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.
An object is experiencing an acceleration of 0.4 m/s^2 while traveling in a circle of 35 m. What is it’s velocity?
Answer:
v = 3.74 m/s
Explanation:
Given that,
The acceleration of the object in circular path, a = 0.4 m/s²
The radius of the circle, r = 35 m
We need to find the velocity of the object. The acceleration of an object on the circular path is given by :
[tex]a=\dfrac{v^2}{r}\\\\v=\sqrt{ar} \\\\v=\sqrt{0.4\times35}\\\\v=3.74\ m/s[/tex]
So, the velocity of the object is equal to 3.74 m/s.
Which of the following statements about treatment for self-injury (SI) is not true?
Answer:
Its true
Explanation:
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.
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.
Learn more about Collision here: https://brainly.com/question/25121535
A storage tank has the shape of an inverted circular cone with height 15 m and base radius of 5 m. It is filled with water to a height of 11 m. Find the work required to empty the tank by pumping all of the water to the top of the tank. (The density of water is 1000 kg/m3. Assume g = 9.8 m/s2 is the acceleration due to gravity. Round your answer to the nearest integer.) g
Answer:
THE CORRECT ANSWER FOR THIS KS
Explanation:
STOP USING THIS APP FOR ANSWERS U KNOW NOTHING
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.
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:
Which image best illustrates diffraction?
Answer: A
Explanation:
What is the chemical formula for magnesium sulfide?
Answer:
MgS
Explanation: