Answer:
a) 23 m/s
Explanation:
Assuming no external forces acting during the collision, total momentum must be conserved, as follows:[tex]p_{o} = p_{f} (1)[/tex]
The initial momentum p₀, can be written as follows:[tex]p_{o} = m_{1} * v_{1o} + m_{2}* v_{2o} = 6.0 kg * 5.0 m/s + 2.0 kg * v_{2o} (2)[/tex]
The final momentum pf, can be written as follows:[tex]p_{f} = (m_{1} + m_{2} )* v_{f} = 8.0 kg* (-2.0 m/s) (3)[/tex]
Since (2) and (3) are equal each other, we can solve for the only unknown that remains, v₂₀, as follows:[tex]v_{2o} = \frac{-6.0kg* 5m/s -8.0 kg*2.0m/s}{2.0kg} = \frac{-46kg*m/s}{2.0kg} = -23.0 m/s (4)[/tex]
This means that the 2.0-kg object was moving at 23 m/s in a direction opposite to the 6.0-kg object, so its initial speed, before the collision, was 23.0 m/s.The speed of the 2.0-kg object before the collision will be 23 m/s.Option A is correct.
What is the law of conservation of momentum?According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
The given data in the problem is;
m₁ is the mass of objthe ct = 6.0-kg
v₁ is the speed moving = 5
m₂ is the mass of object 2 = 2.0 Kg
V is the final speed = 2.0 m/s
v₂ is the speed of the 2.0-kg object before the collision =?
According to the law of conservation of momentum;
Momentum before collision =Momentum after collision
[tex]\rm m_1v_1 + m_2v_2 = V(m_1 + m_2)\\\\(6 \times 5) + (2 \times v_2) = -2.0 \times (8) \\\\ \rm v_2 = \frac{-46}{2.0} \\\\ \rm v_2 =-23.0\ m/sec[/tex]
Hence the speed of the 2.0-kg object before the collision will be 23 m/s.Option A is correct.
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A boy on a treasure hunt walks 12 paces West, then 21 paces North, then 25 paces East. What is the magnitude of boy’s resultant displacement in meters?
Answer: The displacement is 18.8 meters.
Explanation:
Let's define the North as the positive y-axis and the East as the positive x-axis.
We also can assume that if the point (x, y) represents the position of the boy, the initial position is (0 paces, 0 paces).
"A boy on a treasure hunt walks 12 paces West,"
West would be the negative x-axis in this case, then:
the position will be (-12 paces, 0 paces)
"then 21 paces North"
Now the position will be (-12 paces, 21 paces)
"then 25 paces East."
Now the position will be (-12 paces + 25 paces, 21 paces)
= (13 paces, 21 paces)
Now we have the initial and final positions of the boy, (0 paces, 0 paces) and (13 paces, 21 paces) respectively.
We want to find the displacement, which is defined as the distance between the final position and the initial position.
Remember that for two vectors (a, b) and (c, d), the distance is:
D = √( (a - c)^2 + (b - d)^2)
In this case, the displacement will be:
D = √( ( 13 paces - 0 paces)^2 + (21 paces - 0 paces)^2) = 24.7 paces.
But we want this quantity in meters, so we can use the relation:
1 pace = 0.762 meters.
Then 24.7 paces, are 24.7 times 0.762 meters.
D = 24.7*0.762 m = 18.8 meters.
How high of a hill should an 80-kg person climb to expend 40,000 joules of energy?
A. 4.1 km
B. 4.9 km
C. 51 m
D. 500 m
Answer:
1: 51 m
2: some energy was transformed to other forms
3: 3.24
4: 45j
5: 1020
Explanation:
The required height of hill is 51 m. Hence, option (C) is correct.
Given data:
The mass of person is, m = 80 kg.
The energy expended during climbing is, E = 40,000 J.
The energy possessed by the body by virtue of height is known as potential energy. In the given case, the energy expended by the person will be stored in the form of potential energy. Then,
E = U
E = mgh
here, h is the height of hill and g is the gravitational acceleration.
Solving as,
40000 = 80(9.8) h
h ≈ 51 m
Thus, we can conclude that the required height of hill is 51 m. Hence, option (C) is correct.
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HELP ASAP !!!
A train rolls past a stationary observer. To him, the train is moving at a speed
of 25 m/s west, and a woman on the train is moving at a speed of 24.6 m/s
west. How long does it take the woman to move 4 m relative to the train?
A. 7.1 s
B. 9.0 s
C. 8.4 s
D. 10 s
Answer:
10 seconds a mile. D. 10 s
Explanation:
25-24.6= .4
To find how long she will take to move 4 m relative to the train, take the distance she wants to travel divided by her velocity relative to the train.
4 / .4 = 10
Hope this helps you! :)
Answer:
10s
Explanation:
A car is traveling at the bottom of a 9.00-meter-radius circular hill with a constant speed v. The moment the car is at the bottom of the hill, it is noted that a person sitting on a scale in the car reads a value off the scale that is 80% more than normally when the scale is at rest in a bathroom. With what speed is the car traveling
Answer:
Explanation:
reading of scale = reaction force of surface R
centripetal force = R - mg = m v² / R , m is mass , v is velocity and R is radius of the circular path .
R = mg + m v² / R
given ,
m v² / R = .80 mg
v² = .80 x g x R
= .8 x 9.8 x 9 = 70.56
v = 8.4 m /s
Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1.1 m, b = 0.9 m, q = 2.3 × 10-9C)?
Answer:
F = 93.49 × 10^(-9) N
Explanation:
We are given;
Length of rectangle; a = 1.1 m
Width of rectangle; b = 0.9 m
Charge on rectangle; q = 2.3 × 10^(-9) C
Formula for force is;
F = kq²/r²
Where;
k is a constant = 8.99 x 10^(9) N.m²/C²
a) on the width side, we have;
F = [8.99 x 10^(9) × (2.3 × 10^(-9))²]/0.9²
F = 58.79 × 10^(-9) N
This is on the y-axis
b) on the length side, we have;
F = [8.99 x 10^(9) × (2.3 × 10^(-9))²]/1.1²
F = 39.3 × 10^(-9) N
This is on the x-axis
C) using pythagoras theorem, for the diagonal side, we have c² = a² + b².
Thus;
F = [8.99 x 10^(9) × (2.3 × 10^(-9))²]/(1.1² + 0.9²)
F = 23.54 × 10^(-9) N
Using trigonometric ratios, we can find the angle θ.
tan θ = b/a
tan θ = 0.9/1.1
tan θ = 0.8182
θ = tan^(-1) 0.8182
θ = 39.29°
Resolving along x and y axis, we have;
F_x = 23.54 × 10^(-9) × cos 39.29°
F_x = 18.22 × 10^(-9) N
F_y = 23.54 × 10^(-9) × sin 39.29°
F_y = 14.91 × 10^(-9) N
Resultant force will be;
F = √((Σf_x)² + (ΣF_y)²)
F = √[(18.22 × 10^(-9)) + (39.3 × 10^(-9))]² + [(14.91 × 10^(-9)) + (58.79 × 10^(-9))²]
F = √[(33.0855 × 10^(-16)) + (54.317 × 10^(-16))]
F = 93.49 × 10^(-9) N
What does BMI (Body Mass Index) attempt to measure?
O A. Target heart rate
O B. Energy levels
O C. Body fat percentage
O D. Weight
Answer: C. Body fat percentage
Explanation:
Answer:
your answer is C
Explanation:
When discussing Newton's laws of motion which terms do people most likely use when talking about Newton's third law of motion
Answer:
Explanation:
When discussing Newton's laws of motion, the most likely used terms when talking about Newton's third law of motion are action and reaction. According to this law, for every action there is an equal and opposite reaction
Answer: C. "action" and "reaction"
Explanation: Newtons 3rd law of motion: for every action, there is an equal and opposite reaction (action and reaction forces are described by this law).
Have a nice day. :)
What's the value of 96,745 joules in Btus?
Answer:
The value of 96,745 joules in Btus is 91.6965673 or 91.7 Btus.
Explanation:
Btus stands for British thermal unit. It is the unit of energy. 96,745 Joules is equal to 91.7 Btus of energy.
What is Energy?
Energy is the quantitative property of an object which is transferred to an object or to a physical system, that is recognizable in the performance of the work done and in the form of heat and light generated by the object or system. Energy is a conserved quantity, according to the law of conservation of energy which states that energy can be transformed, but not created or destroyed.
A British thermal unit (Btu) is a measure of the heat content or energy of fuels or energy sources. 1 BTU is roughly equal to the amount of energy which is required to raise the temperature of one pound of water by 1 degree Fahrenheit.
1 Joule = 0.000947817 Btu
Therefore, 96,745 Joules = 91.696 or 91.7 Btus
The value of 96,745 joules in Btus is 91.6965673 or 91.7 Btus.
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An object with a mass of 10.5kg is traveling at a velocity of 9m/s. What is the kinetic energy of
the object?
An astronaut with mass 84kg is at rest in space, before firing her water pack to move toward the shuttle. If the amount of water shot out is
2kg and it is fired at a speed of 10m/s, what will the speed of the astronaut be?
Answer:
The astronaut is moving at a speed of 0.238 m/s in a direction opposite the direction of the water shot out.
Explanation:
We are given;
Mass of astronaut; m1 = 84 kg
Mass of water shoot out; m2 = 2 kg
Initial speed of astronaut; u1 = 0 m/s
Initial speed of water shoot out; u2 = 0 m/s
Final speed of shoot out; v2 = 10 m/s
From law of conservation of momentum, we can say that;
Initial momentum = final momentum
Thus;
m1•u1 + m2•u2 = m1•v1 + m2•v2
Where v1 is the final speed of the astronaut
Plugging in the relevant values, we get;
(84 × 0) + (2 × 0) = (84 × v1) + (2 × 10)
0 = 84v1 + 20
-20 = 84v1
v1 = -20/84
v1 = -0.238 m/s
The negative sign indicates that the astronaut is moving 0.238 m/s in a direction opposite the direction of the water shot out.
When the magnetic flux through a coil of wire changes, what is generated between the ends of the coil? Which equation predicts this?
Answer:
induced electromotive force (Voltage) E = - N dΦ / dt
Explanation:
When the magnetic flux this coil induces a current in each turn of the coil, which is why an induced electromotive force (Voltage) appears at the ends of the coil.
This phenomenon is fully explained by Faraday's law
E = - dΦ / dt
where in the case of a coil with N turns of has
E = - N dΦ / dt
Rl flux is the product of the normal to the area by the magnetic field, in this case the flux changes so we can assume that the area of the coil is constant
Find the magnitude of the vector v given its initial and terminal points. Round your answer to four decimal places.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The value is [tex]|v| = 6.93[/tex]
Explanation:
From the question we are told that
The initial point is [tex](x_1 , y_1 , z_1 ) = (-1 , 7 , 4 )[/tex]
The terminal point is [tex](x_2 , y_2 , z_2) = (-5 , 11, 8 )[/tex]
Generally the magnitude of the vector is mathematically represented as
[tex]|v| = \sqrt{(x_2 -x_1 )^2 + (y_2 - y_1 )^2 + (z_2 -z_1)^2}[/tex]
=> [tex]|v| = \sqrt{(-5 -(-1) )^2 + (11 - 7 )^2 + (8 -4)^2}[/tex]
=> [tex]|v| = 6.93[/tex]
Riding a bicycle on a flat, smooth surface is a lot easier than riding it along a bumpy surface or up a hill. A bumpy surface creates more friction with your bike tires than a smooth surface does, and going up a hill means fighting gravity.
Write about a time you had to ride a bicycle on a difficult surface. What did you have to do to adjust your riding?
Answer:
one time i was one the flat ground at my aunts house then we went on a hike so i brought my bike it had just rained that day so it was kinda muddy so there was sticks everywhere.i was riding up hill and noticed that it was very hard,then i rode down hill and it was much better
Explanation:
In a Young's double slit experiment, the separation between the slits is 1.20 × 10–4 m; and the screen is located 3.50 m from the slits. The distance between the central bright fringe and the second-order bright fringe is 0.0375 m. What is the wavelength of the light used in this experiment?
Answer:
Explanation:
separation between slit d = 1.2 x 10⁻⁴ m
distance of screed D = 3.5 m
distance of second order right fringe
= 2λD / d where λ is wavelength of light .
2λD / d = .0375
2 x λ x 3.5 / 1.2 x 10⁻⁴ = .0375
λ = 6428 x 10⁻¹⁰ m
= 643 nm .
Need help with this physics question!
A baseball is hit straight up at 60 m/s. At 9 seconds what is the displacement, the acceleration and velocity?
Answer:
Acceleration: -9.8 m/s^2
Velocity: -28.2 m/s
Displacement: 143.1 m
Explanation:
The acceleration of gravity for any object close to earth is approximately -9.8 m/s^2.
Now, to find the velocity after 9 seconds, we can use a kinematics formula, where x is the final velocity:
Final Velocity = Initial Velocity + Acceleration * Time
x = 60 + -9.8*9
x = 60 - 88.2
x = -28.2
The velocity is -28.2 m/s.
Lastly, to find the displacement, we can use another kinematics formula, where y is the displacement:
Displacement = (Final Velocity + Initial Velocity)/2 * Time
y = (-28.2 + 60)/2 * 9
y = 143.1
The displacement is 143.1 meters.
A person swings a 0.546-kg tether ball tied to a 4.56-m rope in an approximately horizontal circle. If the maximum tension the rope can withstand before breaking is 11.0 N, what is the maximum angular speed of the ball
Answer:
2.1 rad/s
Explanation:
Given that,
Mass of a tether ball, m = 0.546 kg
Length of a rope, l = 4.56 m
The maximum tension the rope can withstand before breaking is 11.0 N
We need to find the maximum angular speed of the ball. Let v is the linear velocity. The maximum tension is balanced by the centripetal force acting on it. It can be given by :
[tex]F=\dfrac{mv^2}{r}\\\\v=\sqrt{\dfrac{Fr}{m}} \\\\v=\sqrt{\dfrac{11\times 4.56}{0.546}} \\\\=9.584\ m/s[/tex]
Let [tex]\omega[/tex] is the angular speed of the ball. The relation between the angular speed and angular velocity is given by :
[tex]v=r\omega\\\\\omega=\dfrac{v}{r}\\\\=\dfrac{9.584}{4.56}\\\\=2.1\ rad/s[/tex]
So, the maximum angular speed of the ball is 2.1 rad/s.
A cup of coffee is sitting on a table in a train that is moving with a constant velocity. The coefficient of static friction between the cup and the table is 0.30. Suddenly, the train accelerates. What is the maximum acceleration that the train can have without the cup sliding backward on the table?
Answer:
a = 2.94 m/s²
Explanation:
In order for the cup not to slip, the unbalanced force on cup must be equal to the frictional force:
Unbalanced Force = Frictional Force
ma = μR = μW
ma = μmg
a = μg
where,
a = maximum acceleration for the cup not to slip = ?
μ = coefficient of static friction = 0.3
g = acceleration due to gravity = 9.8 m/s²
Therefore,
a = (0.3)(9.8 m/s²)
a = 2.94 m/s²
100 POINTS + BRAINLIEST, HEART, & FIVE STAR.
In the one pully system when you move the mass from the 20 cm mark to the 15 cm mark, it moves 5 cm. How far did you pull the string.
Question 1 options:
5 cm
10 cm
15 cm
20 cm
In the two pully system if you lifted the weight from the 20 cm mark to the 15 cm mark moving 5 cm. How far did you pull the rope down?
Question 2 options:
5 cm
10 cm
15 cm
20 cm
Answer:
Question 1 the answer is 5 cm for the one pulley system, I just took the quiz
Question 2 is 10 cm
Explanation:
The rope only needs to move 5 cm for the mass to move from 15 to 20.
For the 2 pulley system the string has to move twice as far making it 10 cm. I took the quiz and got 100%
which of the following require that you also state direction
A. speed
B. displacement
C. acceleration
D. instantaneous speed
SCIENCE QUESTION FOR 20 POINTS
Answer:
d
Explanation:
The figure below shows two forces F1 = 30.0 N and F2 = 20.0 N acting on an object that
can rotate around a center axle. Find the net torque in Nm. (Tolerance +/- 0.05)
Answer:
0.2Nm
Explanation:
F1 = 30.0N
F2 = 20.0N
R = 2.0cm = 0.02m
F1R1 - F2R2 = net Torque
30(0.02) - 20(0.02) = net Torque
0.6-0.4 = net Torque
Therefore net Torque = 0.2Nm
The figure below shows two forces [tex]F_1[/tex] = 30.0 N and [tex]F_2[/tex] = 20.0 N acting on an object that can rotate around a centre axle. The net torque in 0.2 N-m
What is torque?The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction. A vector quantity is a torque.
Torque is defined as Γ=r×F=r F sin(θ). In other words, torque is the cross product of the force vector, where 'a' is the angle between r and F, and the distance vector (the distance between the pivot point and the place where force is applied).
Torque due to [tex]F_1[/tex] = 30.0 N is 0.6 N-m outside the plane and due to [tex]F_2[/tex] = 20.0 N is 0.4 N-m inside the plane so net torque is 0.2 N-m outside the plane.
The figure below shows two forces [tex]F_1[/tex] = 30.0 N and [tex]F_2[/tex] = 20.0 N acting on an object that can rotate around a centre axle. The net torque in 0.2 N-m outside the plane.
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What is the height of a building that an object is dropped from if it has a mass of 3 kg and hits the ground with a velocity of 50 m/s?
Answer:
125 m
Explanation:
m = 3kg
v = 50m/s
u = 0m/s
a = +g = 10m/s²
s = H = ?
using the formula,
v² = u² + 2as
50² = 0² + 2(10)(H)
2500 = 20H
H = 2500/20
H = 125m
By what factor must you increase the intensity of a sound in order to hear a 1.0-dB rise in the sound level?
Answer:
The right approach will be "1.3". A further explanation is given below.
Explanation:
As we know,
In Decibels, the change in sound volume will be:
= [tex]10log\frac{I_1}{I_2}[/tex]
Now,
According to the question,
⇒ [tex]1=10 log \frac{I_1}{I_2}[/tex]
By applying cross multiplication and putting the value of log, we get
⇒ [tex]10^{\frac{1}{10} }=\frac{I_1}{I_2}[/tex]
⇒ [tex]1.26=\frac{I_1}{I_2}[/tex]
⇒ [tex]\frac{I_1}{I_2}=1.3[/tex]
How to play track and field
Explanation:
Track and Field is a sport, which is includes disciplines of running, jumping, and throwing events. The sport traces back to Ancient Greece. The first recorded examples of this sport were at the Ancient Greek Olympics. In Ancient Greece, only one event was contested, the stadion footrace. Later on, the game expanded to more events.Events of track and field are divided into three: track events, field events, and combined events. Track events consist of Sprints, middle-distance, long distance, hurdles and relays; Field events consist of jumps and throws; while combined events consist of pentathlon, heptathlon, and decathlon. Track and field is usually played outdoors in stadiums. The usual features of a track and field stadium are the outer running track, and the field within the track
Your eyes see different wavelengths of light as different ________.
amplitude
color
detectors
spectrum
Answer:
Its color
Explanation: I got it right
A diffraction grating with 230 lines per mm is used in an experiment to study the visible spectrum of a gas discharge tube. At what angle from the beam axis will the first order peak occur if the tube emits light with wavelength of 405.3 nm? Tries 0/20 At what angle will the second order peak occur?
Answer:
θ₁ = 5.4°
θ₂ = 10.86°
Explanation:
The angle ca be found by using grating equation:
mλ = d Sinθ
where,
m = order of diffraction
λ = wavelength = 405.3 nm = 4.053 x 10⁻⁷ m
d = grating element = 1/230 lines/mm = 0.0043 mm/line = 4.3 x 10⁻⁶ m/line
θ = angle = ?
FOR m = 1:
(1)(4.053 x 10⁻⁷ m) = (4.3 x 10⁻⁶ m/line) Sin θ₁
Sin θ₁ = 0.09425
θ₁ = Sin⁻¹(0.09425)
θ₁ = 5.4°
FOR m = 2:
(2)(4.053 x 10⁻⁷ m) = (4.3 x 10⁻⁶ m/line) Sin θ₁
Sin θ₂ = 0.1885
θ₂ = Sin⁻¹(0.1885)
θ₂ = 10.86°
Two cylinders P and Q are made of copper
P
The height of P is twice the height of Q. The diameter of P is half the diameter of
Which statement is comrect?
A The density of cylinder Pis four times that of cylinder o
The density of cylinder Pis twice that of cylinder
The density of cylinder P is equal to that of cylinder Q
The density of cylinder P is half that of cylinder o
с
D
Let H and D denote the height and diameter, respectively, of cylinder P, and h and d the height and diameter of cylinder Q.
Then the volumes of P and D, denoted V and v, respectively, are
V = π (D / 2)² H = π D ² H / 4
v = π (d / 2)² h = π d ² h / 4
The height of P is twice the height of Q, so H = 2h.
The diameter of P is half the diameter of Q, so D = d / 2.
Substitute these into equation for the volume of cylinder P:
V = π (d / 2)² (2h) / 4
V = π (d ² / 4) (2h) / 4
V = π d ² h / 8
V = 1/2 • π d ² h / 4
V = v / 2
That is, cylinder P has half the volume of cylinder Q.
Recall that density is equal to mass per unit of volume. So R and ρ, the respective densities of cylinders P and Q, are
R = m / V = m / (v / 2) = 2 m / v
ρ = m / v
which means cylinder P has twice the density of cylinder Q (assuming both cylinders have the same mass m).
Solve for the unknown variables: (8, 3) + (b, 2) = (4, a).
Answer:
The value of a is 5 and b is -4.
Explanation:
You have to solve it by comparison :
(8 , 3) + (b , 2) = (4 , a)
(8+b , 3+2) = (4 , a)
8 + b = 4
b = 4 - 8
b = -4
3 + 2 = a
a = 5
When a person wearing a helmet rides a bicycle, the helmet experiences which type of friction?
A. Fluid
B. Static
C. Sliding
D. Rolling
Answer:
B
Explanation:
Answer:
B.)Static
Hope I helped
A 500 g ball and a 200 g ball are dropped from a tower. Both balls are the same size and there is no air resistance. When do they hit the ground? The 200 g mass hits the ground first. They both hit the ground at the same time. The 500 g mass hits the ground first.
Answer:
They both hit the ground at the same time.
Explanation:
if you drop a 100 g and 200 g mass simultaneously from the same height they’ll hit the ground at the same time.
Yes, there is a role of a very simple equation of kinematics i.e.
s=ut+1/2(at^2)
so, s means the height is the same for both masses(h), u(initial velocity) is obviously zero cause you are dropping it, a (acceleration) is due to the gravity here only ‘g’.
time is taken for a particular object to hit the ground,
t= (2h/g)^1/2 .
We can see that there is no term for the mass of objects, meanwhile, the mass of the object has nothing to do with the time taken in hitting the ground in this case.
How much energy is stored in a 2.80-cm-diameter, 14.0-cm-long solenoid that has 200 turns of wire and carries a current of 0.800 A
Answer:
The energy stored in the solenoid is 7.078 x 10⁻⁵ J
Explanation:
Given;
diameter of the solenoid, d = 2.80 cm
radius of the solenoid, r = d/2 = 1.4 cm
length of the solenoid, L = 14 cm = 0.14 m
number of turns, N = 200 turns
current in the solenoid, I = 0.8 A
The cross sectional area of the solenoid is given as;
[tex]A = \pi r^2\\\\A = \pi (0.014)^2\\\\A = 6.16*10^{-4} \ m^2[/tex]
The inductance of the solenoid is given by;
[tex]L = \frac{\mu_0 N^2A}{l} \\\\L = \frac{(4\pi*10^{-7})(200^2)(6.16*10^{-4})}{0.14}\\\\L = 2.212*10^{-4} \ H[/tex]
The energy stored in the solenoid is given by;
E = ¹/₂LI²
E = ¹/₂(2.212 x 10⁻⁴)(0.8)²
E = 7.078 x 10⁻⁵ J
Therefore, the energy stored in the solenoid is 7.078 x 10⁻⁵ J
The energy stored in a 2.80-cm-diameter, 14.0-cm-long solenoid that has 200 turns of wire and carries a current of 0.800 A is 7.07 × 10⁻⁵ J.
A solenoid is a type of electromagnet, whose purpose is to generate a controlled magnetic field through a coil wound into a tightly packed helix.
First, given the diameter of the solenoid (d) is 2.80 cm (0.0280 m), we can calculate the cross-sectional area (A) using the following expression.
[tex]A =\pi \times (\frac{d}{2} )^{2} = \pi \times (\frac{0.0280}{2} )^{2} = 6.16 \times 10^{-4} m^{2}[/tex]
Next, we will calculate the inductance (L) of the solenoid using the following expression.
[tex]L = \frac{\mu _0 \times N^{2} \times A}{l} = \frac{(4\pi \times 10^{-7}H/m ) \times 200^{2} \times (6.16 \times 10^{-4}m^{2} )}{0.140m} = 2.21 \times 10^{-4} H[/tex]
where,
μ₀ is the vacuum permeabilityN is the number of turnsl is the length of the solenoidFinally, for a current (I) of 0.800 A, we can calculate the energy stored (E) using the following expression.
[tex]E = \frac{1}{2} \times L \times I^{2} = \frac{1}{2} \times (2.21 \times 10^{-4}H ) \times (0.800A)^{2} = 7.07 \times 10^{-5} J[/tex]
The energy stored in a 2.80-cm-diameter, 14.0-cm-long solenoid that has 200 turns of wire and carries a current of 0.800 A is 7.07 × 10⁻⁵ J.
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