Answer:
a) a = 5.3 km, b) sum fulfills the commutative property
Explanation:
This is a vector exercise, If you drive east from north, we can find the vector using the Pythagorean theorem
R² = a² + b²
where R is the resultant vector R = 7.5 km and the others are the legs
If we assume that the two legs are equal to = be
R² = 2 a²
r = √2 a
a = r /√2
we calculate
a = 7.5 /√2
a = 5.3 km
therefore, you must drive 5.3 km east and then 5.3 km north and you will reach the same point
b) As the sum fulfills the commutative property, the order of the elements does not alter the result
a + b = b + a
therefore, it does not matter in what order the path is carried out, it always reaches the same end point
In a single-slit diffraction pattern, the central fringe is 360 times as wide as the slit. The screen is 14,000 times farther from the slit than the slit is wide. What is the ratio /W, where is the wavelength of the light shining through the slit and W is the width of the slit
Answer:
0.01286
Explanation:
In a given single-slit, the central fringe (Y) is 360 times as wide as the slit (a). Then
2Y₁ = 360a
Y₁ = 360a/2
= 180a
The distance D = 14000a
In a given single-slit diffraction, the ratio = [tex]\dfrac{\lambda }{W}[/tex]
and since the angle is infinitesimally small;
sin θ ≅ tan θ = [tex]\dfrac{Y}{D}[/tex]
∴
For the first dark fringe;
Suppose: [tex]\dfrac{a}{2}sin \theta = \dfrac{\lambda }{2}[/tex]
then,
[tex]\dfrac{a}{2} \ \dfrac{Y_1}{D} = \dfrac{\lambda }{2}[/tex]
[tex]aY_1 = \lambda D[/tex]
[tex]\dfrac{\lambda }{a} = \dfrac{Y_1}{D}\\ \\ \\ \implies \dfrac{180\ a}{14000 \ a} \\ \\ \mathbf{\dfrac{\lambda }{a} = 0.01286}[/tex]
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Answer:
(A) Series and Parallel
Explanation:
Circuit Component: These are electrical devices that makes up the circuit. They include, resistors, capacitors, inductors, voltmeters, ammeters, cell/batteries, earth connection, bulb, switch, connecting wire etc.
These component can either be connected in series or in parallel.
(1) Series Connection: This can be refered as end to end connection of electric component.
(2) Paralel Connection: This can be refered as the side to side connection of electric component.
From the question above,
A electric component in a circuit can be combined in series and in parallel.
The right option is (A) Series and Parallel
Light takes 1.2 sec to get from the moon to the Earth. Assume you are looking at the moon with noticeable earth shine. If the Sun burned out, you would eventually see the crescent of the moon disappear. The earth shine part of the moon would disappear Answer 2.4 s after the crescent disappeared.
Answer:
1.2 seconds
Explanation:
Answer to the following question is 1.2 seconds
Because light from the moon takes 1.2 seconds to reach Earth, the light released from the crescent immediately before it vanishes will also take 1.2 seconds to reach Earth. As a result, the earth-shine portion of the moon will vanish 1.2 seconds after the crescent has vanished.
A person runs up the stairs elevating his 102 kg body a vertical distance of 2.29 meters in a time of 1.32 seconds at a constant speed.
Determine the work done by the person climbing the stair case.
Answer:
Work done = 2289.084 Joules
Explanation:
Given the following data;
Mass = 102 Kg
Height = 2.29
Time = 1.32 seconds
We know that acceleration due to gravity, g = 9.8 m/s²
a. To find the work done by the person;
Here, work would be done in the form of gravitational potential energy.
Gravitational potential energy (GPE) is an energy possessed by an object or body due to its position above the earth.
Mathematically, gravitational potential energy is given by the formula;
G.P.E = mgh
Where;
G.P.E represents potential energy measured in Joules.
m represents the mass of an object.
g represents acceleration due to gravity measured in meters per seconds square.
h represents the height measured in meters.
Substituting into the formula, we have;
Work done = 102 * 2.29 * 9.8
Work done = 2289.084 Joules
A bus moving on a straight road increases its speed uniformly from rest to 20m's over a time period of 1 min. The distance travelled during the time is (a) 150 m (b) 300 m (c) 600 m (d) 900 m
Explanation:
Given that,
Initial velocity (u) = 0 m/sFinal velocity (v) = 20 m/sTime taken (t) = 1 minute = 60 secondsIn order to find the distance travelled, firstly we need calculate the acceleration.
→ v = u + at
→ 20 = 0 + 60a
→ 20 = 60a
→ 20 ÷ 60 = a
→ ⅓ m/s² = a
Now, by using the 2nd equation of motion :
→ s = ut + ½at²
→ s = 0(60) + ½ × ⅓ × (60)²
→ s = ⅙ × 3600
→ s = 1 × 600
→ s = 600 m
Hence, the distance travelled is 600 m.
What is a measure between the difference in start and end positions?
Answer:
Displacement
General Formulas and Concepts:
Kinematics
Displacement vs Total DistanceExplanation:
Displacement is the difference between the start position and end position.
Total Distance is the entire distance traveled between the start and end position.
Topic: AP Physics 1 Algebra-Based
Unit: Kinematics
A capacitor consists of two metal surfaces separated by an electrical insulator with no electrically conductive path through it. Why does a current flow in a resistor-capacitor circuit when the switch is closed?
Answer:
Displacement current flows in the dielectric material(insulated region)
Explanation:
Firstly a capacitor stores charge when a capacitor is charging (or discharging), current flows in the circuit. Also, there is no charge transfer in the dielectric material in the capacitor which is contradictory to the flow of current. Hence, displacement current is the current in the insulated region due to the changing electric flux.
Maximum range of a projectile is 1.6 m. Then the velocity of projection will be..... (g=10m/s)
Answer:
4 m/s
Explanation:
From the question given above, the following data were obtained:
Maximum range (Rₘₐₓ) = 1.6 m
Acceleration due to gravity (g) = 10 m/s²
Initial velocity (u) =?
The initial velocity of the projectile can be obtained as follow:
Rₘₐₓ = u² / g
1.6 = u² / 10
Cross multiply
u² = 1.6 × 10
u² = 16
Take the square root of both side
u = √16
u = 4 m/s
Therefore, the velocity of the projectile is 4 m/s
If ∆H = + VE , THEN WHAT REACTION IT IS
1) exothermic
2) endothermic
Answer:
endothermic
Explanation:
An endothermic is any process with an increase in the enthalpy H (or internal energy U) of the system. In such a process, a closed system usually absorbs thermal energy from its surroundings, which is heat transfer into the system.
An electron is moving through a magnetic field whose magnitude is 83 x 10-5 T. The electron experiences only a magnetic force and has an acceleration of magnitude 34 x 10+13 m/s2. At a certain instant, it has a speed of 72 x 10+5 m/s. Determine the angle (less than 90°) between the electron's velocity and the magnetic field.
Answer:
the angle between the electron's velocity and the magnetic field is 19⁰
Explanation:
Given;
magnitude of the magnetic field, B = 83 x 10⁻⁵ T
acceleration of the electron, a = 34 x 10¹³ m/s²
speed of the electron, v = 72 x 10⁵ m/s
mass of electron, m = 9.11 x 10⁻³¹ kg
The magnetic force experienced by the electron is calculated as;
F = ma = qvB sinθ
where;
q is charge of electron = 1.602 x 10⁻¹⁹ C
θ is the angle between the electron's velocity and the magnetic field.
[tex]sin(\theta ) = \frac{ma}{qvB} \\\\sin(\theta ) = \frac{(9.11\times 10^{-31})(34\times 10^{13})}{(1.602\times 10^{-19})\times (72\times 10^5) \times (83 \times 10^{-5})} \\\\sin(\theta ) = 0.3235\\\\\theta =sin^{-1}(0.3235)\\\\\theta =18.9^0[/tex]
[tex]\theta \approx 19^ 0[/tex]
Therefore, the angle between the electron's velocity and the magnetic field is 19⁰
A force of 1000N is used to kick a football of mass 0.8kg find the velocity with which the ball moves if it takes 0.8 sec to be kicked.
The velocity of the ball is 100m/s
The first step is to write out the parameters;
The force used to kick the ball is 1000N
The mass of the ball is 0.8 kg
Time is 0.8 seconds
Therefore the velocity can be calculated as follows
F= Mv-mu/t
1000= 0.8(v) - 0.8(0)/0.8
1000= 0.8v- 0.8/0.8
Cross multiply both sides
1000(0.8) = 0.8v
800= 0.8v
divide both sides by the coefficient of v which is 8
800/0.8= 0.8v/0.8
v= 1000m/s
Hence the velocity is 1000m/s
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b. Projectile on cliff (range)
An object of mass 5 kg is projected at an angle of 25° to the horizontal with a speed of 22 ms-1 from the top of the cliff.
The height of the cliff is 21 m. Take g, the acceleration due to gravity, to be 9.81 ms2
How far horizontally (to 1 decimal place) from the base of the cliff does the object land?
Answer:
x = 41.28 m
Explanation:
This is a projectile launching exercise, let's find the time it takes to get to the base of the cliff.
Let's start by using trigonometry to find the initial velocity
cos 25 = v₀ₓ / v₀
sin 25 = Iv_{oy} / v₀
v₀ₓ = v₀ cos 25
v_{oy} = v₀ sin 25
v₀ₓ = 22 cos 25 = 19.94 m / s
v_{oy} = 22 sin 25 = 0.0192 m / s
let's use movement on the vertical axis
y = y₀ + v_{oy} t - ½ g t²
when reaching the base of the cliff y = 0 and the initial height is y₀ = 21 m
0 = 21 + 0.0192 t - ½ 9.81 t²
4.905 t² - 0.0192 t - 21 = 0
t² - 0.003914 t - 4.2813 =0
we solve the quadratic equation
t = [tex]\frac{ 0.003914\ \pm \sqrt{0.003914^2 + 4 \ 4.2813 } }{2}[/tex]
t = [tex]\frac{0.003914 \ \pm 4.13828}{2}[/tex]
t₁ = 2.07 s
t₂ = -2.067 s
since time must be a positive scalar quantity, the correct result is
t = 2.07 s
now we can look up the distance traveled
x = v₀ₓ t
x = 19.94 2.07
x = 41.28 m
The water evaporated. How did that help ?
Answer:
hellooooo. hi hellooooo and programming laptops
Answer:
The molecules move and vibrate so quickly that they escape into the atmosphere as molecules of water vapor. Evaporation is a very important part of the water cycle. The Heat from the sun, or solar energy, powers the evaporation process. ... Once the water evaporates, it also helps form clouds.
Explanation:
A car is traveling at 104 km/h when the driver sees an accident 50 m ahead and slams on the brakes. What minimum constant deceleration is required to stop the car in time to avoid a pileup
a = - 8.34 m/sec² ( deceleration or negative)
Equations for UAM ( uniformly accelerated motion) are:
vf = v₀ ± a*t and s = s₀ + v₀*t + (1/2)*a*t²
In our case, the motion is with deceleration, then
vf = v₀ - a*t and s = s₀ + v₀*t - (1/2)*a*t²
working on these equatios we get:
vf = v₀ - a*t (1) s - s₀ = v₀*t - (1/2)*a*t² (2)
v₀ - vf = a*t
t = (v₀ - vf)/a
By substitution of (1) in equation (2)
s - s₀ = v₀ * (v₀ - vf)/a - (1/2) * a* [(v₀ - vf)/a]²
s - s₀ = (v₀² - v₀*vf)/a - (1/2) * a* (1/a²)* (v₀ - vf)²
s - s₀ = 1/a * ( v₀² - v₀*vf ) - 1/a* (1/2) * (v₀ - vf)²
s - s₀ = 1/a* [ ( v₀² - v₀*vf ) - (1/2) * (v₀ - vf)²]
a * (s - s₀ ) = v₀² - v₀*vf - v₀²/2 - vf²/2 + v₀*vf
a * (s - s₀ ) = (1/2) * v₀² - (1/2)*vf²
a * (s - s₀ ) = (1/2) * ( v₀² - vf²)
We find an expression to calculate the minimum deceleration to stop the car in time to avoid crashing
s₀ = 50 meters s = 0 v₀ = 104 Km/h vf = 0
1 Km = 1000 m and 1 h = 3600 sec
v₀ = 104 Km/h = 28.88 m/sec
a = (1/2) [ (28.88)² - 0 ] / 0 - 50
a = - 8.34 m/sec² ( deceleration or negative)
A hydraulic vane pump has a real flow of 20 liters per minute, a pressure of 230 bar, a pump speed of 1400 rpm. Know that the input power is 10kW and the mechanical efficiency is 88%.
a) Calculate the volumetric efficiency of the pump
b) Calculate the specific volume of the pump (cm/rev). Question 3 (2,5d): Design a pneumatic transmission system to control 02 single-acting cylinders, using 02 reversing valves 3/2 acting by push button, 02 throttle valves - one-way. Describe the working principle of the system.
Explanation:
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Light of frequency f falls on a metal surface and ejects electrons of maximum kinetic energy K by the photoelectric effect. If the frequency of this light is doubled, the maximum kinetic energy of the emitted electrons will be
The question is incomplete, the complete question is;
Light of frequency f falls on a metal surface and ejects electrons of maximum kinetic energy K by the photoelectric effect.
Part A If the frequency of this light is doubled, the maximum kinetic energy of the emitted electrons will be If the frequency of this light is doubled, the maximum kinetic energy of the emitted electrons will be
K/2.
K.
2K.
greater than 2K.
Answer:
2K
Explanation:
Given that the kinetic energy of photo electrons is given by;
K= E -Wo
Where;
K = kinetic energy
E= energy of incident photon
Wo = work function
But;
E= hf
Wo = fo
h= Plank's constant
f= frequency of incident photon
fo= Threshold frequency
So:
K= hf - hfo
Where the frequency of incident light is doubled;
K= 2hf - hfo
Hence, maximum kinetic energy of the emitted electrons in this case will be 2K
Vặt nhỏ được ném lên từ điểm A trên mặt đất với vận tốc đầu 20m/s theo phương thẳng đứng. Xác định độ cao của điểm O mà vật đạt được. Bỏ qua ma sát
Explanation:
mặt đất với vận tốc ban đầu 20m/s. Bỏ qua mọi ma sát, lấy g = 10 m/s2. Độ cao cực đại mà vật đạt được là.
describe four energy changes that happen in the process.
Driving a motor........
chemical energy is converted into kinetic energy.
Falling off of cliff
.........gravitational potential energy is converted into kinetic energy.
Hydroelectric energy generation
.......gravitational potential energy is converted into kinetic energy (i.e. driving a generator), which is then converted into electrical energy.
Nuclear power generation
.........mass is converted into energy, which then drives a steam turbine, which is then converted into electrical energy.
g A thin uniform film of oil that can be varied in thickness covers a sheet of glass of refractive index 1.52. The refractive index of the oil is 1.64. Light of wavelength 555 nm is shone from air at normal incidence on the film. Starting with no oil on the glass, you gradually increase the thickness of the oil film until the first interference maximum in the reflected light occurs. What is the thickness of the oil film at that instant
Answer:
The right solution is "84.09 nm".
Explanation:
The given values are:
Refractive index of glass,
= 1.52
Refractive index of oil (n),
= 1.64
Wavelength (λ),
= 555 nm
Now,
The thickness of the film (t) will be:
= [tex]\frac{\lambda}{4n}[/tex]
= [tex]\frac{555}{4\times 1.65}[/tex]
= [tex]\frac{555}{6.6}[/tex]
= [tex]84.09 \ nm[/tex]
what are the two main types of sound like soundwave
Answer:
acoustic energy and mechanical energy
Explanation:
each type of sounds has to be tackled in their own way.
b. Block on an incline
A block of mass mı = 3.9 kg on a smooth inclined plane of angle 38° is connected by a cord over a small frictionless
pulley to a second block of mass m2 = 2.6 kg hanging vertically. Take the positive direction up the incline and use 9.81
m/s2 for g.
What is the tension in the cord to the nearest whole number?
Block on the incline:
• net force parallel to the incline
∑ F (para.) = m₁ g sin(38°) - T = m₁ a
where T is the magnitude of tension in the cord.
Notice that we take down-the-incline to be the positive direction, so that if the 3.9-kg block pulls the 2.6-kg block upwards, then the acceleration of the system is positive.
Suspended block:
• net vertical force
∑ F (vert.) = T - m₂ g = m₂ a
Solve both equations for the acceleration a, set the results equal to one another, and solve for T :
a = g sin(38°) - T/m₁
a = T/m₂ - g
==> g sin(38°) - T/m₁ = T/m₂ - g
==> T (1/m₂ + 1/m₁) = g (sin(38°) + 1)
==> T = g (sin(38°) + 1) / (1/m₂ + 1/m₁)
==> T = (9.81 m/s²) (sin(38°) + 1) / (1/(2.6 kg) + 1/(3.9 kg)) ≈ 25 N
A stone with a mass of 0.100kg rests on a frictionless, horizontal surface. A bullet of mass 2.50g traveling horizontally at 500m/s strikes the stone and rebounds horizontally at right angles to its original direction with a speed of 300m/s.
A) Compute the magnitude of the velocity of the stone after it is struck.
B) Compute the direction of the velocity of the stone after it is struck. (degrees from the initial direction of the bullet)
Answer:
Explanation:
Given that:
mass of stone (M) = 0.100 kg
mass of bullet (m) = 2.50 g = 2.5 ×10 ⁻³ kg
initial velocity of stone ([tex]u_{stone}[/tex]) = 0 m/s
Initial velocity of bullet ([tex]u_{bullet}[/tex]) = (500 m/s)i
Speed of the bullet after collision ([tex]v_{bullet}[/tex]) = (300 m/s) j
Suppose we represent [tex](v_{stone})[/tex] to be the velocity of the stone after the truck, then:
From linear momentum, the law of conservation can be applied which is expressed as:
[tex]m*u_{bullet} + M*{u_{stone}}= mv_{bullet}+Mv_{stone}[/tex]
[tex](2.50*10^{-3} \ kg) (500)i+0 = (2.50*10^{-3} \ kg)(300 \ m/s)j + (0.100 \ kg)v_{stone}[/tex]
[tex](2.50*10^{-3} \ kg) (500)i- (2.50*10^{-3} \ kg)(300 \ m/s)j= (0.100 \ kg)v_{stone}[/tex]
[tex]v_{stone}= (1.25\ kg.m/s)i-(0.75\ kg m/s)j[/tex]
[tex]v_{stone}= (12.5\ m/s)i-(7.5\ m/s)j[/tex]
∴
The magnitude now is:
[tex]v_{stone}=\sqrt{ (12.5\ m/s)^2-(7.5\ m/s)^2}[/tex]
[tex]\mathbf{v_{stone}= 14.6 \ m/s}[/tex]
Using the tangent of an angle to determine the direction of the velocity after the struck;
Let θ represent the direction:
[tex]\theta = tan^{-1} (\dfrac{-7.5}{12.5})[/tex]
[tex]\mathbf{\theta = 30.96^0 \ below \ the \ horizontal\ level}[/tex]
Which of the following is true about resistivity of any given metal? depends on its temperature. varies nearly linearly with temperature. has units of ohm-meter. A. II and III only B. I and II only C. I and III only D. I, II and III E. III only
___________________
[tex]\huge{\underline{\sf{\blue{Answer}}}}[/tex]
___________________
[tex]\sf{C. \:I\: and \:III}[/tex]
___________________
The correct statements about resistivity of any given metal are The resistivity of metal is more than that of insulators and Metals can carry electricity more easily than insulators. Option a and c are correct answer.
Resistivity is a property that quantifies how strongly a material opposes the flow of electric current. Metals have lower resistivity compared to insulators. This means that metals allow electric current to flow more easily than insulators.
Due to their lower resistivity, metals have higher electrical conductivity and can carry electric current more easily compared to insulators. Insulators, on the other hand, have high resistivity and hinder the flow of electric current. Resistivity is a material-specific property and varies for different substances. Metals, such as copper or aluminum, have low resistivity and are often used as conductors for transmitting electricity. Insulators, such as rubber or plastic, have high resistivity and are used to prevent the flow of electricity.
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The complete question is, "Which of the following statements are true about resistivity of any given metal?
A. The resistivity of metal is more than that of insulators.
B. The insulators and metals have same resistivity.
C. Metals can carry electricity more easily than insulators.
D. The resistivity of insulators is more than that of metals.
You want to swim from one side of a river to another side. Assume your speed is three miles per hour in the west direction, with negligible water velocity. When you reach a certain point, you will encounter water flow with a velocity of 6.2 miles per hour in the north direction. What is your resultant speed and direction
Answer:
speed = 6.71 mph and angle is 71.2 degree.
Explanation:
speed of person, u = 3 miles per hour
speed of water, v = 6 miles per hour
Resultant speed
[tex]V =\sqrt{v^2 + u^2}\\\\V = \sqrt{3^2 + 6^2}\\\\V = 6.71 mph[/tex]
The angle from the west is
tan A = 6/2 = 3
A = 71.6 degree
A bullet 2cm log is fired at 420m/s and passes straight a 10cm thick board exiting at 280m/s
Complete question:
A bullet 2 cm long is fired at 420m/s and passes straight through a 10.0 cm thick board, exiting at 280m/s? What is the average acceleration of the bullet through the board?
Answer:
The average acceleration of the bullet through the board is -4.083 x 10⁵ m/s²
Explanation:
Given;
initial velocity of the bullet, u = 420 m/s
final velocity of the bullet, v = 280 m/s
length of the bullet, d₁ = 2 cm
thickness of the board, d₂ = 10 cm
total distance penetrated by the bullet through the board;
d = d₁ + d₂ = 2 cm + 10 cm = 12 cm = 0.12 m
The average acceleration of the bullet through the board is calculated as;
[tex]v^2 = u^2 + 2ad\\\\2ad = v^2 - u^2\\\\a = \frac{v^2 - u^2}{2d} \\\\a = \frac{(280^2) - (420^2)}{2(0.12)} = -4.083 \times 10^{5} \ m/s^2[/tex]
Therefore, the average acceleration of the bullet through the board is -4.083 x 10⁵ m/s²
find the upward force in Newton when each of these is under water(density of 1g/cm3) a lump of iron of volume 2000cm3
Answer:
Upthrust = 19.6 N
Explanation:
When an object is immersed under water, the upward force it experience is called an upthrust. An upthrust is a force which is applied on any object in a fluid which acts in an opposite direction to the direction of the weight of the object.
Upthrust = density of liquid x gravitational force x volume of object
i.e U = ρ x g x vol
Given: ρ = 1g/[tex]cm^{3}[/tex] (1000 kg/[tex]m^{3}[/tex]), volume = 2000 c[tex]m^{3}[/tex] (0.002 [tex]m^{3}[/tex]) and g = 9.8 m/[tex]s^{2}[/tex]
So that;
U = 1000 x 9.8 x 0.002 (kg/[tex]m^{3}[/tex] x [tex]m^{3}[/tex] x m/[tex]s^{2}[/tex])
= 19.6 Kg m/[tex]s^{2}[/tex]
U = 19.6 Newtons
The upthrust on the iron is 19.6 N.
Describe how you could whether sound travels best through wood, plastic, or metal.
Answer:
metal
Explanation:
sound can travel best in materials with higher elastic properties like metal than it can through other solids like plastic or rubber which have lower elastic properties
I hope this helps
A space ship has four thrusters positioned on the top and bottom, and left and right as shown below. The thrusters can be operated independently or together to help the ship navigate in all directions.
Initially, the Space Probe is floating towards the East, as shown below, with a velocity, v. The pilot then turns on thruster #2.
Select one:
a.
Space ship will have a velocity to the West and will be speeding up.
b.
Space ship will have a velocity to the East and will be speeding up.
c.
Space ship will have a velocity to the East and will be slowing down.
d.
Space ship will have a velocity to the West and will be slowing down.
e.
Ship experiences no change in motion.
Answer:
The correct answer is - c. Spaceship will have a velocity to the East and will be slowing down.
Explanation:
In this case, if turned on thruster #2 then it will exert force on the west side as thruster 2 is on the east side and it can be understood by Newton's third law that says each action has the same but opposite reaction.
As the spaceship engine applies force on the east side then according to the law the exhauster gas applies on towards west direction. It will try to decrease the velocity of the spaceship however, the direction of floating still be east side initally.
What is the mass of the diver in (Figure 1) if she exerts a torque of 2200 N⋅m on the board, relative to the left (A) support post?
A-->B = 1.0m
B--> end of board = 3.0m
Answer:
56.1 kg
Explanation:
Given
[tex]T = 2200Nm[/tex] -- torque
[tex]d_1 = 1.0m[/tex]
[tex]d_2 = 3.0m[/tex]
Required
The mass of the diver
From the question, we understand that the diver is at the extreme of the board.
So, we make use of the following torque equation
[tex]T = F * (d_1 + d_2)[/tex]
Where:
[tex]F \to Force[/tex]
So, we have:
[tex]2200 = F * (1.0 + 3.0)[/tex]
[tex]2200 = F * 4.0[/tex]
Divide both sides by 4.0
[tex]550 = F[/tex]
[tex]F = 550 N[/tex] --- This is the force exerted by the diver (in other words, the weight).
To calculate the mass, we use:
[tex]F = mg[/tex]
Make m the subject
[tex]m = \frac{F}{g}[/tex]
This gives:
[tex]m = \frac{550}{9.8}[/tex]
[tex]m = 56.1kg[/tex]
A solenoid has a length , a radius , and turns. The solenoid has a net resistance . A circular loop with radius is placed around the solenoid, such that it lies in a plane whose normal is aligned with the solenoid axis, and the center of the outer loop lies on the solenoid axis. The outer loop has a resistance . At a time , the solenoid is connected to a battery that supplies a potential . At a time , what current flows through the outer loop
This question is incomplete, the complete question is;
A solenoid has a length 11.34 cm , a radius 1.85 cm , and 1627 turns. The solenoid has a net resistance of 144.9 Ω . A circular loop with radius of 3.77 cm is placed around the solenoid, such that it lies in a plane whose normal is aligned with the solenoid axis, and the center of the outer loop lies on the solenoid axis. The outer loop has a resistance of 1651.6 Ω. At a time of 0 s , the solenoid is connected to a battery that supplies a potential 34.95 V. At a time 2.58 μs , what current flows through the outer loop?
Answer:
the current flows through the outer loop is 1.3 × 10⁻⁵ A
Explanation:
Given the data in the question;
Length [tex]l[/tex] = 11.34 cm = 0.1134 m
radius a = 1.85 cm = 0.0185 m
turns N = 1627
Net resistance [tex]R_{sol[/tex] = 144.9 Ω
radius b = 3.77 cm = 0.0377 m
[tex]R_o[/tex] = 1651.6 Ω
ε = 34.95 V
t = 2.58 μs = 2.58 × 10⁻⁶ s
Now, Inductance; L = μ₀N²πa² / [tex]l[/tex]
so
L = [ ( 4π × 10⁻⁷ ) × ( 1627 )² × π( 0.0185 )² ] / 0.1134
L = 0.003576665 / 0.1134
L = 0.03154
Now,
ε = d∅/dt = [tex]\frac{d}{dt}[/tex]( BA ) = [tex]\frac{d}{dt}[/tex][ (μ₀In)πa² ]
so
ε = μ₀n [tex]\frac{dI}{dt}[/tex]( πa² )
ε = [ μ₀Nπa² / [tex]l[/tex] ] [tex]\frac{dI}{dt}[/tex]
ε = [ μ₀Nπa² / [tex]l[/tex] ] [ (ε/L)e^( -t/[tex]R_{sol[/tex]) ]
I = ε/[tex]R_o[/tex] = [ μ₀Nπa² / [tex]R_o[/tex][tex]l[/tex] ] [ (ε/L)e^( -t/[tex]R_{sol[/tex]) ]
so we substitute in our values;
I = [ (( 4π × 10⁻⁷ ) × 1627 × π(0.0185)²) / (1651.6 ×0.1134) ] [ ( 34.95 / 0.03154)e^( -2.58 × 10⁻⁶ / 144.9 ) ]
I = [ 2.198319 × 10⁻⁶ / 187.29144 ] [ 1108.116677 × e^( -1.7805 × 10⁻⁸ )
I = [ 1.17374 × 10⁻⁸ ] × [ 1108.116677 × 0.99999998 ]
I = [ 1.17374 × 10⁻⁸ ] × [ 1108.11665 ]
I = 1.3 × 10⁻⁵ A
Therefore, the current flows through the outer loop is 1.3 × 10⁻⁵ A
Answer:
1.28 *10^-5 A
Explanation:
Same work as above answer. Needs to be more precise
