Answer:
0.229AExplanation:
Before we determine the amount of current in each bulb, we must first know that the same current flows in a series connected resistors. Since the Two 15-Ω and three 25-Ω light bulbs are connected in series, same current will flow in all of them.
According to Ohm's law, E = IRt where;
E is the supply voltage = 24V
I is the total current flowing in the circuit
Rt is the total equivalent resistance.
First, we need to calculate Rt.
Rt = 15Ω+15Ω+25Ω+25Ω+25Ω (Two 15-Ω and three 25-Ω light bulb in series)
Rt = 105Ω
From ohms law formula, I = E/Rt
I = 24/105
I = 0.229Amp
Since the total current in the circuit is 0.229A, therefore the amount of current that passes through each bulb is the same as the total current i.e 0.229A
The current that passes via each bulb is 0.229A
Ohm law:According to the above law,
E = IRt
Here
E should be the supply voltage = 24V
I should be the total current flowing in the circuit
Rt should be the total equivalent resistance.
Now Rt should be
Rt = 15Ω+15Ω+25Ω+25Ω+25Ω
Rt = 105Ω
Now the current is
I = E/Rt
I = 24/105
I = 0.229Amp
Therefore, The current that passes via each bulb is 0.229A.
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Red light is bent the least of all colors as it passes through a prism. What does this tell you about red light? It has a short wavelength. It has a long wavelength. It has a high intensity. It has a low intensity.
Answer:
Longest wavelength, lowest intensity
Explanation:
Answer:
It has a long wavelength
Explanation:
GRADPOINT
Suppose you are looking into the end of a long cylindrical tube in which there is a uniform magnetic field pointing away from you. If the magnitude of the field is decreasing with time the direction of the induced magnetic field is
Answer:
If the magnitude of the field is decreasing with time the direction of the induced magnetic field is CLOCKWISE
Explanation
This is because If the magnetic field decreases with time, the electric field will be produced in order to oppose the change in line with lenz law. Thus The right hand rule can be applied to find that the direction of electric field is in the clockwise direction.
a uniform rod of 30cm is pivoted at its center.a 40N weight is hung 5cm from left.from where 50N weight be hung to maintain equilibrium?
Answer:
The 50N weight be hung at 23 cm to maintain equilibrium
Explanation:
Given;
length of the uniform rod = 30 cm
center of the uniform rod = 15 cm
weight of 40N is hung at 5 cm mark
weight of 50 N will be hung at ?
0------5cm-----------------15cm-------------P---------30cm
↓ 10cm Δ xcm ↓
40N 50N
Take moment about the pivot point and apply the principle of moment
50N (x cm) = 40N (10 cm)
x = (400) / 50
x = 8cm
P = x cm + 15 cm
P = 8 cm + 15 cm
P = 23 cm
Therefore, the 50N weight be hung at 23 cm to maintain equilibrium
Two charges, +9 µC and +16 µC, are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force (in N) on a −7 nC charge when placed at the following locations.
(a) halfway between the two
(b) half a meter to the left of the +9 µC charge
(c) half a meter above the +16 µC charge in a direction perpendicular to the line joining the two fixed charges (Assume this line is the x-axis with the +x-direction toward the right. Indicate the direction of the force in degrees counterclockwise from the +x-axis.)
Answer:
A) 1.76U×10⁻³N
B) 2.716×10⁻³N
C) 264.5⁰
Explanation:
See detailed workings for (a), (b), (c) attached.
A skateboarder jumps horizontally off the top of a staircase and lands at bottom of the stairs. The staircase has a horizontal length of 12.0 m, and the jump lasts 1.10s. We can ignore air resistance. What is the skater's vertical velocity upon landing? Round your answer to three significant digits.
Answer:
The vertical velocity of the skater upon landing is 10.788 meters per second.
Explanation:
Skateboarder experiments a parabolic movement. As skateboarder jumps horizontally off the top of the staircase, it means that vertical component of initial velocity is zero and accelerates by gravity, the final vertical speed is calculated by the following expression:
[tex]v = v_{o} + g\cdot t[/tex]
Where:
[tex]v_{o}[/tex] - Initial vertical speed, measured in meters per second.
[tex]v[/tex] - Final vertical speed, measured in meters per second.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]t[/tex] - Time, measured in seconds.
Given that [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 1.10\,s[/tex], the final velocity of the skater upon landing is:
[tex]v = 0\,\frac{m}{s} + \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (1.10\,s)[/tex]
[tex]v = -10.788\,\frac{m}{s}[/tex]
The vertical velocity of the skater upon landing is 10.788 meters per second.
Answer:
-10.8
Explanation:
Answer on Khan Academy
A person can survive a feet-first impact at a speed of about 12 m/s (27 mi/h) on concrete, 15 m/s (34 mi/h) on soil, and 34 m/s (76 mi/h) on water. What is the reason for the different values for different surfaces
Answer:
Different surfaces have different impact force during collision which depends on the time it takes the person to come to rest after collision.
Explanation:
Given;
speed on concrete = 12 m/s (27 mi/h)
speed on soil = 15 m/s (34 mi/h)
speed on water = 34 m/s (76 mi/h)
The impact force on this person during collision is rate of change of momentum;
[tex]F = \frac{\delta P}{\delta t}[/tex]
During collision, the force exerted on this person depends on how long the collision lasts; that is, how long it takes for this person to come to rest after collision with each of the surfaces.
The longer the time of collision, the smaller the force exerted by each.
It takes shorter time for the person to come to rest on concrete surface than on soil surface, also it takes shorter time for the person to come to rest on soil surface than on water surface.
As a result of the reason above, the force exerted on the person during collision by the concrete surface is greater than that of soil surface which is greater than that of water surface.
Three identical resistors are connected in series to a battery. If the current of 12 A flows from the battery, how much current flows through any one of the resistors
Answer:
Current that flows through any one of the resistors has a value of 12 amperes.
Explanation:
When a group of resistors are connected in series, the same current flows through each resistor. According to the Ohm's Law, the circuit can be represented as follows:
[tex]V_{batt} = i\cdot (R_{1}+R_{2}+R_{3})[/tex]
[tex]i = \frac{V_{batt}}{R_{1}+R_{2}+R_{3}}[/tex]
Where:
[tex]V_{batt}[/tex] - Voltage of the battery, measured in volts.
[tex]R_{1}[/tex], [tex]R_{2}[/tex], [tex]R_{3}[/tex] - Electric resistance of the first, second and third resistors, measured in ohms.
[tex]i[/tex] - Current, measured in amperes.
If [tex]R_{1} = R_{2} = R_{3} = R[/tex], then:
[tex]i = \frac{V_{batt}}{3\cdot R}[/tex]
Current that flows through any one of the resistors has a value of 12 amperes.
The current flows via any of the resistors should have a value of 12 amperes.
Ohm law:At the time When a group of resistors are linked in series, so there is a similar current flow via each resistor.
Here the circuit should be
vbatt = i.(R1 + R2+ R3)
i = Vbatt/R1 + R2 + R3
here
Vbatt means the voltage of the battery
R1,R2, and R3 means the resistance of the first, second and third resistors
I means the current
So, in the case when
R1 = R2 = R3 = R
So,
i = Vbatt/3.R
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A proton moving at 4.80 106 m/s through a magnetic field of magnitude 1.74 T experiences a magnetic force of magnitude 7.00 10-13 N. What is the angle between the proton's velocity and the field? (Enter both possible answers from smallest to largest. Enter only positive values between 0 and 360.)
Answer:
31.55° and 148.45°
Explanation:
Formula for calculating the force experiences by the proton placed in a magnetic field is as expressed below;
F = qvBsinθ where;
F is the magnetic force experienced by the proton
q is the charge on the proton
v is the velocity of the proton
B is the magnetic field
θ is the angle between the proton's velocity and the field (Required)
Given parameters
F = 7.00 * 10⁻¹³N
q = 1.602*10⁻¹⁹C
v = 4.80 * 10⁶ m/s
B = 1.74 T
θ =?
From the formula F = qvBsinθ;
sinθ = F/qvB
sinθ = 7.00 * 10⁻¹³/1.602*10⁻¹⁹* 4.80 * 10⁶*1.74
sinθ = 7.00 * 10⁻¹³/13.38*10⁻¹³
sinθ = 0.5231689 * 10⁰
sinθ = 0.5231689
θ = sin⁻¹0.5231689
θ = 31.55°
The following are the positive values of the angle between 0° and 360°
Sin is positive in the first and second quadrant. In the second quadrant the angle is equal to 180°-31.55° = 148.45°.
Hence the possible values of the angle from smallest to largest are 31.55° and 148.45°
An unknown additional charge q3q3q_3 is now placed at point B, located at coordinates (0 mm, 15.0 mm ). Find the magnitude and sign of q3q3q_3 needed to make the total electric field at point A equal to zero.
Answer:
0.3nanocouloumb
Explanation:
Pls see attached file
An electron initially at rest is accelerated over a distance of 0.210 m in 33.3 ns. Assuming its acceleration is constant, what voltage was used to accelerate it
Answer:
V = 451.47 volts
Explanation:
Given that,
Distance, d = 0.21 m
Initial speed, u = 0
Time, t = 33.3 ns
Let v is the final velocity. Using second equation of motion as :
[tex]d=ut+\dfrac{1}{2}at^2[/tex]
a is acceleration, [tex]a=\dfrac{v-u}{t}[/tex] and u = 0
So,
[tex]d=\dfrac{1}{2}(v-u)t[/tex]
[tex]v=\dfrac{2d}{t}\\\\v=\dfrac{2\times 0.21}{33.3\times 10^{-9}}\\\\v=1.26\times 10^7\ m/s[/tex]
Now applying the conservation of energy i.e.
[tex]\dfrac{1}{2}mv^2=qV[/tex]
V is voltage
[tex]V=\dfrac{mv^2}{2q}\\\\V=\dfrac{9.1\times 10^{-31}\times (1.26\times 10^7)^2}{2\times 1.6\times 10^{-19}}\\\\V=451.47\ V[/tex]
So, the voltage is 451.47 V.
Sally who weighs 450 N, stands on a skate board while roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100 N force.
Work done on the skateboard
a. Rodger Work= 0J
b. Rodger work= 1300J
c. sally work= 1300J
d. sally work= 5850J
e. rodger work= 5850J
Answer:
b. Rodger work = 1300 J
Explanation:
Work done: This can be defined as the product of force and distance along the direction of the force.
From the question,
Work is done by Rodger using a force of 100 N in pushing the skateboard through a distance of 13.0 m.
W = F×d............. Equation 1
Where W = work done, F = force, d = distance.
Given: F = 100 N, d = 13 m
Substitute these values into equation 1
W = 100(13)
W = 1300 J.
Hence the right option is b. Rodger work = 1300 J
If the speed of a "cheetah" is 150 m / s. How long does it take to cover 800 m?
Answer:
5.33333... seconds
Explanation:
800 divided by 150 is equal to 5.33333... because it is per second that the cheetah moves at 150miles, the answer is 5.3333.....
You set two parallel slits 0.1 mm apart at a distance of 2 m from a screen and illuminate them with light of wavelength 450 nm. The distance between a bright spot in the interference pattern and the dark spot adjacent to it is Group of answer choices
Answer:
Δx = 9 x 10⁻³ m = 9 mm
Explanation:
The formula for fringe spacing in Young's Double Slit Experiment is given as follows:
Δx = λL/d
where,
Δx = fringe spacing = ?
λ = wavelength of light = 450 nm = 450 x 10⁻⁹ m
L = Distance between slits and screen = 2 m
d = distance between slits = 0.1 mm = 0.1 x 10⁻³ m
Therefore,
Δx = (450 x 10⁻⁹ m)(2 m)/(0.1 x 10⁻³ m)
Δx = 9 x 10⁻³ m = 9 mm
A square coil of wire with side 8.0 cm and 50 turns sits in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is pulled quickly out of the magnetic field in 0.2 s. If the resistance of the coil is 15 ohm and a current of 12 mA is induced in the coil, calculate the value of the magnetic field.
Answer:
Explanation:
area of the coil A = .08 x .08 = 64 x 10⁻⁴ m ²
flux through the coil Φ = area of coil x no of turns x magnetic field
= 64 x 10⁻⁴ x 50 x B where B is magnetic field
emf induced = dΦ / dt = ( 64 x 10⁻⁴ x 50 x B - 0 ) / .2
= 1.6 B
current induced = emf induced / resistance
12 x 10⁻³ = 1.6 B / 15
B = 112.5 x 10⁻³ T .
For every particle there is a corresponding ______________.
Answer:
Anti-Particle
Help me with these question and please explainnn
Explanation:
1. Impulse = change in momentum
J = Δp
J = mΔv
In the x direction:
Jₓ = mΔvₓ
Jₓ = (0.40 kg) (30 m/s cos 45° − (-20 m/s))
Jₓ = 16.5 kg m/s
In the y direction:
Jᵧ = mΔvᵧ
Jᵧ = (0.40 kg) (30 m/s sin 45° − 0 m/s)
Jᵧ = 8.49 kg m/s
The magnitude of the impulse is:
J = √(Jₓ² + Jᵧ²)
J = 18.5 kg m/s
The average force is:
FΔt = J
F = J/Δt
F = 1850 N
2. Momentum is conserved.
m₁u₁ + m₂u₂ = (m₁ + m₂) v
In the x direction:
(1000 kg) (0 m/s) + (1500 kg) (-12 m/s) = (1000 kg + 1500 kg) vₓ
vₓ = -7.2 m/s
In the y direction:
(1000 kg) (20 m/s) + (1500 kg) (0 m/s) = (1000 kg + 1500 kg) vᵧ
vᵧ = 8 m/s
The magnitude of the final speed is:
v = √(vₓ² + vᵧ²)
v = 10.8 m/s
3. Momentum is conserved.
m₁u₁ + m₂u₂ = (m₁ + m₂) v
In the x direction:
(0.8 kg) (18 m/s cos 45°) + (0.36 kg) (9.0 m/s) = (0.8 kg + 0.36 kg) vₓ
vₓ = 11.6 m/s
In the y direction:
(0.8 kg) (-18 m/s sin 45°) + (0.36 kg) (0 m/s) = (0.8 kg + 0.36 kg) vᵧ
vᵧ = -8.78 m/s
The magnitude of the final speed is:
v = √(vₓ² + vᵧ²)
v = 14.5 m/s
why was the observation of the double-slit interference pattern more convincing evidence for the wave theory of light than the observation of diffraction
Answer:
The double slit experiment showed for the first time that light can be interfered, producing bands of light and dark fringes on a screen. This phenomenon was a unique and typical characteristic of waves.
Explanation:
Th double slit experiment by Thomas Young proved, and sealed for the first time the wave nature of light; showing that light just as any other wave can produce interference which was a unique, typical phenomenon of waves. The Interference of light was shown by allowing light to pass through narrow slits and superimpose on a wall or screen, at a distance away from the slit, producing a clear pattern of light and dark fringes. This was the first experiment to proof that darkness can be produced by the addition of light on light. Interference is accompanied by a spatial redistribution of the optical intensity without violation of power conservation. The phenomenon of interference proved the intuitive ideas of Huygens regarding the wave nature of light against Newton's particle nature of light theory.
An inventor claims to have developed a food freezer that, in steady-state conditions, requires a power input of 0.25 kW to extract energy by heat transfer at a rate of 3050 J/s from the freezer contents, which are at a temperature of 270 K. Determine if this claim is real considering an ambient temperature of 293 K. (a) Can the freezer operation in such conditions
Answer:
The inventors claim is not real
a) No the the freezer cannot operate in such conditions
Explanation:
From the question we are told that
The power input is [tex]P_i = 0.25 kW = 0.25 *10^{3} \ W[/tex]
The rate of heat transfer [tex]J = 3050 J/s[/tex]
The temperature of the freezer content is [tex]T = 270 \ K[/tex]
The ambient temperature is [tex]T_a = 293 \ K[/tex]
Generally the coefficient of performance of a refrigerator at idea conditions is mathematically represented as
[tex]COP = \frac{T }{Ta - T}[/tex]
substituting values
[tex]COP = \frac{270 }{293 - 270}[/tex]
[tex]COP =11.7[/tex]
Generally the coefficient of performance of a refrigerator at real conditions is mathematically represented as
[tex]COP = \frac{J}{P_i}[/tex]
substituting values
[tex]COP = \frac{3050}{0.25 *10^{3}}[/tex]
[tex]COP = 12.2[/tex]
Now given that the COP of an ideal refrigerator is less that that of a real refrigerator then the claims of the inventor is rejected
This is because the there are loss in the real refrigerator cycle that are suppose to reduce the COP compared to an ideal refrigerator cycle where there no loss that will reduce the COP
A rectangular block of metal of resistivity rho has dimensions d x 2d x 3d . A potential difference V is to be applied between two opposite faces of the block.
(A) To which two faces of the block should the potential difference be applied to give the maximum current density?
(B) What is the maximum current density j(subscript max) from part A?
(C) To which two faces of the block should the potential difference be applied to give the maximum current?
1. to the faces that area a distance d apart
2. to the faces that are a distance 2d apart
3. to the faces that are a distance 3d apart
Answer:
a) The potential difference should be applied to the d dimension face.
b) The maximum current density j = V/3ρd
c) 3. to the faces that are a distance 3d apart
Explanation:
a) Current density is the ratio of current flowing through a conductor, and cross-sectional area of the conductor. mathematically, it is written as
j = I/A
where I is the electric current, and
A is the area of the conductor.
From the equation, we can see that reducing the area of the conductor will increase the current density for a given amount of current passing through the conductor. The face d wide will give the least cross-sectional area of current flow.
b) current density can be gotten from
j = σE ....equ 1
where σ is the conductivity of the conductor which is the inverse of resistivity ρ. this means that
σ = 1/ρ ....equ 2
where ρ is the resistivity of the conductor
E is the electric field and is the volt through the conductor per unit length of the conductor
in this case, the maximum current density will be when the length is length 3d, and the volt is the potential difference V
therefore,
E = V/3d ....equ 3
substituting equ 2 and equ 3 in equ1, we'll have
the maximum current density j = V/3ρd
c) To get the maximum current, the potential difference should be applied to the faces that are 3d wide apart because the resistance of a conductor varies inversely as the cross-sectional area. The maximum current will be gotten when the resistance is at its minimum, and the minimum resistance will be gotten with the most cross-sectional area. The 3d wide face will give the maximum cross-sectional area.
g A particle (charge = +40 mC) is located on the x axis at the point x = -20 cm, and a second particle (charge = -50 mC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = -4.0 mC) placed at the origin (x = 0)? Group of answer choices
Answer:
Explanation:
We shall find electric field at origin due to two given charges sitting on the either side of origin .
Total field will add up due to their same direction .
Field due to a charge Q
= 9 x 10⁹ x Q / R² ; R is distance of point , Q is charge
Field due to first charge
= 9 x 10⁹ x 40 x 10⁻³ / 2² x 10⁻⁴
= 90 x 10¹⁰ N/C
Field due to second charge
= 9 x 10⁹ x 50 x 10⁻³ / 2² x 10⁻⁴
= 112.5 x 10¹⁰ N/C
Total field
= 202.5 x 10¹⁰ N/C
Force on given charge at origin
= charge x field
= 4 x 10⁻³ x 202.5 x 10¹⁰
= 810 x 10⁷ N .
A spherical capacitor contains a charge of 3.40 nC when connected to a potential difference of 240.0 V. Its plates are separated by vacuum and the inner radius of the outer shell is 4.10 cm.
Calculate:
a. The capacitance
b. The radius of the inner sphere.
c. The electric field just outside the surface of the inner sphere.
Answer:
A) 1.4167 × 10^(-11) F
B) r_a = 0.031 m
C) E = 3.181 × 10⁴ N/C
Explanation:
We are given;
Charge;Q = 3.40 nC = 3.4 × 10^(-9) C
Potential difference;V = 240 V
Inner radius of outer sphere;r_b = 4.1 cm = 0.041 m
A) The formula for capacitance is given by;
C = Q/V
C = (3.4 × 10^(-9))/240
C = 1.4167 × 10^(-11) F
B) To find the radius of the inner sphere,we will make use of the formula for capacitance of spherical coordinates.
C = (4πε_o)/(1/r_a - 1/r_b)
Rearranging, we have;
(1/r_a - 1/r_b) = (4πε_o)/C
ε_o is a constant with a value of 8.85 × 10^(−12) C²/N.m
Plugging in the relevant values, we have;
(1/r_a - 1/0.041) = (4π × 8.85 × 10^(−12) )/(1.4167 × 10^(-11))
(1/r_a) - 24.3902 = 7.8501
1/r_a = 7.8501 + 24.3902
1/r_a = 32.2403
r_a = 1/32.2403
r_a = 0.031 m
C) Formula for Electric field just outside the surface of the inner sphere is given by;
E = kQ/r_a²
Where k is a constant value of 8.99 × 10^(9) Nm²/C²
Thus;
E = (8.99 × 10^(9) × 3.4 × 10^(-9))/0.031²
E = 3.181 × 10⁴ N/C
action and reaction are equal in magnitude and opposite in direction.Then why do they not balance each other.
Explanation:
Newton's third law of motion states that every action has an equal and opposite reaction. This means that forces always act in pairs. Action and reaction forces are equal and opposite, but they are not balanced forces because they act on different objects so they don't cancel out.
A skater spins at 3rev/s when she stretches her arms outward. If she keeps her fists on her chest she can spin at 4.5rev/s and her body inertia is 3kg.m2. What is her body inertia when she stretches her arms outward?
Answer:
Body inertia I = 4.5 kg/m^2
Explanation:
Here, we want to calculate the body inertia when the arms are stretched outwards.
We know from the question that angular momentum is conserved
Thus;
I * 3 = 4.5 * 3
I = 4.5 kg/m^2
A car is moving along a road at 28.0 m/s with an engine that exerts a force of
2,300.0 N on the car to balance the drag and friction so that the car maintains a
constant speed. What is the power output of the engine?
Answer:
Power = Force × Distance/time
Power = Force × Velocity
Power = 2,300.0 N × 28.0 m/s²
Power = 64400 Nm/s
Explanation:
First show the formula of Power
Re-arrange formula and used to work out Power
Pretty simple stuff!
Hope this Helps!!
"Pipe A has length L and is open at one end and closed at the other. Pipe B is open at both ends and has length 2L. Which harmonic of pipe B matches in frequency the fundamental of pipe A?"
Answer:
Explanation:
length of pipe A is L
frequency of fundamental note of pipe A which is closed organ pipe
= velocity of sound / 4 x length of pipe
= V / 4 x L where V is velocity of sound .
Similarly frequency of fundamental note of pipe B which is open organ pipe
= velocity of sound / 2 x length of pipe
= V / (2 x 2L) = V / 4L , This is also called first harmonic
so fundamental frequency of pipe A will be equal to first harmonic of pipe B .
In a polar coordinate system, the velocity vector can be written as . The term theta with dot on top is called _______________________ angular velocity transverse velocity radial velocity angular acceleration
Answer:
I believe it's called rapid growth
Explanation:
that is my answer no matter what
The 2-Mg truck is traveling at 15 m/s when the brakes on all its wheels are applied, causing it to skid for 10 m before coming to rest. The total mass of the boat and trailer is 1 Mg. Determine the constant horizontal force developed in the coupling C, and the friction force developed between the tires of the truck and the road during this time.
Answer:
constant horizontal force developed in the coupling C = 11.25KN
the friction force developed between the tires of the truck and the road during this time is 33.75KN
Explanation:
See attached file
The friction force between the tires of the truck and the road is 22500 N.
Calculating the friction force:It is given that a 2 Mg truck ( m = 2000 Kg) is initially moving with a speed of u = 15 m/s.
Distance traveled before coming to rest, s = 10m
The final velocity of the truck will be zero, v = 0
When the breaks are applied, only the frictional force is acting on the truck and it is opposite to the motion of the truck.
The frictional force is given by:
f = -ma
the acceleration of the truck = -a
The negative sign indicates that the acceleration is opposite to the motion.
Applying the third equation of motion we get:
v² = u² -2as
0 = 15² - 2×a×10
225 = 20a
a = 11.25 m/s²
So the magnitude of frictional force is:
f = ma = 2000 × 11.25 N
f = 22500 N
Learn more about friction force:
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A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius 5 mm , and the outer one a radius 11 mm . The common length of the cylinders is 160 m . What is the potential energy stored in this capacitor when a potential difference 6 V is
Answer:
The potential energy is [tex]PE = 2.031 *10^{-7} \ J[/tex]
Explanation:
From the question we are told that
The inner radius is [tex]r_i = 5 \ mm = 0.005 \ m[/tex]
The outer radius is [tex]r_o = 11 \ mm = 0.011 \ m[/tex]
The common length is [tex]l = 160 \ m[/tex]
The potential difference is [tex]V = 6 \ V[/tex]
Generally the capacitance of the cylindrical capacitor is mathematically represented as
[tex]C = \frac{2 \pi * k * \epsilon_o }{ ln \frac{ r_o }{r_i} } * l[/tex]
Where [tex]\epsilon _o[/tex] is the permitivity of free space with the values [tex]\epsilon _o = 8.85*10^{-12} \ m^{-3} \cdot kg^{-1}\cdot s^4 \cdot A^2[/tex]
and k is the dielectric constant of the dielectric material here the dielectric material is free space so k = 1
Substituting values
[tex]C = \frac{2* 3.142 * 1 * 8.85*10^{-12} }{ ln \frac{ 0.011}{0.005} } * 160[/tex]
[tex]C = 1.129 *10^{-8} \ F[/tex]
The potential energy stored is mathematically represented as
[tex]PE = \frac{1}{2} * C * V ^2[/tex]
substituting values
[tex]PE = 0.5 * 1.129 *10^{-8} * (6)^2[/tex]
[tex]PE = 2.031 *10^{-7} \ J[/tex]
A helicopter blade starts to rotate from rest with a constant angular acceleration of \alpha=\:α = 0.98 radians/second2. How many revolutions will the blade make before it is rotating at 500 revolutions per minute (RPM)?
Answer:
n = 223 revolutions
Explanation:
It is given that,
The angular acceleration of a helicopter blade, [tex]\alpha =0.98\ rad/s^2[/tex]
Initial speed of the helicopter blade, [tex]\omega_i=0[/tex]
The final speed of the blade, [tex]\omega_f=500\ rpm=500\times \dfrac{2\pi}{60}\ rad/s=52.35\ rad/s[/tex]
We need to find the number of revolutions. Firstly we will find the angle turned by the blade. Let the angle is [tex]\theta[/tex]. So,
[tex]\omega_f^2-\omega_i^2=2\alpha \theta[/tex]
[tex]\theta=\dfrac{\omega_f^2}{2\alpha}[/tex]
[tex]\theta=1398.22\ rad [/tex]
Let there are n number of revolutions made by the blade. So,
[tex]n=\dfrac{\theta}{2\pi}\\\\n=\dfrac{1398.22}{2\pi}\\\\n=222.53\ rev[/tex]
or
n = 223 rev
So, there are 223 revolutions.
Determine the position in the oscillation where an object in simple harmonic motion: (Be very specific, and give some reasoning to your answer.) has the greatest speed has the greatest acceleration experiences the greatest restoring force experiences zero restoring force g
Answer:
Explanation:
The greatest speed is attained at middle point or equilibrium point or where displacement from equilibrium point is zero .
When the object remains at one of the extreme point it experiences greatest acceleration but at that point velocity is zero . Due to acceleration , its velocity goes on increasing till it come to equilibrium point . At this point acceleration becomes zero . After that its velocity starts decreasing because of negative acceleration . Hence at middle point velocity is maximum .
The greatest acceleration is attained at maximum displacement or at one of the two extreme end .
Greatest restoring force too will be at position where acceleration is maximum because acceleration is produced by restoring force .
Restoring force is proportional to displacement or extension against restoring force . So it will be maximum when displacement is maximum .
Zero restoring force exists at equilibrium position or middle point or at point where displacement is zero . It is so because acceleration at that point is zero .