An airplane is attempting to land on a runway when the wind is blowing at a velocity of 10 m/s perpendicular to the runway. Given that the airplane is flying at an airspeed of 47 m/s, at what angle relative to the runway direction must the pilot keep the nose pointed into the wind to maintain a flight path aligned with the runway?

Explanation:

Given that,

[tex]T_{\frac{1}{2}}=8.04\ days[/tex]

We need to calculate the decay constant

Using formula of decay constant

[tex]\lambda=\dfrac{0.693}{t_{\frac{1}{2}}}[/tex]

[tex]\lambda=\dfrac{0.693}{8.04\times24\times3600}[/tex]

[tex]\lambda=9.97\times10^{-7}\ sec^{-1}[/tex]

We need to calculate the number of [tex]^{131}I[/tex] nuclei

[tex]N=\dfrac{A\ ci}{\lambda}[/tex]

Where,

A= activity

ci = disintegration

[tex]N=\dfrac{0.5\times10^{-6}\times3.7\times10^{10}}{9.97\times10^{-7}}[/tex]

[tex]N=1.855\times10^{10}[/tex]

Hence, This is the required solution.

Answer:

9.74 x 10^7 m/s

Explanation:

V = 27000 V

energy of electrons = e x V

K = 1.6 x 10^-19 x 27000 = 43200 x 10^-19 J

Energy = 1/2 m v^2

43200 x 10^-19 = 0.5 x 9.1 x 10^-31 x v^2

v^2 = 9.495 x 10^15

v = 9.74 x 10^7 m/s

Answer:

Explanation:

Answer:

0.632 m

Explanation:

let the equilibrium separation between the charges is d and the angle made by string with the vertical is θ.

According to the diagram,

d = L Sinθ + L Sinθ = 2 L Sinθ      .....(1)

Let T be the tension in the string.

Resolve the components of T.

T Sinθ  = k q1 q2 / d^2

T Sinθ = k q1 q2 / (2LSinθ)²     .....(2)

T Cosθ = mg    .....(3)

Dividing equation (2) by equation (3), we get

tanθ = k q1 q2 / (4 L² Sin²θ x mg)

tan θ Sin²θ = k q1 q2 / (4 L² m g)

For small value of θ, tan θ = Sin θ

So,

Sin³θ = k q1 q2 / (4 L² m g)

Sin³θ = (9 x 10^9 x 0.785 x 10^-6 x 1.47 x 10^-6) / (4 x 0.5 x 0.5 x 4.20 x 10^-3 x 9.8)

Sin³θ =  0.2523

Sinθ = 0.632

θ = 39.2 degree

So, the separation between the two charges, d = 2 x L x Sin θ

d = 2 x 0.5 x 0.632 = 0.632 m

The weight of an 8 kg substance can be calculated in various units using the weight equation w = mg and the appropriate conversion factors. The weight is 78.4 N, 0.0784 kN, 78.4 kg·m/s², 8 kgf, 17.64 lbf, and 10.83 lbm·ft/s².

To calculate the weight of an object in different units, we need to use the equation for weight: w = mg, where m is the mass of the object and g is the acceleration due to gravity. In this case, the mass (m) of the substance is given as 8 kg, and the value of g on Earth is approximately 9.80 m/s².

Therefore, the weight of the substance in various units is:

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Answer:

55 ft/s

Explanation:

A₁ = Area of rectangular cross-section at input side = 1.5 x 11 = 16.5 ft²

A₂ = Area of rectangular cross-section at far end = 1.5 x 6 = 9 ft²

v₁ = speed of water at the input side of channel = 30 ft/s

v₂ = speed of water at the input side of channel = ?

Using equation of continuity

A₁ v₁ = A₂ v₂

(16.5) (30) = (9) v₂

v₂ = 55 ft/s

Answer:

Frequency, f = 0.38 Hz

Explanation:

Time period of the spring, T = 2.6 seconds

We need to find the frequency of oscillation for a mass on the end of spring. The relation between the time period and the frequency is given by :

Let f is the frequency of oscillation. So,

[tex]f=\dfrac{1}{T}[/tex]

[tex]f=\dfrac{1}{2.6\ s}[/tex]

f = 0.38 Hz

or

f = 0.4 Hz

So, the frequency of oscillation for a mass on the end of a spring is 0.38 hertz. Hence, this is the required solution.

Answer:

Option B is the correct answer.

Explanation:

Final velocity = 5.3 m/s

Acceleration till 5.3 m/s = 1.2 m/s²

Time taken for this

           [tex]t_1=\frac{5.3}{1.2}=4.42s[/tex]

Distance traveled in 4.42 s can be calculated

          s = ut + 0.5 at²

          s = 0 x 4.42 + 0.5 x 1.2 x 4.42² = 11.72 m

Remaining distance = 118 - 11.72 = 106.28 m

Uniform velocity = 5.3 m/s

Time taken

       [tex]t_2=\frac{106.28}{5.3}=20.05s[/tex]

Total time, t = t₁ + t₂  = 4.42 + 20.05 = 24.47 s

Option B is the correct answer.

The runner takes approximately 24.47 seconds to travel 118 meters, considering the time spent accelerating and then running at constant velocity. Therefore, the correct answer is option B.

To determine the time it takes for the runner to travel 118 meters, we need to consider two phases of her motion: acceleration and constant velocity.

Phase 1: Acceleration

Initially, the runner starts from rest (initial velocity, u = 0) and accelerates at a constant rate of 1.2 m/s² until she reaches a velocity of 5.3 m/s.

Step 1: Calculate the time (t1) taken to reach the velocity of 5.3 m/s using the formula v = u + at.

v = 5.3 m/s, u = 0, a = 1.2 m/s²

t1 = (v - u) / a = (5.3 - 0) / 1.2 ≈ 4.417 s

Step 2: Calculate the distance (s1) covered during this acceleration phase using the formula s = ut + 0.5at².

s1 = 0 + 0.5 * 1.2 * (4.417)² ≈ 11.7 m

Phase 2: Constant Velocity

After reaching 5.3 m/s, the runner continues at this constant velocity. We need to find the distance she covers in this phase and the total time taken.

Step 3: Calculate the remaining distance (s2) that needs to be covered at constant velocity.

s1 = 11.7 m, Total distance = 118 m

s2 = 118 - 11.7 = 106.3 m

Step 4: Calculate the time (t2) taken to cover the distance s2 at the constant velocity using the formula t = s / v.

t2 = 106.3 m / 5.3 m/s ≈ 20.075 s

Total Time

Step 5: Add the time taken in both phases to find the total time.

Total time = t1 + t2 ≈ 4.417 s + 20.075 s ≈ 24.492 s

Therefore, the runner takes approximately 24.47 seconds to travel 118 meters. The correct answer is option B.

Answer:

The man ate eggs.

Explanation:

He should brush his teeth before seeing his girlfriend.

Answer:

The longest wavelength of light is 209 nm.

Explanation:

Given that,

Spring constant = 74 N/m

Mass of electron [tex]m= 9.11\times10^{-31}\ kg[/tex]

Speed of light [tex]c= 3\times10^{8}\ m/s[/tex]

We need to calculate the frequency

Using formula of frequency

[tex]f =\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}[/tex]

Where, k= spring constant

m = mass of the particle

Put the value into the formula

[tex]f=\dfrac{1}{2\pi}\sqrt{\dfrac{74}{9.11\times10^{-31}}}[/tex]

[tex]f=1.434\times10^{15}\ Hz[/tex]

We need to calculate the longest wavelength that the electron  can absorb

[tex]\lambda=\dfrac{c}{f}[/tex]

Where, c = speed of light

f = frequency

Put the value into the formula

[tex]\lambda =\dfrac{3\times10^{8}}{1.434\times10^{15}}[/tex]

[tex]\lambda=2.092\times10^{-7}\ m[/tex]

[tex]\lambda=209\ nm[/tex]

Hence, The longest wavelength of light is 209 nm.

The acceleration of the object at t = 2.50 s in simple harmonic motion can be found using the equation a = -ω²x, where ω is the angular frequency and x is the displacement from the equilibrium position.

The acceleration of the object at t = 2.50 s can be found using the equation for simple harmonic motion:
a = -ω²x

where ω is the angular frequency and x is the displacement from the equilibrium position.

The period of the oscillation is related to the angular frequency by the equation:
T = 2π/ω

Substituting the given period (T = 4.60 s) into the equation and solving for ω, we get:
ω = 2π/T = 2π/4.60 s

Now, substituting the values we have, ω = 2π/4.60 s and x = 8.30 cm, into the acceleration equation:

a = -ω²x = -(2π/4.60 s)² * 8.30 cm

Calculate the value of a to find the acceleration of the object at t = 2.50 s using the given equation for acceleration.

Answer:

so the distance between two points are

[tex]d = 0.246 \times 10^{-3} m[/tex]

Explanation:

Surface charge density of the charged plane is given as

[tex]\sigma = 7.2 \mu C/m^2[/tex]

now we have electric field due to charged planed is given as

[tex]E = \frac{\sigma}{2\epsilon_0}[/tex]

now we have

[tex]E = \frac{7.2 \times 10^{-6}}{2(8.85 \times 10^{-12})}[/tex]

[tex]E = 4.07 \times 10^5 N/C[/tex]

now for the potential difference of 100 Volts we can have the relation as

[tex]E.d = \Delta V[/tex]

[tex]4.07 \times 10^5 (d) = 100[/tex]

[tex]d = \frac{100}{4.07 \times 10^5}[/tex]

[tex]d = 0.246 \times 10^{-3} m[/tex]

Answer:

The velocity of the block is 22 m/s.

Explanation:

Given that,

Mass = 2.50 kg

Velocity = 8 .00 m/s

Force = 7.00 N

Time t = 5.00

We need to calculate the change in velocity it means acceleration

Using newton's law

[tex]F = ma[/tex]

Where,

m = mass

a = acceleration

Put the value into the formula

[tex]a=\dfrac{F}{m}[/tex]

[tex]a = \dfrac{7.00}{2.50}[/tex]

[tex]a= 2.8m/s^2[/tex]

We need to calculate the velocity of the block

Using equation of motion

[tex]v = u+at[/tex]

Where,

v = final velocity

u = initial velocity

a = acceleration

t =time

Put the value in the equation

[tex]v= 8.00+2.8\times5.00[/tex]

[tex]v=22\ m/s[/tex]

Hence, The velocity of the block is 22 m/s.

The final velocity of the block after applying a force of 7.00 N for 5.00 s is approximately -6.00 m/s.

To calculate the velocity of the block after a force of 7.00 N directed to the left has been applied for 5.00 s, we can use Newton's second law of motion.

Newton's second law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

In this case, the mass of the block is given as 2.50 kg and the force applied is 7.00 N. We can calculate the acceleration using the formula:

acceleration = force/mass

Substituting the given values, we get:

acceleration = 7.00 N / 2.50 kg

Calculating, the acceleration is approximately 2.80 m/s² to the left. Since the block initially had a velocity of 8.00 m/s to the right, we subtract the acceleration from the initial velocity to get the final velocity:

final velocity = initial velocity - acceleration * time

Substituting the given values:

final velocity = 8.00 m/s - 2.80 m/s² * 5.00 s

Calculating, the final velocity is approximately 8.00 m/s - 14.00 m/s = -6.00 m/s.

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Well [tex]s=\dfrac{d}{t}[/tex] where s is speed, d is distance and t is time.

We have distance and time so we can calculate speed.

[tex]s=\dfrac{24}{37\cdot10^{-9}}\approx6.5\cdot10^8\frac{\mathbf{m}}{\mathbf{s}}\approx\boxed{6.5\cdot10^2\frac{\mathbf{Mm}}{\mathbf{s}}}[/tex]

Hope this helps.

r3t40

Explanation:

It is given that,

Speed of proton, [tex]v=10^7\ m/s[/tex]

Acceleration of the proton, [tex]a=2\times 10^{13}\ \ m/s^2[/tex]

The force acting on the proton is balanced by the magnetic force. So,

[tex]ma=qvB\ sin(90)[/tex]

[tex]B=\dfrac{ma}{qv}[/tex]

m is the mass of proton

[tex]B=\dfrac{1.67\times 10^{-27}\ kg\times 2\times 10^{13}\ \ m/s^2}{1.6\times 10^{-19}\times 10^7\ m/s}[/tex]

B = 0.020875

or

B = 0.021 T

So, the magnitude of magnetic field is 0.021 T. As the acceleration in +x direction, velocity in +z direction. So, using right hand rule, the magnitude of  B must be in -y direction.

Explanation:

The revolutions of the Earth (also called translation movement), consist of the elliptical orbit that describes the Earth around the Sun.  

In this sense, a complete revolution around the Sun occurs every 365 days, 5 hours, 48 ​​minutes and about 46 seconds. It is thanks to this movement and that the Earth's axis is tilted with respect to the plane of its orbit about [tex]23\º[/tex], that the four seasons of the year exist.

For this reason, some regions receive different amounts of sunlight according to the seasons of the year. These variations are more evident near the poles and softer or imperceptible in the tropics (near the equator). Because near the equator the temperature tends to be more stable, with only two seasons: rain and drought.

The Earth's revolution around the Sun, taking approximately 365.24 days, determines the timing of seasons and the length of the year, and when viewed from the North Pole, the revolution is counterclockwise.

The revolution of the Earth around the Sun characterizes the Earth's journey through space as it orbits the Sun. This movement takes approximately 365.24 days, which equals one year.

The revolution is responsible for the timing of seasons and the length of the year. When observed from above the North Pole, the Earth's revolution around the Sun occurs counterclockwise, which is different from the rotation of the Earth on its own axis, the latter causing day and night cycles. Therefore, the correct answer to the student's question about what characterizes the Earth's revolution is (c) it determines the timing of seasons and the length of the year.

Answer:

[tex]F_{net} = 4.22 N[/tex]

Explanation:

Since charge 1 and charge 2 are positive in nature so here we will have repulsion type of force between them

It is given as

[tex]F_{12} = \frac{kq_1q_2}{r^2}[/tex]

[tex]F_{12} = \frac{(9\times 10^9)(5 \mu C)(24 \mu C)}{0.23^2 + 0.69^2}\frac{-0.23\hat i + 0.69 \hat j}{\sqrt{0.23^2 + 0.69^2}}[/tex]

[tex]F_{12} = 2.81(-0.23\hat i + 0.69\hat j)[/tex]

Since charge three is a negative charge so the force between charge 1 and charge 3 is attraction type of force

[tex]F_{13} = \frac{(9\times 10^9)(5 \mu C)(5 \mu C)}{0.27^2 + 0^2} (-\hat i)[/tex]

[tex]F_{13} = 3.1(- \hat i)[/tex]

Now we will have net force on charge 1 as

[tex]F_{net} = F_{12} + F_{13}[/tex]

[tex]F_{net} = (-0.65 \hat i + 1.94 \hat j) + (-3.1 \hat i)[/tex]

[tex]F_{net} = (-3.75 \hat i + 1.94 \hat j)[/tex]

now magnitude of total force on the charge is given as

[tex]F_{net} = 4.22 N[/tex]

Answer:

L / 16

Explanation:

Mass = m, Radius = R, angular momentum = L

Now, new radius, R' = R/4, mass = m, angular momentum, L' = ?

By the law of conservation of angular momentum

If there is no external torque is applied, the angular momentum of the system remains conserved.

L = I x w

Moment of inertia I depends on the mass and the square of radius of the star.

If the radius is one fourth, the angular momentum becomes one sixteenth.

So, L' = L / 16

Answer:

143 batteries does Benny need to sample

Explanation:

Given data

confidence level = 97%

error  = ±10 hours

standard deviation SD = 55 hours

to find out

how many batteries does Benny need to sample

solution

confidence level is 97%

so a will be 1 - 0.97 = 0.03

the value of Z will be for a 0.03 is 2.17 from standard table

so now we calculate no of sample i.e

no of sample  = (Z× SD/ error)²

no of sample = (2.16 × 55 / 10)²

no of sample = 142.44

so  143 batteries does Benny need to sample

Answer:

Charge on least sphere, q = 570 nC

Explanation:

It is given that,

Two small plastic spheres are given positive electrical charges. The distance between the spheres, r = 30 cm = 0.3 m

The repulsive force acting on the spheres, F = 0.13 N

If one sphere has four times the charge of the other.

Let charge on other sphere is, q₁ = q. So, the charge on first sphere is, q₂ = 4 q. The electrostatic force is given by :

[tex]F=k\dfrac{q_1q_2}{r^2}[/tex]

[tex]0.13=9\times 10^9\times \dfrac{q\times 4q}{(0.3\ m)^2}[/tex]

[tex]q^2=\dfrac{0.13\times (0.3)^2}{9\times 10^9\times 4}[/tex]

[tex]q=5.7\times 10^{-7}\ C[/tex]

q = 570 nC

So, the charge on the least sphere is 570 nC. Hence, this is the required solution.

Answer:

       stress   = 366515913.6 Pa

Explanation:

given data:

density of alloy = 8.5 g/cm^3 = 8500 kg/m^3

length turbine blade = 10 cm =  0.1 m

cross sectional area = 15 cm^2 = 15*10^-4 m^2

disc radius = 70 cm = 0.7 m

angular velocity = 7500 rpm = 7500/60 rotation per sec

we know that

stress = force/ area

force = m*a

where a_{c} is centripetal acceleration =

[tex]a_{c} =r*\omega ^{2}= r*(2*\pi*\omega)^{2}[/tex]

         =[tex]0.70*(2*\pi*\frac{7500}{60})^{2}[/tex]

         = 431795.19 m/s^2

mass = [tex]\rho* V[/tex]

Volume = area* length = 15*10^{-5}  m^3

[tex]mass = m = \rho*V = 8500*15*10^{-5} kg[/tex]

force = m*a_{c}

         [tex]=8500*15*10^{-5}*0.70*(2*\pi*\frac{7500}{60})^{2}[/tex]

force = 549773.87 N

stress = force/ area

          = [tex]\frac{549773.87}{15*10^{-5}}[/tex]

       stress   = 366515913.6 Pa

Final answer:

The question requires the calculation of stress on jet turbine blades using physics principles involving centrifugal force and material stress.

Explanation:

The question involves calculating the stress on the turbine blades of a jet engine, which requires a knowledge of physics concepts, particularly mechanics and dynamics. The given data include the turbine's rotational velocity (7,500 rpm), radius of the turbine disc (70 cm), the cross-sectional area of the blades (15 cm2), the length of the blades (10 cm), and the alloy density (8.5 g/cm3). To solve this, one would need to calculate the centrifugal force acting on the blades due to rotation and then divide that force by the cross-sectional area to find the stress. However, the calculation involves steps and concepts not provided in the information above, so the direct calculation cannot be completed without additional physics formulae and explanation.

Using  the formula for power:

P = V^2 / R  

130 W = (9.00 V)^2 / R  

Solve for r:

R = 81/130

R = 0.623 ohms

Now solve for the length of wire:

R = rho L / A  

A must be in m^2 - 2.32 mm^2 * 1 m^2/10^6 mm^2 = 2.132x10^-6 m^2  

Now you have:

0.623 = (6.47x10^-8) L / (2.32x10^-6)  

L = 22.34 m (Round answer as needed.)

Answer:

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Answer:

600.6 m/s^2

Explanation:

α = 155 rad/s^2

ω = 20 rad/s

r = 1.4 m

Tangential acceleration, aT = r x α = 1.4 x 155 = 217 m/s^2

Centripetal acceleration, ac = rω^2 = 1.4 x 20 x 20 = 560 m/s^2

The tangential acceleration and the centripetal acceleration both are perpendicular to each other. Let a be the resultant acceleration.

a^2 = aT^2 + ac^2

a^2 = 217^2 + 560^2

a = 600.6 m/s^2

The total acceleration of the top of the racket during the tennis serve is approximately 580 m/s². This is determined by considering both the centripetal and tangential accelerations as perpendicular components and using the Pythagorean theorem for calculations.

In this physics problem, we're given the angular acceleration, angular speed, and the distance between the top of the racket and shoulder (radius) to determine the total acceleration of the racket top during a tennis serve. To find the total acceleration, we must take into account both the centripetal (or radial) acceleration and the tangential acceleration (due to the change in speed).

First, let's calculate the centripetal acceleration, given by the formula ac=ω²r, where ω is the angular speed and r is the radius of the motion (in this case, the length of the arm). So, ac = (20.0 rad/s)² x 1.4m = 560 rad/s².

The tangential acceleration (at) is simply equal to the angular acceleration, which is 155 rad/s² (as provided in the question).

To find the total acceleration, we consider these two accelerations as perpendicular components and use the Pythagorean theorem: a = sqrt(ac² + at²). Substituting the values, we get a = sqrt((560 m/s²)² + (155 m/s²)²) ≈ 580 m/s².

Therefore, the total acceleration of the top of the racket is approximately 580 m/s².

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Explanation:

It is given that,

Mass of golf club, m₁ = 210 g = 0.21 kg

Initial velocity of golf club, u₁ = 56 m/s

Mass of another golf ball which is at rest, m₂ = 46 g = 0.046 kg

After the collision, the club head travels (in the same direction) at 42 m/s. We need to find the speed of the golf ball just after impact. Let it is v.

Initial momentum of golf ball, [tex]p_i=m_1u_1=0.21\ kg\times 56\ m/s=11.76\ kg-m/s[/tex]

After the collision, final momentum [tex]p_f=0.21\ kg\times 42\ m/s+0.046v[/tex]

Using the conservation of momentum as :

[tex]p_i=p_f[/tex]

[tex]11.76\ kg-m/s=0.21\ kg\times 42\ m/s+0.046v[/tex]

v = 63.91 m/s

So, the speed of the  golf ball just after impact is 63.91 m/s. Hence, this is the required solution.

Answer:

[tex]l=222.803mm[/tex]

Explanation:

Given:

Elastic modulus, E = 102 GPa

Diameter, d  = 3.8mm = 0.0038 m

Applied tensile load = 2440N

Maximum allowable elongation, = 0.47mm = 0.00047

Now,

The cross-sectional area of the specimen,[tex]A_o=\frac{\pi d^2}{4}[/tex]

substituting the values in the above equation we get

[tex]A_o=\frac{\pi 0.0038^2}{4}[/tex]

or

[tex]A_o=1.134\times 10^{-5}[/tex]

now

the stress (σ) is given as:

[tex]\sigma=\frac{Force}{Area}[/tex]

and[tex]E=\frac{\sigma}{\epsilon}[/tex]

where,

[tex]\epsilon =\ Strain[/tex]

also,

[tex]\epsilon=\frac{\Delta l}{l}[/tex]

where,

[tex]l=initial \ length[/tex]

thus,

[tex]E=\frac{\frac{F}{A_o}}{\frac{\Delta l}{l}}[/tex]

or on rearranging we get,

[tex]l=\frac{E\times \Delta l\times A}{F}[/tex]

substituting the values in the above equation we get

[tex]l=\frac{102\times 10^9\times 0.00047\times 1.134\times 10^{-5}}{2440}[/tex]

or

[tex]l=0.222803m[/tex]

or

[tex]l=222.803mm[/tex]

Answer:

[tex]L(y)=12\times 10^{5}(y-0.325)^2[/tex]

Explanation:

We know that Taguchi loss function given as

[tex]L(y)=k(y-m)^2[/tex]

Where L is the loss when quality will deviate from target(m) ,y is the performance characteristics and k is the quality loss coefficient.

Given that 0.325±0.010 ,Here over target is m=0.325 .

When y=0.335 then L=$120,or when y=0.315 then L=$120.

Now to find value of k we will use above condition

[tex]L(y)=k(y-m)^2[/tex]

[tex]120=k(0.335-0.325)^2[/tex]

[tex]k=12\times 10^{5}[/tex]

So Taguchi loss function given as

[tex]L(y)=12\times 10^{5}(y-0.325)^2[/tex]

Answer:

Explanation:

Manufacturing specification

0.325 ± 0.010 I'm

The quality characteristic is 0.325

Functional tolerance is $120

The lost function is given

λ = C (x—t)²

Where, C is a constant

t is quality characteristic

And x is target value

Constant’ is the coefficient of the Taguchi Loss, or the ratio of functional tolerance and customer loss.

Then, C= tolerance / loss²

Measurement loss is

Loss = 0.335-0.315

Loss =0.01cm

Therefore,

C = 120/0.01²

C = 1,200,000

λ = C (x —t)²

λ = 1,200,00 (x—0.325)²

Answer:

Distance from the center of wire is 0.05 meters.

Explanation:

It is given that,

Current flowing in the wire, I = 2 A

Magnetic field, [tex]B=8\ \mu T=8\times 10^{-6}\ T[/tex]

Let d is the distance from the center of the wire. The magnetic field at a distance d from the wire is given by :

[tex]B=\dfrac{\mu_oI}{2\pi d}[/tex]

[tex]d=\dfrac{\mu_oI}{2\pi B}[/tex]

[tex]d=\dfrac{4\pi \times 10^{-7}\times 2\ A}{2\pi \times 8\times 10^{-6}\ T}[/tex]

d = 0.05 meters

So, the distance from the wire is 0.05 meters. Hence, this is the required solution.

To find the distance from the wire to point P where the magnetic field is 8 μT due to a 2-A current, the formula B = μ₀I/(2πR) is used, and the calculation reveals that R = 0.1 mm.

To, calculating the distance from the center of the wire to a point P where the magnetic field due to a 2-A current flowing in a long, straight wire is 8 μT.

To find this distance, we use the formula for the magnetic field around a long straight wire, given by B = μ₀I/(2πR), where B is the magnetic field strength, μ₀ is the permeability of free space (4π x 10⁻⁷ Tm/A), I is the current, and R is the distance from the wire.

Plugging the given values into this equation, we get:

8 x 10⁻⁶ T = (4π x 10⁻⁷ Tm/A)(2A) / (2πR)

Simplifying, we find that R = (4π x 10⁻⁷ Tm/A)(2A) / (2π x 8 x 10⁻⁶ T) = 0.0001 m or 0.1 mm.

(a) [tex]-3.5 m/s^2[/tex]

The car's acceleration is given by

[tex]a=\frac{v-u}{t}[/tex]

where

v = 0 is the final velocity

u = 14 m/s is the initial velocity

t = 4 s is the time elapsed

Substituting,

[tex]a=\frac{0-14}{4}=-3.5 m/s^2[/tex]

where the negative sign means the car is slowing down.

(b) 5.7 s

We can use again the same equation

[tex]a=\frac{v-u}{t}[/tex]

where in this case we have

[tex]a=-3.5 m/s^2[/tex] is again the acceleration of the car

v = 0 is the final velocity

u = 20 m/s is the initial velocity

Re-arranging the equation and solving for t, we find the time the car takes to come to a stop:

[tex]t=\frac{v-u}{a}=\frac{0-20}{-3.5}=5.7 s[/tex]

(c) [tex]2.9 s[/tex]

As before, we can use the equation

[tex]a=\frac{v-u}{t}[/tex]

Here we have

[tex]a=-3.5 m/s^2[/tex] is again the acceleration of the car

v = 10 is the final velocity

u = 20 m/s is the initial velocity

Re-arranging the equation and solving for t, we find

[tex]t=\frac{v-u}{a}=\frac{10-20}{-3.5}=2.9 s[/tex]

(1) The acceleration of the car will be [tex]a=-3.5\frac{m}{s^2}[/tex]

(2) The time taken [tex]t=5.7s[/tex]

(3)  The time is taken by the car  to slow down from 20m/s to 10m/s [tex]t=2.9s[/tex]

(1) The acceleration of the car will be calculated as

[tex]a=\dfrac{v-u}{t}[/tex]

Here

u= 14 [tex]\frac{m}{s}[/tex]

[tex]a=\dfrac{0-14}{4} =-3.5\dfrac{m}{s^2}[/tex]

(2) The time is taken for the same acceleration to 20[tex]\frac{m}{s}[/tex]

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]t=\dfrac{v-u}{a}[/tex]

u=20[tex]\frac{m}{s}[/tex]

[tex]t=\dfrac{0-20}{-3.5} =5.7s[/tex]

(3) The time is taken to slow down from 20m/s to 10m/s with the same acceleration

From same formula

[tex]t=\dfrac{v-u}{a}[/tex]

v=10[tex]\frac{m}{s}[/tex]

u=20[tex]\frac{m}{s}[/tex]

[tex]t=\dfrac{10-20}{-3.5} =2.9s[/tex]

Thus

(1) The acceleration of the car will be [tex]a=-3.5\frac{m}{s^2}[/tex]

(2) The time taken [tex]t=5.7s[/tex]

(3)  The time is taken by the car  to slow down from 20m/s to 10m/s [tex]t=2.9s[/tex]

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Answer:

The speed is [tex]7.07\times10^{4}\ m/s[/tex]

Explanation:

Given that,

Speed of proton [tex]v= 10^{5}\ m/s[/tex]

Final potential = 10 v

Initial potential = 5 V

We need to calculate the speed

Using formula of energy

[tex]\dfrac{1}{2}mv^2=eV[/tex]

[tex]v^2=\dfrac{2eV}{m}[/tex]

The speed of the particle is directly proportional to the potential.

[tex]v^2\propto V[/tex]

Put the value into the formula

[tex](10^{5})\propto 10[/tex]....(I)

For 5 V,

[tex]v^2\propto 5[/tex].....(II)

From equation (I) and (II)

[tex]\dfrac{(10^{5})^2}{v^2}=\dfrac{10}{5}[/tex]

[tex]v=70710.67\ m/s[/tex]

[tex]v=7.07\times10^{4}\ m/s[/tex]

Hence, The speed is [tex]7.07\times10^{4}\ m/s[/tex]

The speed of the proton in the second place is 74.3 m/s.

To calculate the speed of the proton in the second place, first, we need to find the mass of the proton.

Using,

Where:

Make m the subject of the equation

Given:

Substitute these values into equation 2

Finally, to calculate the speed in the second place, we make v the subject of equation 1

Given:

Substitute these values into equation 3

Hence, The speed of the proton in second place is 74.3 m/s.

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The mass of a sphere of gold with a radius of 12.5 cm is 1.5789752 x 10^5 g in scientific notation. A cube of platinum with an edge length of 0.049 mm has a mass of 2.517269 x 10^-3 g. The mass of 67.1 mL of ethanol with a density of 0.798 g/mL is 53.5458 g.

To calculate the mass of a sphere of gold with a radius of 12.5 cm using the density formula (density = mass/volume), first we need to find the volume of the sphere using the formula V = (4/3)πr^3. Then we can multiply the volume by the density of gold, which is 19.3 g/cm^3.

(a) Volume of gold sphere = (4/3)π(12.5 cm)^3 = 8,181.229 cm^3
Mass of gold sphere = volume × density = 8,181.229 cm^3 × 19.3 g/cm^3 = 157,897.52 g
The mass in scientific notation is 1.5789752 × 105 g.

(b) Volume of platinum cube = edge^3 = (0.049 cm)^3 = 1.17649 × 10^-4 cm^3
Mass of platinum cube = volume × density
= 1.17649 × 10^-4 cm^3 × 21.4 g/cm^3 = 2.517269 × 10^-3 g

(c) Mass of ethanol = volume × density
= 67.1 mL × 0.798 g/mL = 53.5458 g