Answer:
F = 1.63 x 10⁻⁹ N
Explanation:
Complete question is as follows:
The diagram below shows two bowling balls, A and B, each having a mass of 7.0 kg, placed 2.00 m apart between their centers. Find the magnitude of Gravitational Force?
Answer:
The gravitational force is given by Newton's Gravitational Law as follows:
F = Gm₁m₂/r²
where,
F = Gravitational Force = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m₁ = m₂ = mass of each ball = 7 kg
r = distance between balls = 2 m
Therefore,
F = (6.67 x 10⁻¹¹ N.m²/kg²)(7 kg)(7 kg)/(2 m)²
F = 1.63 x 10⁻⁹ N
The image blow shows a certain type of global wind:
What best describes these winds? Polar easterlies caused by air above poles being relatively warmer.
Polar easterlies caused by air above poles being relatively cooler.
Trade winds caused by air above equator being relatively warmer.
Trade winds caused by air above equator being relatively cooler.
Answer:
i got u its a
Explanation:
A twirlers baton is 0.76 m long and spins around its center. The end of the baton has a centripetal acceleration of 47.8 m/s2?
A 0.31 s
B 0.56 s
C 4.3s
D 70s
Answer:
C. 4.3 seconds
Explanation:
B 0.56 s is the time period of a twirlers baton.
What is Centripetal Acceleration?Centripetal acceleration is defined as the property of the motion of an object which traversing a circular path.
Any object that is moving in a circle and has an acceleration vector pointed towards the center of that circle is known as Centripetal acceleration.
The centripetal acceleration is given by:
a = 4π²R/T²
Given values are:
a = 47.8 m/s²
D = 0.76 m so , R = 0.76/2 = 0.38m
Using this formula,
47.8*T² = 4π² x0.38
T² = [tex]\frac{4*3.14^2*0.38}{47.8}[/tex]
T = 0.56 s
Therefore,
A twirlers baton is 0.76 m long and spins around its center. The end of the baton has a centripetal acceleration of 47.8 m/s2 which have time period of 0.56 s.
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.
If it requires 7.0 J of work to stretch a particular spring by 1.8 cm from its equilibrium length, how much more work will be required to stretch it an additional 3.6 cm?
Answer:
56 J
Explanation:
The following data were obtained from the question:
Energy 1 (E₁) = 7 J
Extention 1 (e₁) = 1.8 cm
Extention 2 (e₂) = 1.8 + 3.6 = 5.4 cm
Energy 2 (E₂) =?
Energy stored in a spring is given by the following equation:
E = ke²
Where E is the energy.
K is the spring constant.
e is the extension.
E = ke²
Divide both side by e²
K = E/e²
Thus,
E₁/e₁² = E₂/e₂²
7/ 1.8² = E₂/ 5.4²
7 / 3.24 = E₂/ 29.16
Cross multiply
3.24 × E₂ = 7 × 29.16
3.24 × E₂ = 204.12
Divide both side by 3.24
E₂ = 204.12 / 3.24
E₂ = 63 J
Thus, the additional energy required can be obtained as follow:
Energy 1 (E₁) = 7 J
Energy 2 (E₂) = 63 J
Additional energy = 63 – 7
Additional energy = 56 J
A 36.3 kg cart has a velocity of 3 m/s. How much kinetic energy does the object have?
Answer:
163.35
__________________________________________________________
We are given:
Mass of the object (m) = 36.3 kg
Velocity of the object (v) = 3 m/s
Kinetic Energy of the object:
We know that:
Kinetic Energy = 1/2(mv²)
KE = 1/2(36.3)(3)² [replacing the variables with the given values]
KE = 18.15 * 9
KE = 163.35 Joules
Hence, the cart has a Kinetic Energy of 163.35 Joules
In a simulation on earth, an astronaut in his space suit climbs up a vertical ladder. On the moon, the same astronaut makes the same climb. In which case does the gravitational potential energy of the astronaut change by a greater amount?
Answer:
Gravitational potential energy of the astronaut will change by a greater amount on the earth
Explanation:
Gravitational potential energy is expressed by the formula;
GPE = mgh
This means that the gravitational potential energy is directly proportional to the gravity(g)
Now, from constant values, gravity of moon is 1.62 m/s² while gravity of the earth is 9.81 m/s².
This means that if we plug in the values of g on the earth and g on the moon, the potential energy on the earth would be greater than that of the moon
Thus, gravitational potential energy of the astronaut will change by a greater amount on the earth
Section 4.1- Newton's First Law
Answer:
Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. ... If that velocity is zero, then the object remains at rest.
Explanation:
Answer:
Newton's First Law is about inertia; objects at rest stay at rest unless acted upon and objects in motion continue that motion in a straight line unless acted upon. The amount of inertia an object has is simply related to the mass of the object.
A mass of 100 g is tied to the end of an 80.0-cm string and swings in a vertical circle about a fixed center under the influence of gravity. The speed of the mass at the top of the swing is 3.50 m/s. What is the speed of the mass at the bottom of its swing?
Answer:
the speed of the mass at the bottom of its swing is 6.61m/s
Explanation:
Applying energy conservation
[tex]\frac{1}{2}m(Vlowest)^2 = mg(2R) + \frac{1}{2}m(Vtop)^2[/tex]
There is no potential energy at the bottom as the body will have a kinetic energy there.
h= 2R = 1.6m as the diameter of the circle will represent the height in the circle.
g = 9.8m/s^2
m will cancel out, so the net equation becomes.
[tex]\frac{(Vbottom)^2}{2} = 2gR + \frac{(Vtop)^2}{2}[/tex]
= [tex]2*9.8*0.8 + \frac{(3.5)^2}{2}[/tex]
= 15.68+ 6.125
[tex]\frac{(Vbottom)^2 }{2}[/tex] = 21.805
(Vb)^2 = 2*21.805
= 43.64
Vb = 6.61m/s
A car starts from rest and accelerates uniformly over a time of 7 seconds for a distance of 190m. Find the the acceleration of the car.
Answer:
a = 7.75 [m/²]
Explanation:
To solve this problem we must use the following equation of kinematics.
[tex]x=x_{0} +v_{o} *t + (\frac{1}{2})*a*t^{2}[/tex]
where:
x = final distance = 190 [m]
Xo = initial distance = 0
Vo = initial velocity = 0 (car starts from the rest)
a = acceleration [m/s²]
t = time = 7 [s]
190 = 0 + (0*7) + 0.5*a*(7²)
190 = 0.5*49*a
a = 7.75 [m/²]
can vectors be strung together?
Answer:
The head-to-tail method is a graphical way to add vectors, The tail of the vector is the starting point of the vector, and the head (or tip) of a vector is the final, pointed end of the arrow.
Explanation:
A 760-kg horse whose power output is 1 hp is pulling a sled over the snow at 3.9 m/s. Find the force the horse exerts on the sled. Round your intermediate step to one decimal place and the final answer to two decimal places.
Answer:
191 N
Explanation:
Power can be regarded as the amount of energy that is been transfered at a unit time and can be calculated using the Express below
Po = F*V
P= power
F= force
V= velocity
From the question, we were given power output as 1 hp and velocity= 3.9 m/s.
But
1hp= 746 Watts = 746 Joules/s.
Then substitute the values
Po = F*V = 746 J/s
F ×3.9 = 746
F= 746/3.9
F = 191 N.
Therefore, the force the horse exerts on the sled iss 191 N
1. When an object is at rest, not moving, and is crashed into by another
object...which object is experiencing a force and in what direction? Or are
both experiencing a force - what direction?
Answer:
both experience forces or at least a force
Explanation:
it would go in the direction the other object
(second object, the one that crashed) was going
si if going right then right if left then left
plus or minus
Starting from rest, a coin and a ring roll down a ramp without slipping. Which of the following are true:
A. The ring reaches the bottom first
B. The coin reaches the bottom first
C. The coin and the ring arrive at the same time
D. The one the reaches the bottom first is the one with the largest mass
E. The one that reaches the bottom first is the one with the largest diameter.
Answer:
The answer is D
Explanation:
The object with the heavy mass will reach first because the cause it is heaver so it will go faster
A typical elevator car with people has a mass of 1500.0 kg. Elevators are currently approaching speeds of 20.0 m/s - faster than the speed.
Required:
What is the upward force required if the elevator moves upward 200.0 meters before reaching 20.0 m/s?
Answer:
1500NExplanation:
Force = mass * acceleration
Given
Mass = 1500kg
Get the acceleration using the equation of motion;
v² = u²+2aS
20² = 0+2s(200)
400 = 400a
a = 400/400
a = 1m/s²
Get the upward force required
F = 1500 * 1
F = 1500N
Hence the upward force required if the elevator moves upward 200.0 meters before reaching 20.0 m/s is 1500N
if you increase the frequency of a wave by 5x whats it’s period?
We know that Period of a wave is the inverse of its Frequency
So, Period = 1 / Frequency
From the above, we can say that Period is inversely proportional to Frequency and hence, any change in Frequency will be the inverse change in the period
Therefore, we can say that if the frequency is increased by 5 times, the period will increase by 1/5 times
A student throws a 110 g snowball at 6.5 m/s at the side of the schoolhouse, where it hits and sticks.
What is the magnitude of the average force on the wall if the duration of the collision is 0.19 s ?
Answer:
3.6NExplanation:
Impulse is the change of momentum of an object when the object is acted upon by a force for an interval of time.
the expression is Ft=mv
where F= force
m= mass
t= time
v= velocity
Step one:
given data
mass m= 110g= 0.11kg
velocity v= 6.5m/s
time t= 0.19seconds
Step two:
we also know that the force on impulse is given as
Ft=mv
F=0.11*6.5/0.19
F=0.715/0.19
F=3.76N
The magnitude of the average force on the wall if the duration of the collision is 0.19 is 14N
I NEED THIS ASAP!!
Which formula defines the unit for electrical power?
Answer:
1 W = 1 V x 1 A
Explanation:
Other dude is wrong this is right
Find analytically the velocity of the object at the end point of the inclined plane for a certain angle Ө
I don't know if there is other given information that's missing here, so I'll try to fill in the gaps as best I can.
Let m be the mass of the object and v₀ its initial velocity at some distance x up the plane. Then the velocity v of the object at the bottom of the plane can be determined via the equation
v² - v₀² = 2 a x
where a is the acceleration.
At any point during its motion down the plane, the net force acting on the object points in the same direction. If friction is negligible, the only forces acting on the object are due to its weight (magnitude w) and the normal force (mag. n); if there is friction, let f denote its magnitude and let µ denote the coefficient of kinetic friction.
Recall Newton's second law,
∑ F = m a
where the symbols in boldface are vectors.
Split up the forces into their horizontal and vertical components. Then by Newton's second law,
• net horizontal force:
∑ F = n cos(θ + 90º) = m a cos(θ + 180º)
→ - n sin(θ) = - m a cos(θ)
→ n sin(θ) = m a cos(θ) ……… [1]
• net vertical force:
∑ F = n sin(θ + 90º) - w = m a sin(θ + 180º)
→ n cos(θ) - m g = - m a sin(θ)
→ n cos(θ) = m (g - a sin(θ)) ……… [2]
where in both equations, a is the magnitude of acceleration, g = 9.80 m/s², and friction is ignored.
Then by multiplying [1] by cos(θ) and [2] by sin(θ), we have
n sin(θ) cos(θ) = m a cos²(θ)
n cos(θ) sin(θ) = m (g sin(θ) - a sin²(θ))
m a cos²(θ) = m (g sin(θ) - a sin²(θ))
a cos²(θ) + a sin²(θ) = g sin(θ)
a = g sin(θ)
and so the object attains a velocity of
v = √(v₀² + 2 g x sin(θ))
If there is friction to consider, then f = µ n, and Newton's second law instead gives
• net horizontal force:
∑ F = n cos(θ + 90º) + f cos(θ) = m a cos(θ + 180º)
→ - n sin(θ) + µ n cos(θ) = - m a cos(θ)
→ n sin(θ) - µ n cos(θ) = m a cos(θ) ……… [3]
• net vertical force:
∑ F = n sin(θ + 90º) + f sin(θ) - w = m a sin(θ + 180º)
→ n cos(θ) + µ n sin(θ) - m g = - m a sin(θ)
→ n cos(θ) + µ n sin(θ) = m g - m a sin(θ) ……… [4]
Then multiply [3] by cos(θ) and [4] by sin(θ) to get
- n sin(θ) cos(θ) + µ n cos²(θ) = - m a cos²(θ)
n cos(θ) sin(θ) + µ n sin²(θ) = m g sin(θ) - m a sin²(θ)
and adding these together gives
µ n (cos²(θ) + sin²(θ)) = m g sin(θ) - m a (cos²(θ) + sin²(θ))
µ n = m g sin(θ) - m a
m a = m g sin(θ) - µ n
m a = m g sin(θ) - µ m g cos (θ)
a = g (sin(θ) - µ cos (θ))
and so the object would instead attain a velocity of
v = √(v₀² + 2 g x (sin(θ) - µ cos (θ)))
Select the correct answer.
The motion of a car on a position-time graph is represented with a horizontal line. What does this indicate about the car's motion?
A. It's not moving.
B.It's moving at a constant speed.
C.It's moving at a constant velocity
D.It's speeding up.
Answer:
It isn't moving
Explanation:
A sample with a path length of 1 cm absorbs 99.0% of the incident light at a wavelength of 274 nm, measured with respect to an appropriate solvent blank. Tyrosine is known to be the only chromophore present in the sample that has significant absorption at 274 nm. Calculate the molar concentration of tyrosine in the sample.
Answer:
17. NADH has a molar extinction coefficient of 6200 M2 cm at 340 nm. Calculate the molar concentration of NADH required to obtain an absorbance of 0.1 at 340 nm in a 1-cm path length cuvette. 18. A sample with a path length of 1 cm absorbs 99.0% of the incident light at a wavelength of 274 nm, measured with respect to an appropriate solvent blank. Tyrosine is known to be the only chromophore present in the sample that has significant absorption at 274 nm. Calculate the molar concentration of tyrosine in the sample.
Explanation:
Your teacher placed a 3.5 kg block at the position marked with a “ + ” (horizontally, 0.5 m from the origin) on a large incline outlined on the graph below and let it slide, starting from rest. ***There are two images included!***
Answer:
x = 10.75 m
Explanation:
For this problem we will solve it in two parts, the first using energy and the second with kinematics
Let's use the energy work relationship to find the velocity of the block as it exits the ramp
W = [tex]Em_{f}[/tex] - Em₀
Starting point. Higher
Em₀ = U = m g h
the height from the edge of the ramp of the graph has a value
h = 9-3 = 6 m
Final point. At the bottom of the ramp
Em_{f} = K = ½ m v²
Friction force work
W = - fr d
The friction force has the formula
fr = μ N
On the ramp, we can use Newton's second law
N - W cos θ = 0
N = W cos θ
where the angle is obtained from the graph
tan θ = (9-3) / (0.5-4) = -6 / 3.5
θ = tan⁻¹ (-1,714)
θ = -59.7º
the distance d is
d = √ (Δx² + Δy²)
d = √ [(0.5-4)² + (9-3)²]
d = 6.95 m
for which the work is
W = - μ mg cos 59.7 d
we substitute
W = Em_{f} -Em₀
- μ mg cos 59.7 d = ½ m v² - m g h
In the graph o text the value of the friction coefficient is not observed, suppose that it is μvery = 0.2
- μ g cos 59.7 d = ½ v² - g h
v² = 2g (h - very d coss 59.7)
let's calculate
v² = 2 9.8 (6 - 0.2 6.95 cos 59.7)
v = √ 103.8546
v = 10.19 m / s
in the same direction as the ramp
in the second part we use projectile launch kinematics
let's look for the components of velocity
v₀ₓ = vo cos -59.7
[tex]v_{oy}[/tex] = vo sin (-59,7)
v₀ₓ = 10.19 cos (-59.7) = 5.14 m / s
v_{oy} = 10.19 if (-59.7) = -8.798 m / s
Let's find the time to get to the floor (y = o)
y = y₀ + v_{oy} t - ½ g t²
to de groph y₀=3 m
0 = 3 - 8.798 t - ½ 9.8 t²
t² - 1.796 t - 0.612 = 0
we solve the quadratic equation
t = [1.796 ±√(1.796² + 4 0.612)] / 2
t = [1,795 ± 2,382] / 2
t₁ = 2.09 s
t₂ = -0.29 s
since time must be a positive quantity the correct value is t = 2.09 s
we calculate the horizontal displacement
x = v₀ₓ t
x = 5.14 2.09
x = 10.75 m
The motion of the box, after it exits the incline is the motion and trajectory
of a projectile.
Horizontal distance from the right-hand edge of the incline to the point of
contact with the floor is approximately 1.24613 m.
Reasons:
Mass of the block, m = 3.5 kg
Coefficient of kinetic friction, μ = 1.2
Location of the = 0.5 m from the origin
Required:
Horizontal distance between the block's point of contact with the floor and
the bottom right-hand edge of the incline.
Solution:
Let θ represent the angle the incline make with the horizontal.
The normal reaction of the incline on the block, [tex]F_N[/tex] = m·g·cos(θ)
Work done on friction = [tex]F_N[/tex]×μ×Length of the incline, L
Rise of the incline = 10 - 3 = 7
Run of the incline = 4
L = √(6.125² + 3.5²) = [tex]\dfrac{7 \times \sqrt{65} }{8}[/tex]
Let ΔP.E.₁ represent the potential energy transferred to kinetic energy
and work along the incline, we have;
Energy of the block at the bottom of the incline, M.E.₂, is found as follows;
K.E.₂ = mgh - m·g·μ·cos(θ)·L
[tex]K.E. =\frac{1}{2} \times 3.5 \times v^2 = 3.5 \times 9.81 \times 6.125 - 3.5 \times 9.81 \times 1.2 \times \dfrac{4}{\sqrt{65} } \times \dfrac{7 \times \sqrt{65} }{8}[/tex]
v ≈ 6.1456 m/s
The vertical component of the velocity is therefore;
[tex]v_y = v \cdot sin(\theta)[/tex]
[tex]v_y = 6.1456 \times \dfrac{7}{\sqrt{65} } \approx 5.33588[/tex]
From the equation, h = u·t + 0.5·g·t² derived from Newton's Laws of motion, we have;
ΔP.E.₁ = 3.5×9.81×7
3 = 5.33588·t + 0.5×9.81·t²
Factorizing, the above quadratic equation, we get;
The time it takes the block to reach the floor, t ≈ 0.40869 seconds
Horizontal component of the velocity is [tex]v_x \approx 6.1456 \times \dfrac{4}{\sqrt{65} } \approx 3.04908[/tex]
The horizontal distance, x = vₓ × t
∴ x = 3.04908 × 0.40869 ≈ 1.08194
Horizontal distance from the right-hand edge of the incline to the point of
contact with the floor, x ≈ 1.24613 m.
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A boxer is punching the heavy bag. The impact of the glove with the bag is 0.10s. The mass of the glove and his hand is 3kg. The velocity of the glove just before impact is 25m/s. What is the average impact force exerted on the glove?
Answer:
750NExplanation:
Impulse is the change of momentum of an object when the object is acted upon by a force for an interval of time.
the expression is Ft=mv
where F= force
m= mass
t= time
v= velocity
Step one:
given data
mass m=3kg
velocity v= 25m/s
time t= 0.10seconds
Step two:
we also know that the force on impulse is given as
Ft=mv
F=3*25/0.10
F=75/0.10
F=750N
The magnitude of the average force on the heavy bag if the duration of the collision is 0.1 is 750N
A block of mass 12.2 kg is sliding at an initial velocity of 3.9 m/s in the positive x-direction. The surface has a coefficient of kinetic friction of 0.173. (indicate the direction with signs of your answer) (a) What is the force of kinetic friction in N acting on the block? (b) What is the block's acceleration in /s^2? (c) How Far will it slide (in m) before coming to rest? Plz answer as soon as possible
Answer:
Explanation:
a) Force of friction = μ R where μ is coefficient of kinetic friction and R is reaction force
R = mg where m is mass of the block
Force of friction F = μ x mg
= .173 x 12.2 x 9.8
= 20.68 N
b ) Only force of friction is acting on the body so
deceleration = force / mass = 20.68 / 12.2 = 1.7 m /s²
acceleration = - 1.7 m /s²
c )
v² = u² - 2 a s
v = 0 , u = 3.9 m /s
a = 1.7 m /s
0 = 3.9² - 2 x 1.7 x s
s = 4.47 m
3. Which object has more inertia?
A. A tractor trailer rig moving at 2 m/s
B. A pingpong ball rolling a 2 m/s
C. A bowling ball rolling at 1m/s
D. A car rolling at 5 m/s
Answer:
A. A tractor trailer rig moving at 2 m/s
Explanation:
Inertia can be defined as the tendency of an object or a body to continue in its state of motion or remain at rest unless acted upon by an external force.
In physics, Sir Isaac Newton's first law of motion is known as law of inertia and it states that, an object or a physical body in motion will continue in its state of motion at continuous velocity (the same speed and direction) or, if at rest, will remain at rest unless acted upon by an external force.
The inertia of an object such as a tractor trailer rig is greatly dependent or influenced by its mass; the higher quantity of matter in a tractor trailer rig, the greater will be its tendency to continuously remain at rest.
Hence, the object that has more inertia is a tractor trailer rig moving at 2 m/s because it has more mass than all the other objects in the category. Also, the mass of an object is directly proportional to its inertia.
g When the movable mirror of the Michelson interferometer is moved a small distance X while making a measurement, 246 fringes are counted moving into the field of the viewing mirror. What is X if the wavelength of the light entering the interferometer is 562 nm
Answer:
X = 69.1 x 10⁻⁶ m = 69.1 μm
Explanation:
The relationship between the motion of the moveable mirror and the fringe count of the Michelson's Interferometer is given by the following formula:
d = mλ/2
where,
d = distance moved by the mirror = X = ?
m = No. of Fringes counted = 246
λ = wavelength of light entering interferometer = 562 nm = 5.62 x 10⁻⁷ m
Therefore,
X = (246)(5.62 x 10⁻⁷ m)/2
Therefore,
X = 69.1 x 10⁻⁶ m = 69.1 μm
Use the above picture to fill in the blanks for the following statement.
One of the element carbon combines with one of the element oxygen to form one of the compound carbon dioxide.
Answer:
C + 2O ------ CO2
Explanation:
"One" element of Carbon combines with "Two" elements of Oxygen, to form "One" compound of Carbon dioxide.
I didn't really get what you meant but this is my guess of what you meant
gravities limit is under which sphere as the perimeter?
A 0.22 caliber handgun fires a 1.9g bullet at a velocity of 765m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for the bullets?
Answer:
de Broglie wavelength of the bullet is 4.56 x 10⁻³⁴ mThe value of the wavelength shows that wave nature of matter is insignificant for the bullet because it is larger than particles.Explanation:
Given;
mass of the bullet, m = 1.9 g = 0.0019 kg
velocity of the bullet, v = 765 m/s
de Broglie wavelength of the bullet is given by;
[tex]\lambda = \frac{h}{mv}[/tex]
where;
h is Planck's constant = 6.626 x 10⁻³⁴ J/s
λ is de Broglie wavelength of the bullet
[tex]\lambda = \frac{h}{mv}\\\\ \lambda =\frac{(6.626*10^{-34})}{(0.0019)(765)}\\\\ \lambda =4.56 *10^{-34} \ m[/tex]
Thus, this value of the wavelength shows that wave nature of matter is insignificant for the bullet because it is larger than particles.
Given:
Mass, m = 1.9 g or, 0.0019 kgVelocity, v = 765 mPlank's constant, h = 6.626 × 10⁻³⁴ J/sThe De-Broglie wavelength,
→ [tex]\lambda = \frac{h}{mv}[/tex]
By putting the values,
[tex]= \frac{6.626\times 10^{-34}}{0.0019\times 765}[/tex]
[tex]= 4.56\times 10^{-34} \ m[/tex]
Thus the response above is right.
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1. Opposite charges
O repel
attract
Answer:
attract
Explanation:
that is the answer
Answer:
Attract.
Explanation:
I took the quiz.
If a penny is dropped from rest from a building takes 2 seconds to hit the ground, calculate the velocity of the penny right before it touches the ground?
a. 19.6 m/s
b 9.8 m/s
c. 0 m/s
d 29.4 m/s
Answer:
20m/s
Explanation:
u = 0m/s
t = 2s
a = +g = 10m/s²
t = 2d
v = ?
v = ut + 1/2at²
v = 0(2) + 1/2(10)(2)²
v = 0 + 5(4)
v = 20m/s
A parallel plate capacitor is made up of two metal squares with sides of length 8.8 cm, separated by a distance 5.0 mm. When a voltage 187 V is set up across the terminals of the capacitor, the charge stored on the positive plate is equal to __________ nC. g
Answer:
2.56 nC
Explanation:
By definition, the capacitance is expressed by the following relationship between the charge stored on one of the plates of the capacitor and the potential difference between them, as follows:[tex]C =\frac{Q}{V} (1)[/tex]
For a parallel-plate capacitor, assuming a uniform surface charge density σ, if the area of the plates is A, the charge on one of the plates can be written as follows:[tex]Q = \sigma * A (2)[/tex]
Assuming an uniform electric field E, the potential difference V can be expressed as follows:[tex]V = E*d (3)[/tex]
where d is the distance between plates.
Applying Gauss 'Law to a closed surface half within one plate, half outside it, we find that E can be written as follows:[tex]E =\frac{\sigma}{\epsilon_{0}} (4)[/tex]
Replacing (4) in (3), and (2) in (1), we can express the capacitance C as follows:[tex]C= \frac{\epsilon_{0}*A}{d} (5)[/tex]
Taking (1) and (5), as both left sides are equal each other, the right sides are also equal, so we can write the following equality:[tex]\frac{Q}{V} = \frac{\epsilon_{0}*A}{d} (6)[/tex]
Solving for Q, we get:[tex]Q = \frac{\epsilon_{0}*A*V}{d} = \frac{8.85e-12F/m*(0.088m)^{2}*187 V}{5.0e-3m} = 2.56 nC[/tex]