A pendulum string with the length of 105 cm has the 325 g bob attached to it. At the lowest point of the swing the pendulum bob moves with the speed of 2.15 m/s. Determine: a) the centripetal acceleration of the pendulum bob at this point; b) the force of tension in the string at this point; c) the kinetic energy of the pendulum bob at this point;

Answer:

2.86J

Explanation:

M = 3.0kg

R₁ = 1.0m

R₂ = 0.3m

I₁ = I(mass) + I(student + stool)

I₁ = 2mr₁² + I(student + stool)

I₁ = 2*(3*1²) + 3.0

I₁ = 9.0kgm²

the initial moment of inertia of the system = 9.0kgm²

I₂ = 2mr₂² + I(student + stool)

I₂ = 2*(3 * 0.3²) + 3.0

I₂ = 0.54 + 3.0

I₂ = 3.54kgm²

the final moment of inertia of the system is 3.54kgm²

From conservation of angular momentum

I₁ω₁ = I₂ω₂

ω₂ = (I₁ * ω₁) / I₂

ω₂ = (0.75 * 9) / 3.54

ω₂ = 1.09rad/s

kinetic energy of rotation (k.e) =½ Iω²

K.E = (K.E)₂ - (K.E)₁

k.e = [½ * 3.54 * (1.90)²] - [½ * 9.0 * 0.75²]

K.E = 6.3897 - 2.53125

K.E = 2.85845

K.E = 2.86J

The image is missing, so i have attached it;

Answer:

A) V_rel = [-(2.711)i - (0.2588)j] m/s

B) a_rel = (0.8637i + 0.0642j) m/s²

Explanation:

We are given;

the cruise ship velocity; V_b = 1 m/s

Angular velocity; ω = 1 deg/s = 1° × π/180 rad = 0.01745 rad/s

Angular acceleration;α = -0.5 deg/s² = 0.5 x π/180 rad = -0.008727 rad/s²

Now, let's write Velocity (V_a) at A in terms of the velocity at B(V_b) with r_ba being the position vector from B to A and relative velocity (V_rel)

Thus,

V_a = V_b + (ω•r_ba) + V_rel

Now, V_a = 0. Thus;

0 = V_b + (ω•r_ba) + V_rel

V_rel = -V_b - (ω•r_ba)

From the image and plugging in relevant values, we have;

V_rel = -1[(cos15)i + (sin15)j] - (0.01745k * -100j)

V_rel = - (cos15)i - (sin15)j - 1.745i

Note that; k x j = - i

V_rel = [-(2.711)i - (0.2588)j] m/s

B) Let's write the acceleration at A with respect to B in terms of a_b.

Thus,

a_a = a_b + (α*r_ba) + (ω(ω•r_ba)) + (2ω*v_rel) + a_rel

a_a and a_b = 0.

Thus;

0 = (α*r_ba) + (ω(ω•r_ba)) + (2ω*v_rel) + a_rel

a_rel = - (α*r_ba) - (ω(ω•r_ba)) - (2ω*v_rel)

Plugging in the relevant values with their respective position vectors, we have;

a_rel = - (-0.008727k * -100j) - (0.01745k(0.01745k * -100j)) - (2*0.01745k * [-(2.711)i - (0.2588)j])

a_rel = 0.8727i - (0.01745² x 100)j + 0.0946j - 0.009i

Note that; k x j = - i and k x i = j

Thus,simplifying further ;

a_rel = 0.8637i + 0.0642j m/s²

Final answer:

From the ship's frame of reference, person A has a velocity of -1 m/s (opposite to the ship's motion). The acceleration observed would be the negative ship's angular deceleration converted to linear acceleration, needing more data for calculation.

Explanation:

The problem presents a rotational kinematics and relative motion scenario common in physics. Person A is stationary on the dock while the ship moves with velocity vB = 1 m/s and has an angular velocity of ω = 1 deg/s, decreasing at 0.5 deg/s2. From the ship's reference frame, the velocity of person A will appear as the opposite of the ship's velocity, which is -1 m/s. However, since person A is stationary, A's acceleration as observed from the ship would be the opposite of the ship's angular deceleration translated into linear acceleration at the radius person A is perceived to be from the ship's center of rotation, which requires further information to calculate.

The electric force between charges can be determined using Coulomb's law. Positive-positive and negative-negative combinations have repulsive forces, while positive-negative combinations have attractive forces. Neutral charges do not exert any force.

The electric force between two charges can be determined using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Using this information, we can rank the six combinations of electric charges based on the electric force acting on q1:

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Answer:

The direction is due south

Explanation:

From the question we are told that

     The energy of the electron is [tex]E = 19.0keV = 19.0 *10^3 eV[/tex]

      The earths magnetic field is [tex]B = 42.3 \muT = 42.3 *10^{-6} T[/tex]

Generally the force on the electron is perpendicular to the velocity of the elecrton and the magnetic field and this is mathematically reresented as

          [tex]\= F = q (\= v * \=B)[/tex]

On the first uploaded image is an  illustration of the movement of the electron

    Looking at the diagram  we can see that in terms of direction  the magnetic force  is

             [tex]\= F =q(\=v * \= B)= -( -\r i * - \r k)[/tex]

                [tex]= -(- (\r i * \r k))[/tex]

generally  i cross k = -j

      so the equation above becomes

             [tex]\= F = -(-(- \r j))[/tex]

                [tex]= - \r j[/tex]

This show that the direction is towards the south  

Answer:

Frequencies are 0.86Hz

Explanation:

Given v=0.74m/s

d= 0.43m

Lambda/2=0.43m

Thus lambda= 0.86m

And F= v/lambda

0.74/0.86= 0.86Hz

Answer:

The obsrved  frquencies are [tex]f= n (0.86) Hz[/tex] n = 1,2,3,...,n.

Explanation:

   From the question we are told that

        The speed of the wave is v = 0.740 m/s

         The distance from the post is [tex]d = 43.0cm = \frac{43}{10} = 0.43m[/tex]

Generally frequency is mathematically represented as

           [tex]f = \frac{v}{\lambda }[/tex]

so for the first frequency which the the fundamental frequency(first harmonic frequency)  the clothesline(string) would form only one loop and hence the length between the  vertical post and throcky hands is mathematically represented as

        [tex]L = \frac{\lambda}{2}[/tex]

=>    [tex]\lambda = 2L[/tex]

    So

             [tex]f_f =f_1= \frac{v}{2L}[/tex]

       Substituting values

              [tex]f_f = f_1 = \frac{0.740}{2* 0.43}[/tex]

                  [tex]= 0.860 Hz[/tex]

For the second  harmonic frequency  i.e is when the clothesline(string) forms two loops the length is mathematically represented as

        [tex]L = \lambda[/tex]

So the second harmonic frequency is            

           [tex]f_2 = \frac{v}{L}[/tex]

        [tex]f_2 = 2 * \frac{v}{2L}[/tex]

                [tex]f_2 =\frac{0.740}{0.430}[/tex]

                    [tex]= 1.72Hz[/tex]

For the third harmonic frequency i.e  when the clothesline(string) forms three loops the length  is mathematically represented as

                  [tex]L = 3 * \frac{\lambda }{2}[/tex]

So the wavelength is

               [tex]\lambda = \frac{2L}{3}[/tex]

And the third harmonic frequency is mathematically evaluated as

           [tex]f_3 = \frac{v}{\frac{2L}{3} }[/tex]

               [tex]= 3 * \frac{v}{2L}[/tex]

               [tex]f_3=2.58Hz[/tex]

Looking at the above calculation we can conclude that the harmonic frequency of a vibrating string(clothesline) can be mathematically represented as an integer multiple of the fundamental frequency

  i.e

          [tex]f = n f_f[/tex]

         [tex]f = n \frac{v}{2L}[/tex]

           [tex]f= n (0.86) Hz[/tex]

Where n denotes integer values  i.e  n = 1,2,3,....,n.

Note : The length that exist between two nodes which are successive is equivalent to half of the wavelength so when one loop is form the number of nodes would be 2 and on anti-node

Answer: 2000 J.

Explanation: Since work is force*displacement, we just have to multiply the force by the distance: w = f*d = 400 N*5.0 m = 2000 J.

After collision, truck remains at 14.0 m/s, car stops (0 m/s) due to elastic collision.

To find the velocities of both vehicles after the collision, we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

The momentum [tex]\( p \) of an object is given by its mass \( m \) multiplied by its velocity \( v \)[/tex]:

[tex]\[ p = mv \][/tex]

Before the collision, the total momentum is the sum of the momentum of the truck and the momentum of the car. After the collision, the total momentum remains the same.

Let [tex]\( v_t \) be the velocity of the truck after the collision, and \( v_c \)[/tex] be the velocity of the car after the collision.

Before the collision:

[tex]\[ \text{Total momentum} = \text{momentum of truck} + \text{momentum of car} \][/tex]

[tex]\[ (1400 \, \text{kg}) \times (14.0 \, \text{m/s}) + (641 \, \text{kg}) \times (0 \, \text{m/s}) = (1400 \, \text{kg}) \times (v_t) + (641 \, \text{kg}) \times (v_c) \][/tex]

[tex]\[ 1400 \times 14.0 = 1400v_t + 641v_c \][/tex]

[tex]\[ 19600 = 1400v_t + 641v_c \][/tex]

Since the collision is approximately elastic, we also have the condition that the relative velocity of approach equals the relative velocity of separation.

[tex]\[ v_t - v_c = 14.0 \, \text{m/s} \][/tex]

We now have a system of two equations:

[tex]\[ 19600 = 1400v_t + 641v_c \][/tex]

[tex]\[ v_t - v_c = 14.0 \][/tex]

We can solve this system of equations to find the values of [tex]\( v_t \)[/tex] and [tex]\( v_c \)[/tex].

[tex]\[ v_t = \frac{19600 - 641v_c}{1400} \][/tex]

Substitute this expression for [tex]\( v_t \)[/tex] into the second equation:

[tex]\[ \frac{19600 - 641v_c}{1400} - v_c = 14.0 \][/tex]

Multiply both sides by 1400 to eliminate the denominator:

[tex]\[ 19600 - 641v_c - 1400v_c = 14.0 \times 1400 \][/tex]

[tex]\[ 19600 - 2041v_c = 19600 \][/tex]

Now, isolate [tex]\( v_c \)[/tex] :

[tex]\[ -2041v_c = 0 \][/tex]

[tex]\[ v_c = 0 \][/tex]

Substitute [tex]\( v_c = 0 \)[/tex] into [tex]\( v_t = \frac{19600 - 641v_c}{1400} \)[/tex] :

[tex]\[ v_t = \frac{19600 - 641 \times 0}{1400} \][/tex]

[tex]\[ v_t = \frac{19600}{1400} \][/tex]

[tex]\[ v_t = 14.0 \, \text{m/s} \][/tex]

So, after the collision, the truck's speed remains 14.0 m/s, and the car's speed becomes 0 m/s.

The speed of the truck and car after the collision is approximately 9.47 m/s

Use the principle of conservation of momentum to solve this problem. The total momentum before the collision is equal to the total momentum after the collision. We can express this as:

[tex]$$ m_{\text{truck}} \cdot v_{\text{truck, initial}} + m_{\text{car}} \cdot v_{\text{car, initial}} = (m_{\text{truck}} + m_{\text{car}}) \cdot v_{\text{final}} $$[/tex]

Given the following information:

- Mass of the truck, [tex]\(m_{\text{truck}}\)[/tex]: 1400 kg

- Initial velocity of the truck, [tex]\(v_{\text{truck, initial}}\)[/tex]: 14.0 m/s

- Mass of the car, [tex]\(m_{\text{car}}\):[/tex] 641 kg

- Initial velocity of the car, [tex]\(v_{\text{car, initial}}\)[/tex]: 0 m/s (since the car is stopped)

We can solve for the final velocity, [tex]\(v_{\text{final}}\):[/tex]

[tex]$$ 1400 \cdot 14.0 + 641 \cdot 0 = (1400 + 641) \cdot v_{\text{final}} $$[/tex]

Solving for [tex]\(v_{\text{final}}\):[/tex]

[tex]$$ v_{\text{final}} = \frac{1400 \cdot 14.0}{1400 + 641} $$[/tex]

Calculating the value:

[tex]$$ v_{\text{final}} \approx 9.47 \, \text{m/s} $$[/tex]

Therefore, the speed of the truck and car after the collision is approximately 9.47 m/s.

Answer:

The spaceship is placed at a distance of [tex]1.28\times 10^6\[/tex] meters from the Earth.

Explanation:

Distance between two astronauts, d = 1.4 m  

The time it takes for sound waves to travel at 328 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth.

For sound, time taken is given by :

[tex]t=\dfrac{1.4}{328}\ ........(1)[/tex]

For electromagnetic wave, time taken to travel the Earth is :

[tex]t=\dfrac{d}{3\times 10^8}\ ........(2)[/tex]

d is the distance from the Earth to the spaceship.

As time are same :

[tex]\dfrac{d}{3\times 10^8}=\dfrac{1.4}{328}[/tex]

[tex]d=\dfrac{1.4}{328}\times 3\times 10^8\\\\d=1.28\times 10^6\ m[/tex]

So, the spaceship is placed at a distance of [tex]1.28\times 10^6[/tex] meters from the Earth.

Answer:

The angular velocity of A equals that of B.

Explanation:

Since both coins are on the same turn table that is rotating with a given angular velocity about a particular axis, then the angular velocity of coin A will be equal to the angular velocity of coin B about that same axis.

Answer:

by sweating

Explanation:

The moment of inertia of the solid cylinder can be found by calculating the torque and the angular acceleration of the cylinder, and then relating these quantities using the equation torque equals moment of inertia times angular acceleration.

The moment of inertia of the solid cylinder can be found using the relationship between torque acting on the cylinder and its angular acceleration, both of which can be inferred from the given information. The torque τ on the cylinder is given by the product of the force applied and the radius of the cylinder, τ = Fr. Since this force is causing the cylinder to undergo rotational motion, it is also causing an angular acceleration α, which can be calculated from the slope of plot relating angular displacement θ and time t squared, as α is directly proportional to slope of θ vs t² plot.

By relating these variables using the equation τ = Iα, where I is the moment of inertia, we can solve for I as: I = τ/α = Fr/α. By substituting given values, we can compute specific value for moment of inertia.

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Answer:

A. 2.57 K

Explanation:

From specific heat capacity,

Q = cmΔT........................ Equation 1

Where Q = Amount of heat that entered into silver, m = mass of silver, c = specific heat capacity of silver, ΔT = change in temperature of the silver.

make ΔT the subject of the equation

ΔT = Q/cm................... Equation 2

Given: Q = 300 J, m = 500 g = 0.5 kg

Constant: c = 233 J/kg.K

Substitute into equation 2

ΔT = 300/(0.5×233)

ΔT  = 300/116.5

ΔT = 2.57 K

Hence the right option is A. 2.57 K

The change in the temperature of the silver should be considered as the 2.57 K.

From specific heat capacity,

Q = cmΔT........................ Equation 1

Here

Q = Amount of heat that entered into silver,

m = mass of silver,

c = specific heat capacity of silver,

ΔT = change in temperature of the silver.

Now

ΔT = Q/cm................... Equation 2

Since

Q = 300 J, m = 500 g = 0.5 kg

Constant: c = 233 J/kg.K

So,

ΔT = 300/(0.5×233)

ΔT  = 300/116.5

ΔT = 2.57 K

hence, The change in the temperature of the silver should be considered as the 2.57 K.

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Complete question is:

Two uniform solid spheres have the same mass of 1.65 kg, but one has a radius of 0.206 m and the other has a radius of 0.804 m. Each can rotate about an axis through its center. (a) What is the magnitude τ of the torque required to bring the smaller sphere from rest to an angular speed of 367 rad/s in 14.5 s? (b) What is the magnitude F of the force that must be applied tangentially at the sphere’s equator to give that torque? What are the corresponding values of (c) τ and (d) F for the larger sphere?

Answer:

A) τ = 0.709 N.m

B) F = 3.44 N

C) τ = 10.8 N.m

D) F = 13.43N

Explanation:

We are given;

Mass if each sphere = 1.65kg

Radius of the first sphere; r1 = 0.206m

Radius of second sphere; r2 = 0.804m

A) initial angular speed of smaller sphere; ω_i = 0 rad/s

Final angular speed of smaller sphere; ω_f = 367 rad/s

Time;t = 14.5 s

The constant angular acceleration is calculated from;

ω_f = ω_i + αt

367 = 0 + α(14.5)

Thus,

α = 367/14.5 = 25.31 rad/s²

The torque is given by the formula;

τ = Iα

Where τ is torque ; I is moment of inertia given as (2/5)Mr²

α is angular acceleration

Thus;

τ = (2/5)(1.65)(0.206)² x 25.31

τ = 0.709 N.m

B) The magnitude of the force that must be applied to give the torque τ is gotten from the formula;

τ = F•r•sin90°

0.709 = F x 0.206 x 1

F = 0.709/0.206

F = 3.44 N

C) Now for the larger sphere, we'll repeat the same procedure in a above. Thus;

The torque is given by the formula;

τ = Iα

Where τ is torque ; I is moment of inertia given as (2/5)Mr²

α is angular acceleration

Thus;

τ = (2/5)(1.65)(0.804)² x 25.31

τ = 10.8 N.m

D) Now for the larger sphere, we'll repeat the same procedure in b above. Thus, τ is gotten from the formula;

τ = F•r•sin90°

10.8 = F x 0.804 x 1

F = 10.8/0.804

F = 13.43N

Answer:

Statement 3 is correct.

Heisenberg's uncertainty principle explains that the measurement of an observable quantity in the quantum domain inherently changes the value of that quantity

Explanation:

Classical mechanics is the study of motion of big, relatable bodies that we come in contact with in our day to day lives.

Quantum mechanics refers to this same study, but for particles on a subatomic level.

Obviously, Classical mechanics' theories and principles were first discovered and they worked for their intended uses (still work!). But when studies on particles on a sub-atomic level intensified, it became impractical to apply those theories and principles to these sub-atomic particles that displayed wave-particle duality nature properly.

Heisenberg's Uncertainty principle came in a time that explanations and justifications were needed to adapt these theories to sub-atomic particles.

The principle explains properly that it is impossible to measure the position and velocity (momentum) of a sub-atomic particle in exact terms and at the same time.

Mathematically, it is presented as

Δx.Δp ≥ ℏ

Where ℏ= adjusted Planck's constant.

ℏ= (h/2π)

And Δx and Δp are the uncertainties in measuring the position and momentum of sub-atomic particles.

The major reason for this is the wave-particle duality of sub-atomic particles. They exist as waves and particles at the same time that a complete knowledge of their position mean that a complete ignorance of their velocity and vice versa.

Taking the statements one at a time

Statement 1

Quantum Mechanics studies sub-atomic particles which are mostly always in motion. So, this is false.

Statement 2

It is impossible to calculate with accuracy both the position and momentum of particles in quantum mechanics not classical mechanics. As stated above, the reason for the uncertainty is the wave-particle duality of sub-atomic particles which the particle in classical mechanics do not exhibit obviously enough.

Statement 3

Any attempt to measure precisely the velocity of a subatomic particle, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity.

An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it. This is basically the uncertainty principle rephrased. This is the only true statement.

Hope this Helps!!!

Answer:

He can return to the spacecraft by sacrificing some of the tools employing the principle of conservation of momentum.

Explanation:

By carefully evaluating his direction back to the ship, the astronaut can throw some of his tools in the opposite direction to that. On throwing those tools of a certain mass, they travel at a certain velocity giving him velocity in the form of recoil in the opposite direction of the velocity of the tools. This is same as a gun and bullet recoil momentum conservation. It is also the principle on which the operational principles of their maneuvering unit is designed.

An astronaut stranded far from their spacecraft can return by using the principle of Newton's third law of motion. By throwing tools in the opposite direction of the spacecraft, the astronaut can create a reaction force that propels them back to the spacecraft.

In this scenario, the astronaut working with many tools some distance away from their spacecraft can use the concept of Newton's third law of motion, also known as action-reaction principle, to return to the spacecraft. According to this law, for every action, there is an equal and opposite reaction. So, the astronaut can return to the spacecraft by sacrificing some of the tools that they are carrying, and throwing the tools in the opposite direction of the spacecraft. When the tools are thrown away, the reaction force will propel the astronaut towards the spacecraft. This is a effective method of maneuvering in space because in the vacuum of space, even small forces can have a significant impact due to the absence of air resistance or friction. This way, the astronaut can cleverly convert a threat into an opportunity and solve their problem with minimal risks.

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To solve the problem we will apply the concepts related to the Intensity as a function of the power and the area, as well as the electric field as a function of the current, the speed of light and the permeability in free space, as shown below.

The intensity of the wave at the receiver is

[tex]I = \frac{P_{avg}}{A}[/tex]

[tex]I = \frac{P_{avg}}{4\pi r^2}[/tex]

[tex]I = \frac{3.4*10^3}{4\pi(4*1609.34)^2} \rightarrow 1mile = 1609.3m[/tex]

[tex]I = 6.529*10^{-6}W/m^2[/tex]

The amplitude of electric field at the receiver is

[tex]I = \frac{E_{max}^2}{2\mu_0 c}[/tex]

[tex]E_{max}= \sqrt{2I\mu_0 c}[/tex]

The amplitude of induced emf by this signal between the ends of the receiving antenna is

[tex]\epsilon_{max} = E_{max} d[/tex]

[tex]\epsilon_{max} = \sqrt{2I \mu_0 cd}[/tex]

Here,

I = Current

[tex]\mu_0[/tex] = Permeability at free space

c = Light speed

d = Distance

Replacing,

[tex]\epsilon_{max} = \sqrt{2(6.529*10^{-6})(4\pi*10^{-7})(3*10^{8})(60.0*10^{-2})}[/tex]

[tex]\epsilon_{max} = 0.05434V[/tex]

Thus, the amplitude of induced emf by this signal between the ends of the receiving antenna is 0.0543V

Answer:

b. 0.25cm

Explanation:

You can solve this question by using the formula for the position of the fringes:

[tex]y=\frac{m\lambda D}{d}[/tex]

m: order of the fringes

lambda: wavelength 500nm

D: distance to the screen 5 m

d: separation of the slits 1mm=1*10^{-3}m

With the formula you can calculate the separation of two adjacent slits:

[tex]\Delta y=\frac{(m+1)(\lambda D)}{d}-\frac{m\lambda D }{d}=\frac{\lambda D}{d}\\\\\Delta y=\frac{(500*10^{-9}nm)(5m)}{1*10^{-3}m}=2.5*10^{-3}m=0.25cm[/tex]

hence, the aswer is 0.25cm

The pressure difference (∆P) would be the atmospheric pressure in the room (1.01 x 10⁵ Pa) minus the pressure inside the container (0.41 x 10⁵ Pa).

To calculate the minimum upward applied force required to lift the lid of a partially evacuated vertical cylindrical container, you would need to know two additional quantities: the radius of the lid, and consequently the surface area of the lid.

The force required to lift the lid can be calculated using the equation F = P x A, where F is the force, P is the difference in pressure (external minus internal), and A is the surface area of the lid. Recall that the area of the circular lid would be calculated using the formula A = πr², where r is the radius of the circular lid.

In this case, the pressure difference (∆P) would be the atmospheric pressure in the room (1.01 x 10⁵ Pa) minus the pressure inside the container (0.41 x 10⁵ Pa).

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Answer:

The maximun distance is  [tex]z_1 = z_2 = 0.0138m[/tex]

Explanation:

    From the question we are told that

       The wavelength are  [tex]\lambda _ 1 = 540nm (green) = 540 *10^{-9}m[/tex]

                                           [tex]\lambda_2 = 450nm(blue) = 450 *10^{-9}m[/tex]

        The distance of seperation of the two slit is [tex]d = 0.180mm = 0.180 *10^{-3}m[/tex]

        The distance from the screen is [tex]D = 1.53m[/tex]

Generally the distance of the bright fringe to the center of the screen is mathematically represented as

           [tex]z = \frac{m \lambda D}{d}[/tex]

   Where m is  the order of the fringe

For the first wavelength  we have

        [tex]z_1 = \frac{m_1 (549 *10^{-9} * (1.53))}{0.180*10^{-3}}[/tex]

             [tex]z_1=0.00459m_1 m[/tex]

                 [tex]z_1= 4.6*10^{-3}m_1 m ----(1)[/tex]

For the second  wavelength  we have              

        [tex]z_2 = m_2 \frac{450*10^{-9} * 1.53 }{0.180*10^{-3}}[/tex]

        [tex]z_2 = 0.003825m_2[/tex]

        [tex]z_2 = 3.825 *10^{-3} m_2 m[/tex]  ----(2)

From the question we are told that the two sides coincides with one another so

            [tex]zy_1 =z_2[/tex]

         [tex]4.6*10^{-3}m_1 m = 3.825 *10^{-3} m_2 m[/tex]

          [tex]\frac{m_1}{m_2} = \frac{3.825 *10^{-3}}{4.6*10^{-3}}[/tex]

Hence for this equation to be solved

       [tex]m_1 = 3[/tex]

and  [tex]m_2 = 4[/tex]

Substituting this into the  equation

                      [tex]z_1 = z_2 = 3 * 4.6*10^{-3} = 4* 3.825*10^{-3}[/tex]

      Hence [tex]z_1 = z_2 = 0.0138m[/tex]

The minimum distance from the center of the screen where green and blue bright fringes coincide is calculated using principles of double-slit interference. Applying these principles and trigonometry, we find the minimum distance from the center of the screen to this point.

To find the minimum distance from the center of the screen to a point where a bright fringe of the green light coincides with a bright fringe of the blue light, we can use the formula for double slit interference:

d sin θ = mλ

where d is the separation of the slits, θ is the angle from the central bright fringe, m is the order of fringe, and λ is the wavelength of light.

For the green and blue lights to interfere constructively on the screen for the first time, their path length difference must be equal to their respective wavelengths. Therefore, the order of fringe for the green light will be different from the blue light. The minimum distance can be found when the fringe order for the green light (m1) is 1 and for the blue light (m2) is, by proportion of the wavelengths, rounded to the nearest whole number. Solving the equation for each colour and setting them equal will give the minimum distance.

Finally, the distance from the center to the fringe can be calculated using the trigonometric relationship:

L tan θ, where L is the distance from the slits to the screen.

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Answer:

Explanation:

DetaM=4 x 1.02875 - 4.002603

DetaM= 0.028697u

Using E= mc²

= 0.028697 x 1.49x*10^-10

= 4.2x10^-12J

Answer:

Using larger pieces of solids

Using larger pieces of solid the dissolving rate of a solid in water can be decreased. Therefore, the correct option is option C.

A solution is indeed a specific kind of homogenous combination made up of two or even more components that is used in chemistry. A solute is a material that has been dissolved in a solvent, which is the other substance in the combination.

The solvent particles will pull the solute particles apart surround them if the attractive forces here between solute and solvent particles are stronger than the attractive forces keeping the solute particles together. Using larger pieces of solid the dissolving rate of a solid in water can be decreased.

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

Which of the following decreases the dissolving rate of a solid in water?

A. raising the temperature

B. stirring constantly

C. using larger pieces of solid

D. crushing the solid

Answer:

1.7*10^{12}Ucm^-1

Explanation:

The answer to this question is obtained by using the following formula:

[tex]\sigma=nq\mu_e[/tex]

sigma: conductivity

q: charge of the electron = 1.61019*10^{-19}C

mu_e: electron mobility = 8104 m^2/Vs

n: free electron concentration = 1.31029/m^3

By replacing you get:

[tex]\sigma=(1.31*10^{29}/m^3)(1.61*10^{-19}C)(8104 m2/Vs)=1.709*10^{14}\Omega^{-1}m^{-1} \\\\1.709*10^{14}\Omega^{-1} (1*10^{2}cm})^{-1}=1.7*10^{12}\Omega^{-1}cm^{-1}[/tex]

the result obained is not 5.9mU.cm. This is because temperature effects has not taken into account.

this is the sample Answer:    Spring tides occur when the moon is full or new. Earth, the moon, and the Sun are in a line. The moon’s gravity and the Sun’s gravity pull Earth’s crust and ocean water. This causes tides to be higher than normal. At neap tide, the moon and the Sun are at right angles to each other. This happens during the first and third quarters of the lunar cycle. At neap tide, the Sun’s gravity and the moon’s gravity are balanced. High tides are lower; low tides are higher.

Explanation:

just did the assament

Answer:

Spring tides occur when the moon is full or new. Earth, the moon, and the Sun are in a line. The moon’s gravity and the Sun’s gravity pull Earth’s crust and ocean water. This causes tides to be higher than normal.  At neap tide, the moon and the Sun are at right angles to each other. This happens during the first and third quarters of the lunar cycle. At neap tide, the Sun’s gravity and the moon’s gravity are balanced. High tides are lower; low tides are higher.

Explanation:

Just did the quiz.

Answer:

357 mJ

Explanation:

Parameters given:

Number of turns, N = 113

Radius, r = 2.71 cm = 0.0271 m

Resistance connected to coil, R = 10.3 ohms

Time interval, dt = 0.153 s

Change in magnetic field, dB = 0 - 0.441 T = - 0.441 T

First, we need to find the induced EMF in the coil. It is given as:

V = - (N * A * dB)/dt

A = area of coil = pi * r² = 3.142 * 0.0271² = 0.0023 m²

Therefore:

V = - (113 * 0.0023 * - 0.441) / 0.153

V = 0.75 V

Electrical energy dissipated in the resistor is given as:

E = V² / (R * t)

Where t is the time (0.153 secs)

E = (0.75²) / (10.3 * 0.153)

E = 0.357 J = 357 mJ

The energy dissipated in the resistor is 357 mJ

Answer:

C. The maximum speed of emitted electrons increase

D. The stopping potential increases

Explanation:

Albert Einstein provided a successful explanation of the photoelectric effect on the basis of quantum theory. He proposed that,

“An electron either absorbs one whole photon or it absorbs none. After absorbing a photon, an electron either leaves the surface of metal or dissipate its energy within the metal in such a short time interval that it has almost no chance to absorb a second photon. An increase in intensity of light source simply increase the number of photons and thus, the number of electrons, but the energy of electron remains same. However, increase in frequency of light increases the energy of photons and hence, the energy of electrons too.”

Therefore, due to this increase in energy of photons, the kinetic energy of emitted electrons also increase. And the increase in kinetic energy follows with the increase in velocity.

Now, the stopping potential is directly proportional to Kinetic Energy of the electrons. Thus, the increase in Kinetic Energy, results in an increase in stopping potential.

Therefore, two options apply here:

C. The maximum speed of emitted electrons increases

D. The stopping potential increases

If the frequency of the incident light in the photoelectric effect is increased, C. The maximum speed of the emitted electrons increases and D. The stopping potential increases; however, the work function does not change and the number of electrons emitted per second remains the same at a constant light intensity.

For the question about what happens if the frequency of the incident light in the photoelectric effect is increased, the correct options are:

The work function of the metal (Option A) is a material property and does not change with the frequency of the incident light. Therefore, this option is incorrect. The number of electrons emitted from the metal per second (Option B) depends on the intensity of the light, not its frequency, so increasing the frequency at constant intensity does not increase the emission rate. Thus, this option is also incorrect. When the frequency of the incident light is increased, the kinetic energy of the emitted electrons increases (as per Einstein's equation for the photoelectric effect), which correlates with Option C. The stopping potential, which is the electric potential needed to stop the fastest photoelectrons, also increases with the electron's kinetic energy, confirming Option D as correct.

Answer:

The tension that must be applied to this string = 477 N

Explanation:

y(x,t)= 0.0321m sin (2.05x-524t + pi/4)

Comparing this to the general wave equation

y(x,t) = A sin (kx - wt + Φ)

where

A = amplitude of the wave = 0.0321 m

k = 2.05 /m

w = 524 /s

Φ = phase angle = pi/4

Velocity of a wave is given by

v = (w/k) = (524/2.05) = 255.61 m/s

Tension in the string is then related to the velocity of wave produced and the linear density through

v = √(T/μ)

v = velocity = 255.61 m/s

T = ?

μ = 0.0073 kg/m

v² = (T/μ)

T = v²μ = (255.61² × 0.0073) = 476.96 N

T = 477 N

Hope this Helps!!!

Answer:

3.74 %

Explanation:

Given,

Mass of the fired projectile, m = 0.1 Kg

Mass of the stationary target, M = 2.57 Kg

Speed of the particle after collision

Using conservation of momentum

m v = (m + M) V

0.1 x v = (0.1 + 2.57) V

V = 0.0374 v

Initial KE = [tex]\dfrac{1}{2}mv^2 = \dfrac{1}{2}\times 0.1\times v^2[/tex]

Final KE = [tex]\dfrac{1}{2} (M + m) V^2 = \dfrac{1}{2}\times 2.67\times (0.0374 v)^2[/tex]

Now,

the percent of the projectile's KE carried out by target

  [tex]=\dfrac{\dfrac{1}{2}\times 2.67\times (0.0374 v)^2}{ \dfrac{1}{2}\times 0.1\times v^2}\times 100[/tex]

 [tex]= 3.74\ \%[/tex]

Answer:

(D) The speed of the flow at the second point is 2.5 m/s

Explanation:

Given;

at upstream;

the width of the channel, w = 12 m

the depth of water, d = 6.0 m

the speed of the flow, v = 2.5 m/s

at downstream;

the width of the channel, w = 9 m

the depth of water, d = 8.0 m

the speed of the flow, v = ?

Volumetric flow rate for an Ideal incompressible water is given as;

Q = Av

where;

A is the area of the channel of flow

v is velocity of flow

For a constant volumetric flow rate;

A₁v₁ = A₂v₂

A₁ = area of rectangle = L x d = 12 x 6 = 72 m²

A₂ = area of rectangle = L x d = 9 x 8 = 72 m²

(72 x 2.5) = 72v₂

v₂ = 2.5 m/s

Therefore, the speed of the flow at the second point is 2.5 m/s

Answer:

Explanation:

Range= U²sin2theta/g

= 102²* sin (2*42)/9.8

= 1054.74m

Yes she will be abable to jump

The distance from the edge will be

(1054.74- 420)m

= 634.74m

Answer:

three halves of a wavelength

Explanation:because a

path difference between waves at minimum is (2n+1)*wavelength /2 therefore at second minimum it is for n=1=1.5 times a wavelength. or three halves a wavelength

The path difference in the distance traveled by the wave is three halves of a wavelength. Therefore, option (B) is correct.

Interference can be defined as a phenomenon that takes place in every place. It is a phenomenon in which two waves superpose to create the resultant wave of the higher, lower, or same amplitude.

There are two kinds of Interference which are constructive interference and destructive interference. In constructive interference, the crest of one wave falls on the crest of another wave, and the amplitude increases. In destructive interference, the crest of one wave falls on the trough of another wave, and the amplitude decreases.

For the minima, the path difference is given by (2n -1)/λ.

Here the value of n is given, n = 2

Path difference, = (2×2 - 1)/λ = (3/2)λ

Therefore, the path difference in the distance is (3/2)λ.

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