A particle moves according to the law of motion s(t) = t^{3}-8t^{2}+2t, t\ge 0, where t is measured in seconds and s in feet. a.) Find the velocity at time t. Answer: b.) What is the velocity after 3 seconds? Answer: c.) When is the particle at rest? Enter your answer as a comma separated list. Enter None if the particle is never at rest. At t_1= and t_2= with t_1

Answer:Time constant gets doubled

Explanation:

Given

L-R circuit is given and suppose R and L is the resistance and inductance of the circuit then current is given by

[tex]i=i_0\left [ 1-e^{-\frac{t}{\tau }}\right ][/tex]

where [tex]i_0[/tex] is maximum current

i=current at any time

[tex]\tau =\frac{L}{R}=time\ constant[/tex]

[tex]\tau '=\frac{2L}{R}=2\tau [/tex]

thus if inductance is doubled then time constant also gets doubled or twice to its original value.                                      

Answer:

0.00389 m

Explanation:

Archimedes principle states that the buoyant force when a body is immersed in a liquid equals the weight of the liquid displaced

B = weight of the liquid displaced

density is defined as the mass divided by the volume of the substance and the units is  in kg/m³

Density of glycerin = mass / volume

ρg × volume = mass of glycerin displaced

since the object was floating, the upthrust from the liquid equals the weight of the liquid

ρg × volume × g = mg

divide both side by g

ρg × volume = 0.180  where ρg (density of glycerin) = 1260 kg / m³

1260 × volume of glycerin displaced = 0.18 / 1260 = 0.000143 m³

volume of glycerin displaced = πr²h₁ where h₁ = of liquid displaced

πr²h₁ = 0.000143

h₁ = 0.000143 / ( 3.142 × 0.055² ) = 0.01505 m

when the ice completely melted, it will displaces liquid equal to it own volume

density of water = mass of water /volume

1000 = 0.18 / v

v = 0.18 / 1000 = 0.00018 m³

volume = πr²h₂ where h₂ = height of the melted water

πr²h₂ = 0.00018

h₂ = 0.00018 / ( 3.142 × 0.055²) = 0.01894 m

change in height of the liquid = h₂ - h₁ =  0.01894 m - 0.01505 m = 0.00389 m

When the 0.180 kg ice cube melts, it will form water that spreads out in the glycerin-filled cylinder, raising the level by approximately 1.89 cm.

To solve this problem, we first need to understand that when the ice cube melts, it will not change the overall volume of liquid in the cylinder. In other words, the total volume before the ice melts (volume of glycerin + volume of ice) is equal to the total volume after the ice melts (volume of glycerin +volume of water).

The volume of the water, resulting from the melted ice, can be calculated using the mass of the ice cube and the density of water. The volume (V) is equal to the mass (m) divided by the density (ρ). For ice, m = 0.180 kg and ρ = 1000 kg/m³ (the density of water), which gives V = 0.00018 m³ or 180 cm³.

This water spreads out in the cylinder, raising the level. The height (h) to which it raises can be found by dividing the volume of the water (V) with the cross-sectional area (A) of the cylinder (h = V/A). The area of the cylinder is πr², where r is the radius, so A = π * (5.5 cm)² = 95.03 cm². Thus, h = 180 cm³ / 95.03 cm² = 1.89 cm. Consequently, when the ice cube melts, the glycerin's height will increase by approximately 1.89 cm.

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Answer:

    d = 142.5 m

Explanation:

This is a vector exercise. Let's calculate how much the boat travels in the 40s

     d₀ = [tex]v_{b}[/tex] t

    d₀ = 0.75 40

    d₀ = 30 m

Let's write the kinematic equations

Boat

     x = d₀  +  [tex]v_{b}[/tex] t

     x = 0 +  [tex]v_{h}[/tex] t

At the meeting point the coordinate is the same for both

    d₀  +  [tex]v_{b}[/tex] t =  [tex]v_{h}[/tex] t

    t ( [tex]v_{h}[/tex] -  [tex]v_{b}[/tex]) = d₀  

    t = d₀  / ( [tex]v_{b}[/tex]-  [tex]v_{h}[/tex])

The two go in the same direction therefore the speeds have the same sign

     t = 30 / (0.95-0.775)

     t = 150 s

The distance traveled by man is

     d =  [tex]v_{h}[/tex] t

     d = 0.95 150

     d = 142.5 m

The distance of the boat downstream when you catch it is 60 meters.

To find the distance of the boat downstream when you catch it, we can use the equation d = vt, where d is the distance, v is the velocity, and t is the time.

Given that the current of the river is 0.75 m/s and you hold onto the piling for 40 seconds, the distance drift with the current is:

After you start swimming with a speed of 0.95 m/s and catch up to the boat, the distance you swim against the current is equal to the distance the boat drifts:

Therefore, the total distance downstream when you catch the boat is:

Hence, the total distance downstream when you catch the boat is 60 m.

Answer:

(B) Resistor only

Explanation:

Alternating Current: These are currents that changes periodically with time.

An LRC  Ac circuit is an AC circuit that contains a Resistor, a capacitor and an inductor, connected in series.

In a purely resistive circuit, current and voltage are in phase.

In a purely capacitive circuit, the current leads  the voltage by π/2

In a purely inductive circuit, the current lags the voltage by π/2.

Therefore when a alternating current is set up in LRC circuit, in the resistor, the current and the voltage are in phase.

The right option is (B) Resistor only.

The circuit elements are the current and voltage in phase in:

B) Resistor only

These are flows that changes occasionally with time. A LRC AC circuit is an AC circuit that contains a Resistor, a capacitor and an inductor, associated in series. In an absolutely resistive circuit, current and voltage are in stage. In an absolutely capacitive circuit, the current leads  the voltage by π/2. In an absolutely inductive circuit, the current slacks the voltage by π/2.

Thus, when an alternating current is set up in LRC circuit, in the resistor, the current and the voltage are in phase.

So, correct option is (B).

Find more information about Alternating current here:

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Answer:

d. meteoroid

Explanation:

Answer:

Impulse, |J| = 0.6716 kg-m/s

Force, F = 63.35 N

Explanation:

It is given that,

Mass of the baseball, m = 0.146 kg

Initial speed of the ball, u = 15.3 m/s

Final speed of the ball, v = 10.7 m/s

To find,

(a) The magnitude of this impulse.

(b) The magnitude of the average force of the glass on the ball.

Solution,

(a) Impulse of an object is equal to the change in its momentum. It is given by :

[tex]J=m(v-u)[/tex]

[tex]J=0.146\ kg(10.7-15.3)\ m/s[/tex]

J = -0.6716 kg-m/s

or

|J| = 0.6716 kg-m/s

(b) Another definition of impulse is given by the product of force and time of contact.

t = 0.0106 s

[tex]J=F\times \Delta t[/tex]

[tex]F=\dfrac{J}{\Delta t}[/tex]

[tex]F=\dfrac{0.6716\ kg-m/s}{0.0106\ s}[/tex]

F = 63.35 N

Hence, this is the required solution.

The impulse direction is opposite to the baseball's initial direction, and its magnitude is 0.6716 kg·m/s. The average force magnitude exerted by the window on the baseball is 63.36 N.

The direction of the impulse imparted by the window to the baseball is opposite to the baseball's initial direction of motion. This is because impulse is equal to the change in momentum, and since the window slows the ball down, it is applying a force in the opposite direction of the ball's initial velocity.

To calculate the magnitude of the impulse (I), use the formula

I = change in momentum = m(vf - vi)
where m is the mass of the baseball, vf is the final velocity, and vi is the initial velocity. The mass m = 0.146 kg, vi = 15.3 m/s, and vf = 10.7 m/s.

I = (0.146 kg)(10.7 m/s - 15.3 m/s)
I = (0.146 kg)(-4.6 m/s)
I = -0.6716 kg·m/s.

The negative sign indicates the impulse is in the opposite direction of the ball's initial motion, but since the question asks for the magnitude, we take the absolute value: 0.6716 kg·m/s.

The magnitude of the average force (Favg) exerted on the ball can be found using the formula

Favg = I/t
where t is the contact time. For a contact time of 0.0106 s, we have:
Favg = 0.6716 kg·m/s / 0.0106 s
Favg = 63.36 N.

Answer: 5.5km

Explanation:

Atmospheric pressure will be 500 mb (that is half of the total 1000mb air pressure).

Pressure decreases with increasing altitude. This is because at At higher altitudes, there are fewer air molecules above a the known or given surface than a similar surface at lower levels.

Pressure decreasing with higher altitudes also means that  air pressure decreases rapidly at lowerevels but more slowly at higher levels.

It is also known that more than half of the atmospheric molecules are located below 5.5 km(that is atmospheric pressure decreases within the lowest 5.5 km to about fifty(50) percent( that is 500 millibar).

Answer

Initial radius of the artery is (1.1 cm) / 2 = 0.55 cm

final radius of the artery is (0.90 cm) / 2 = 0.45 cm

initial velocity of the blood is 17 cm/s

Using  equation of continuity is

                                      A₁v₁=A₂v₂

                                 π r₁² x v₁ = π r₂² x v₂

                                  r₁² x v₁ = r₂² x v₂

                                  0.55² x 17 =0.45² x v₂

                                        v₂=25.39 cm/s

Bernoulli's equation is

[tex]P_1 - P_2 = \dfrac{1}{2}\rho (v_2^2-v_1^2)[/tex]

rho is the density of blood = 1060 kg/m^3

[tex]P_1 - P_2 = \dfrac{1}{2}\times 1060 \times (0.254^2-0.17^2)[/tex]

[tex]P_1 - P_2 =18.87\ Pa[/tex]

The student uses the continuity equation to correctly solve the first part, but for pressure drop, they need to apply Bernoulli's principle. Using the equation P1 + 1/2ρv1² = P2 + 1/2ρv2², with ρ being the blood's density and v1 and v2 the speeds, they can find the pressure drop. However, real-life complications due to blood viscosity and turbulence might affect the results.

The subject of this question is Physics (specifically, fluid dynamics). The concept being applied here is that of continuity and Bernoulli's principle. The continuity equation for fluid states that the mass flow rate must be constant throughout the length of the pipe. This translates to: Area 1 × Speed 1 = Area 2 × Speed 2. You correctly set up this equation to find Speed 2, which is the speed of the blood flow within the plaque region.

For the pressure drop, we need to use Bernoulli's principle, which describes that the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume is constant in a non-viscous, steady-flowing system. Applying Bernoulli's Equation: P1 + 1/2ρv1² = P2 + 1/2ρv2². Solving this equation gives us the pressure difference within the plaque region.

Keep in mind that you might have to use the change in blood speed, and also the density of blood within the equations to find the accurate pressure drop. Also, Bernoulli's principle applies to ideal situations and there could be changes in real-life situations due to the viscosity of blood and turbulence caused by plaque.

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Answer:

a)  ΔV = - 4.346 10⁻² , b)   ρ’= 1.082 10³ kg / m³

Explanation:

The volume module is defined as the ratio of the pressure and the unit deformation, with a negative sign, for the module to be positive

       B = - P / (ΔV/V)

a) The ΔV volume change

     ΔV/V = -P / B

     ΔV = - P V / B

     ΔV = - 1.13 10⁸ 0.9 /2.34 10⁹

     ΔV = - 4.346 10⁻²

b) Density at the bottom of the sea

On the surface

     ρ = m / V

      m = ρ V

     m = 1.03 10³ 0.9

     m = 0.927 10³ kg

Body mass does not change with depth

Deep down

    ρ’= m / V’

    ΔV = 4.346 10⁻²

    [tex]V_{f}[/tex]- V₀ = 4,346 10⁻²

    [tex]V_{f}[/tex] = 0.0436 + Vo

    [tex]V_{f}[/tex]= -0.04346 + 0.9

    [tex]V_{f}[/tex] = 0.85654 m³

    ρ’= 0.927 10³ / 0.85654

    ρ’= 1.082 10³ kg / m³

Using the formula for volume change under pressure and density calculations, it can be determined that the change in volume of 0.9 m³ seawater when taken to the Mariana Trench is -0.043 m³ and its density at the bottom is approximately 1072 kg/m³.

The pressure in the ocean increases with depth due to the weight of the overlying water. This high pressure can compress the volume of the water at such depths, altering its density. As the question provides, the bulk modulus of seawater is given as 2.34 x 10⁹ N/m² and the pressure in the Mariana Trench is 1.13 x 10⁸ N/m².

(a) To find the change in volume, we can use the formula ΔV = -(PΔV/B), where P is the pressure, ΔV is the change in volume, and B is the bulk modulus. Inserting the given values, we get the change in volume to be -0.043 m³.

(b) The density of a substance is its mass divided by its volume. At the bottom of the Mariana Trench, the volume of water has decreased due to the high pressure, but its mass remains the same. Therefore, as the volume decreases, the density increases. The new density, ρ', is calculated using the formula ρ' = ρ/(1-ΔV/V), where ρ is the initial density and V is the initial volume. Substituting into this equation, we get ρ' = 1.03 x 10³ kg/m³ / (1 -(-0.043), which gives us a density at the bottom of the Mariana Trench of approximately 1072 kg/m³.

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To find the maximum values that four bricks of length L can be on the verge of falling while stacked on top of each other in equilibrium, we need to consider the moments of each brick and the conditions for equilibrium. The moments of each brick can be calculated by multiplying the mass of the brick by the distance from the axis of rotation, which is half the length of the brick. By setting the sum of the moments equal to zero, we can find the maximum values for the mass of each brick in terms of L.

When four identical and uniform bricks are stacked on top of each other such that part of each brick extends beyond the one beneath, the stack is in equilibrium and on the verge of falling. To find the maximum values in terms of L, we need to consider the moment of each brick and the conditions for equilibrium. The moment is the product of the mass of the brick and the distance from the axis of rotation, which is half the length of the brick.

Let's assume the bricks have a length L and that they are stacked vertically with their centers of mass aligned. The distance from the axis of rotation to the center of mass is L/2 for each brick. The moment of the top brick is then (mass of the brick) * (L/2). The moment of the second brick is (mass of the brick) * (3L/2), considering the length of the first brick as the distance from the axis of rotation. Similarly, the moment of the third brick is (mass of the brick) * (5L/2), and the moment of the fourth brick is (mass of the brick) * (7L/2).

For the stack to be in equilibrium, the sum of the moments must be zero. Therefore, we have the equation:

(mass of the first brick) * (L/2) + (mass of the second brick) * (3L/2) + (mass of the third brick) * (5L/2) + (mass of the fourth brick) * (7L/2)

By simplifying this equation and substituting the mass of each brick with a constant value (let's say M), we can find the maximum values for the mass of each brick such that the stack is in equilibrium on the verge of falling, given a certain length L.

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To determine the convection heat transfer coefficient of air at the upper surface, we need to know the surface area of the plate which is not provided in the given question.

The convection heat transfer coefficient of air at the upper surface can be determined using Newton's law of cooling. According to Newton's law of cooling, the rate of heat transfer through convection is directly proportional to the temperature difference between the solid surface and the surrounding fluid and the surface area of the solid.

Therefore, the heat transfer rate can be calculated using the formula:

Q = h * A * (Ts - T∞)

Where:

In this case, we are given the following values:

To find the surface area, we need to know the dimensions of the plate. Once we have the surface area, we can solve for the convection heat transfer coefficient using the given formula. However, the surface area is not provided in the question, so we cannot determine the convection heat transfer coefficient without that information.

From the definition we have that the Torque corresponds to the Multiplication between the Force (or its respective component) and the radius of distance of the Force to the inertial turning point.

Mathematically this can be expressed,

[tex]\tau = F \times d[/tex]

Where,

F = Perpendicular component of force

d = distance from pivot point

The total sum of the torques would be equivalent to

[tex]\tau_{net} = \tau_1 +\tau_2[/tex]

According to the values given, torque 1 and 2 would be given by

[tex]\tau_1 = 6*1.2 = 7.2N\cdot m (+)[/tex]

[tex]\tau_2 = -5.2sin(30) = -7.8N\cdot m (-)[/tex]

Therefore the net Torque is

[tex]\tau_{net} = \tau_1+\tau_2[/tex]

[tex]\tau_{net} = 7.2-7.8[/tex]

[tex]\tau_{net} = -0.6N\cdot m[/tex]

Therefore the net torque about the pivot is -0.6Nm

Answer:

Part A. 5.36x10²³ molecules of air

Part B. 6.9kg  

Explanation:

Part A.

To calculate the number of molecules of the air we need first find the number of moles of air using the equation of ideal gas law:

[tex] PV = nRT [/tex]    (1)

where P: is the pressure, V: is the volume, n: is the number of moles of the gas, R: is the gas constant and T: is the temperature

[tex] n = \frac{PV}{RT} = \frac{735torr \cdot 1atm/760torr \cdot 2.35L}{0.082 Latm/Kmol \cdot (37 + 273)K} = 0.089 moles [/tex]

Now by using the Avogadro's number we can find the number of molecules of air:

[tex] number of molecules = \frac{6.022 \dot 10^{23}}{1mol} \cdot 0.089moles = 5.36 \cdot 10^{22} molecules [/tex]

Part B.

Similarly, to calculate the mass of air first we need to detemine the number of moles using equation (1):

[tex] n = \frac{PV}{RT} = \frac{1.07atm \cdot 5.0\cdot 10^{3}L}{0.082 Latm/Kmol \cdot (0.5 + 273)K} = 238.55 moles [/tex]

So, the mass of air is:

[tex] m = moles \cdot M [/tex]

where M: is the average molar mass of air

[tex] m = 238.55moles \cdot 28.98g/mol = 6.9 kg [/tex]

I hope it helps you!  

The student needs to use the ideal gas law and Avogadro's number to convert the volume of air to moles and then to molecules. For the blue whale, use the ideal gas law to convert volume to moles, then multiply by the molar mass of air to get mass.

To begin with, we first convert the volume into molecules. Using the ideal gas law (PV = nRT), where P is pressure, V is volume, n is the number of moles, R is the gas constant and T is temperature. The number of moles, n, can be found by rearranging the equation to n=PV/RT.

Substituting the given values (converting pressure to atm and volume to L, and temperature to Kelvin), we will compute n. After finding the no of moles, the number of molecules is calculated by multiplying the number of moles by Avogadro's number.

In the case of the blue whale, we again use the ideal gas law to find the number of moles of air in the lungs, then multiply by the molar mass of air (28.98 g/mol) to find the mass in grams. Finally, we then convert from grams to kilograms.

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Answer

The answer and procedures of the exercise are attached in the following archives.

Explanation  

You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.  

The probability of finding a particle in its first excited state within the center 20% of an infinite square well of length L is approximately 11.8%. This involves integrating the square of the wavefunction over the specific interval. The key steps are defining the potential energy and solving the Schrödinger equation.

To find the probability of locating a particle in its first excited state within the center 20% of a one-dimensional box of length L, we follow these steps:

Define the Potential Energy, V: Inside the box (0 ≤ x ≤ L), V(x) = 0. Outside the box, V(x) = ∞.

Solve the Schrödinger Equation: The normalized wavefunction for the first excited state (n=2) is ψ2(x) = √(2/L) * sin(2πx/L).

The center 20% of the box is the interval from 0.4L to 0.6L. We calculate the probability of finding the particle in this region by integrating the square of the wavefunction:

Prob(center20%) = ∫0.4L0.6L |ψ2(x)|² dx = ∫0.4L0.6L ">2/L * sin²(2πx/L) dx.

Using integration techniques, the result is:

Prob(center20%) = 2 * [0.1 - (sin(0.4π))/(π)]. This computes to approximately 0.118 or 11.8%.

Answer:

33 g.

Explanation:

Assuming no heat transfer can be possible except for heat exchange between water and steel, we can say that the heat lost by the knife, must be equal to the heat gained by the water.

As we have a limit for the maximum temperature of both elements (once reached a final thermal equilibrium), of 100ºC, which means that the maximum allowable change in temperature will be of 300º C for the knife, and of 80º C for the water.

Empirically , it has been showed that for a heat exchange process using only conduction, the heat needed to raise the temperature of a body, is proportional to the mass, being the proportionality constant a factor that depends on the material, called specific heat.

So, we can write the following equation:

cs*mk*Δtk = cw*mw*Δtw

Replacing by the givens of the question, we have:

0.11 cal/gºC * 80 g * 300ºC = 1 cal/gºC*mw*80ºC

Solving for mw = 2,640 cal / 80 cal/g =33 g.

Answer:

w = 4,786 rad / s ,  f = 0.76176 Hz

Explanation:

For this problem let's use the concept of angular momentum

       L = I w

The system is formed by the two discs, during the impact the system remains isolated, we have the forces are internal, this implies that the external torque is zero and the angular momentum is conserved

Initial Before sticking

      L₀ = 0 + I₂ w₂

Final after coupling

      [tex]L_{f}[/tex] = (I₁ + I₂) w

The moments of inertia of a disk with an axis of rotation in its center are

      I = ½ M R²

How the moment is preserved

      L₀ = [tex]L_{f}[/tex]

      I₂ w₂ = (I₁ + I₂) w

      w = w₂ I₂ / (I₁ + I₂)

Let's reduce the units to the SI System

      d₁ = 60 cm = 0.60 m

      d₂ = 40 cm = 0.40 m

      f₂ = 200 min-1 (1 min / 60 s) = 3.33 Hz

Angular velocity and frequency are related.

      w₂ = 2 π f₂

      w₂ = 2π 3.33

      w₂ = 20.94 rad / s

Let's replace

       w = w₂ (½ M₂ R₂²) / (½ M₁ R₁² + ½ M₂ R₂²)

       w = w₂ M₂ R₂² / (M₁ R₁² + M₂ R₂²)

Let's calculate

      w = 20.94 8 0.40² / (12 0.60² + 8 0.40²)

      w = 20.94 1.28 / 5.6

      w = 4,786 rad / s

Angular velocity and frequency are related.

      w = 2π f

      f = w / 2π

      f = 4.786 / 2π

      f = 0.76176 Hz

Answer:

D) True. This is what creates the body weight

Explanation:

Let's write Newton's second law for this case. For inclined planes the reference system takes one axis parallel to the plane (x axis) and the other perpendicular to the plane (y axis)

X axis

          Wx -fr = ma

Y Axis

          N - Wy = 0

With trigonometry we can find the components of weight

          sin θ = Wₓ / W

         cos θ = [tex]W_{y}[/tex] / W

         Wₓ = W sin θ

          [tex]W_{y}[/tex] = W cos θ

        W  sin θ - fr = ma

From this expression as it indicates that the body is descending the force greater is the gravity that create the weight of the body

Let's examine the answers

A False This force does not apply because it is not a spring

B) False. It is balanced at all times with the component (Wy) of the weight

C) False. For there to be a rope, if it exists you should be less than the weight component for the block to lower

D) True. This is what creates the body weight

E) False. The cutting force occurs for force applied at a single point and gravity is applied at all points

For a block to move down an inclined plane, the force of gravity must be greater than the other forces. This includes the normal force and any friction that may be present. Other forces such as compression, tension, and shear are not directly involved in this process.

For a block to move down an inclined plane, the greatest force must be gravity. The force of gravity acts downward and causes the block to slide down the slope. This force must be stronger than the others such as the normal force (the force exerted by the plane on the block) and any friction forces that may be present.

The other forces listed (compression, tension, and shear) are not directly related to the movement of the block down the inclined plane. Compression and tension are forces that act in opposite directions either pushing (compression) or pulling (tension) an object. Shear is a force that causes materials to slide past each other and is not directly applicable to this scenario

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Answer:

Explanation:

Given

initial velocity of particle u=274 m/s

one Particle moves up with velocity of v=235 m/s

and other moves u=484 m/s towards east

let [tex]v_y[/tex] and [tex]v_x[/tex] be the velocity of third Particle is Y and x direction

conserving momentum in y direction  

[tex]m(274)=\frac{m}{3}\times v_y+\frac{m}{3}\times 0+\frac{m}{3}\times 235[/tex]

[tex]v=587 m/s[/tex]

Now conserving momentum in  x direction

[tex]m\times 0=\frac{m}{3}\times v_x+\frac{m}{3}\times 0+\frac{m}{3}\times 484[/tex]

[tex]v_x=-484 m/s[/tex]

Net Velocity of third Particle

[tex]v^2=v_x^2+v_y^2[/tex]

[tex]v=\sqrt{v_x^2+v_y^2}[/tex]

[tex]v=\sqrt{484^2+587^2}[/tex]

[tex]v=760.80 m/s[/tex]  

To find the magnitude of the velocity of the third fragment, we need to consider the conservation of momentum. The magnitude of the velocity of the third fragment is 445 m/s.

To find the magnitude of the velocity of the third fragment, we need to consider the conservation of momentum. According to the law of conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion. The momentum of an object is the product of its mass and velocity.

Let's assume the mass of each fragment is m. Since the first fragment continues to move upward with a speed of 235 m/s and the second fragment has a speed of 484 m/s and is moving east, we can write the momentum equation as:

m(235) + m(484) + m(v3) = m(274)

Simplifying the equation, we get:

719m + m(v3) = 274m

445m = - m(v3)

- 445m = m(v3)

Dividing both sides by m, we get:

-445 = v3

Therefore, the magnitude of the velocity of the third fragment is 445 m/s.

Answer:10000N

Explanation:formuler for calculating force is given by F=Ma

M(mass)=500kg

a(acceleration)=20m/s^2

Therefore by substitution we have F=500*20

F=10000N

To solve this problem it is necessary to apply the concepts related to the magnetic field

the flux density and the magnitude of the magnetization.

Each of these will be tackled as the exercise is carried out, for example for the first part we have to:

Part A) Magnitude of the magnetic field

[tex]H = \frac{NI}{L}[/tex]

Where,

N = Number of loops

I = Current

L = Length

If we replace the given values the value of the magnitude of the magnetic field would be:

[tex]H= \frac{340*13}{0.12}[/tex]

[tex]H = 36833 A\cdot turns/m[/tex]

For the second and third part we will apply the concepts of density both in vacuum and positioned at a point, like this:

PARTE B) Flux density in a vacuum

[tex]B = \mu_0 H[/tex]

Where,

[tex]\mu_0 =[/tex] Permeability constant

[tex]B = (4\pi*10^{-7})(36833)[/tex]

[tex]B = 0.04628T[/tex]

PART C) To find the Flux density inside a bar of metal but the magnetic susceptibility is given

[tex]X_m = 1.9*10^{-4}[/tex]

[tex]\mu_R = 1+X_m[/tex]

[tex]\mu_R = 1.00019[/tex]

Then the flux density would be

[tex]B = \mu_0 \mu_R H[/tex]

[tex]B = (4\pi*10^{-7})(1.00019)(36833)[/tex]

[tex]B = 0.04629T[/tex]

PART D) Finally, the magnetization describes the amount of current per meter, and is given by the magnetic susceptibility, that is:

[tex]M = X_m H[/tex]

[tex]M = 1.9*10^{-4}*36833[/tex]

[tex]M = 6.996A/m[/tex]

This solution calculates the magnetic field strength, flux density and magnetization in a wire coil, as well as the flux density inside a metal bar within the coil, using Ampere's law and the formulas for magnetic field and flux densities.

The calculations are derived from Ampere's law and the formulas for magnetic field strength and flux density. For part (a), to find the magnitude of the magnetic field strength H (in A/m), we consider the given length of the coil and the number of turns. H= nI, where n is the number of turns per unit length and I is the current. In the given case, n= 340/0.12 = 2833.33, so H = 2833.33 turns/m * 13 A = 36833 A/m.

For part (b), we need to calculate the flux density B (in T) inside the coil which is in a vacuum. Using the formula B = μH, where μ = 4π x 10-7 T. m/A is the permeability of vacuum, we find B= 4π x 10^-7 T.m/A * 36833 A/m = 4.6 x 10^-2 T.

For part (c), we need to calculate the flux density B inside a bar of metal with susceptibility χ_m = 1.90 x 10-4. In this case, B = μ(H + M), where M = χ_m H is the magnetization. We find M= 1.90 x 10^-4 * 36833 A/m = 7 A/m, so B in metal = 4π x 10^-7 T.m/A * (36833 A/m + 7 A/m) = 4.6 x 10^-2 T.

For part (d), we've already calculated the magnitude of the magnetization M to be 7 A/m.

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Answer:

l = 3.21 mm

Explanation:

The efficiency of a fiber-reinforced is the following:

[tex] \eta = \frac{l - 2x}{l} [/tex]

Where:

η: is the efficiency

l: is the fiber length

x: is the length of the fiber at each end that doesn't contribute to the load transfer

So the length required for a 0.62 efficiency of reinforcement is:

[tex] l = \frac{2x}{1- \eta} = \frac{2 \cdot 0.61 mm}{1- 0.62} = 3.21 mm [/tex]

I hope it helps you!  

The length required for a 0.62 efficiency of reinforcement in a fiber-reinforced composite can be calculated using the equation η = (l-x)/l, where l represents the total length of the fiber and x represents the length at each end that does not contribute to load transfer. By rearranging the equation, we can solve for l.

To calculate the length required for a 0.62 efficiency of reinforcement in a fiber-reinforced composite, we can use the equation η = (l-x)/l. Here, l represents the total length of the fiber, and x represents the length at each end that does not contribute to load transfer. We are given that x is 0.61 mm. We can rearrange the equation to solve for l:

η = (l-x)/l

0.62 = (l-0.61)/l

0.62l = l - 0.61

0.62l - l = -0.61

0.62l = -0.61

l = -0.61/0.62

l = -0.983

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The normal force of the slide on the child is 217.3 N and the kinetic frictional force from the slide is 166.8 N when the child slides down the slide at a constant speed.

The normal force on a slope, which is always perpendicular to the surface, is equal to the weight component of the object that is perpendicular to the slope. As the child slides down the slide at a constant speed, the net force on the child is zero. In this scenario, let's denote mass (m) as 28 kg, inclination angle (θ) as 38 degrees, and g as gravitational acceleration which is 9.8 m/s². So, the normal force (N), which is equal to m*g*cosθ, can be calculated as: 28 kg * 9.8 m/s² * cos(38) = 217.3 N.

The frictional force from the slide acts in the opposite direction to the motion. When the sliding speed is constant, this kinetic frictional force equals the component of the child's weight that is parallel to the slope (m*g*sinθ). Hence, the kinetic frictional force would be: 28 kg * 9.8 m/s² * sin(38) = 166.8 N.

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The normal force of the slide on the child can be found by multiplying the child's weight by the cosine of the angle of inclination. The kinetic frictional force from the slide is equal to the horizontal force exerted by the rope.

To find the normal force of the slide on the child, we need to determine the component of the child's weight perpendicular to the slide. Since the slide is inclined at 38∘ above horizontal, the normal force is equal in magnitude to the component of the child's weight perpendicular to the slide, which is given by:

Normal force = weight * cos(38∘)

Next, to find the kinetic frictional force from the slide, we need to use the horizontal force exerted by the rope. Since the child slides with a constant speed, the kinetic frictional force must be equal in magnitude to the horizontal force exerted by the rope, which is given as 30 N.

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Answer:

Explanation:

Given

after 5.5 revolution wheel comes to stop

i.e. radian turned before stopping

[tex]\theta =2\pi \times 5.5 rad[/tex]

initial angular velocity [tex]\omega _0=3.5 rad/s[/tex]

[tex]\omega ^2-\omega _0^2=2\cdot \alpha \cdot \theta [/tex]

where  [tex]\alpha =angular\ acceleration\ or\ deceleration[/tex]                                                                                                                                                                                                                                                                                                    

[tex]0-(3.5)^2=2(\alpha )(2\pi \cdot 5.5)[/tex]

[tex]\alpha =-0.1772 rad/s^2[/tex]

angle turned when final angular velocity is [tex]2 rad/s[/tex]

[tex]2^2-3.5^2=2\cdot (-0.1772)(\theta )[/tex]

[tex]\theta =23.27\ radians[/tex]

To solve this problem we need to apply the concepts related to the average electromagnetic energy density. Which is given as

[tex]U = \frac{1}{2}\epsilon_0 E^2[/tex]

Where,

\epsilon_0 = Permettivity of free space constant

E = Electric Field amplitude

Since the average electromagnetic energy density is directly proportional to the amplitude of the magnetic field then we have to

[tex]E = \frac{1}{2} (8.85*10^{-12}C^2/N\cdot m^2)(0.9V/m)^2[/tex]

[tex]E = 3.6*10^{-12}J/m^3[/tex]

[tex]E = 3.6pJ/m^3[/tex]

Therefore the correct answer is C.

Answer:

225 m

Explanation:

[tex]f[/tex] = Frequency of the T wave = 6.8 Hz

[tex]v[/tex] = Speed of sound in seawater = 1530 ms⁻¹

[tex]\lambda[/tex] = Wavelength of the T wave

we know that, frequency, speed and wavelength are related as

[tex]wavelength = \frac{speed}{frequency}[/tex]

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

Inserting the values, we get

[tex]\lambda = \frac{1530}{6.8}\\\lambda = 225 m[/tex]

Final answer:

The wavelength of a T wave with a frequency of 6.8 Hz in seawater, where the speed of sound is 1,530 m/s, is calculated to be approximately 225 meters using the formula for wave speed.

Explanation:

To calculate the wavelength of a T wave with a frequency of 6.8 Hz in the Pacific Ocean, where the speed of sound in seawater is 1,530 m/s, we can use the formula for wave speed: v = f × λ, where v is the speed of sound, f is the frequency, and λ is the wavelength.

By rearranging the formula to solve for the wavelength (λ = v / f), and substituting in the known values, we get λ = 1,530 m/s / 6.8 Hz, which calculates to approximately 225 meters. Therefore, the wavelength of a T wave with a 6.8 Hz frequency in seawater is about 225 meters.

Answer:

In this equation the scale used must be Kelvin

Explanation:

The absolute temperature is the value of the measured temperature relative to a scale starting at Absolute Zero (0 K or -273.15 °C). It is one of the main parameters used in thermodynamics and statistical mechanics. In the international system of units it is expressed in kelvin, whose symbol is K

The absolute temperature should always be used in the ideal gas state equation as this can only be in kelvin grade scale.

Answer:

0.003034 s

1.035 m

4.5 m

Explanation:

[tex]f[/tex] = frequency of the tone = 329.6 Hz

[tex]T[/tex] = Time period of the sound wave

we know that, Time period and frequency are related as

[tex]T =\frac{1}{f}\\T =\frac{1}{329.6}\\T = 0.003034 s[/tex]

[tex]v[/tex] = speed of the sound in the air = 341 ms⁻¹

wavelength of the sound is given as

[tex]\lambda =\frac{v}{f} \\\lambda =\frac{341}{329.6}\\\lambda = 1.035 m[/tex]

[tex]v[/tex] = speed of the sound in the water = 1480 ms⁻¹

wavelength of the sound in water is given as

[tex]\lambda =\frac{v}{f} \\\lambda =\frac{1480}{329.6}\\\lambda = 4.5 m[/tex]

Answer:

The minimum coefficient of static friction should be 0.62.

Explanation:

Given that,

Mass of block = m

Mass of cart = 6.5 kg

Time period = 0.66 s

Displacement = 67 mm

We need to calculate the mass of block

Using formula of time period

[tex]T=2\pi\times(\dfrac{m}{k})[/tex]

Put the value into the formula

[tex]0.66=2\pi\times(\dfrac{m+6}{600})[/tex]

[tex]m=\dfrac{0.66\times600}{4\pi^2}-6[/tex]

[tex]m=4.03\ kg[/tex]

We need to calculate the maximum acceleration of SHM

Using formula of acceleration

[tex]a_{max}=\omega^2 A[/tex]

Maximum force on mass 'm' is [tex]m\omega^2 A[/tex]

Which is being provided by the force of friction between the mass and the cart.

[tex]\mu_{s}mg \geq m\omega^2 A[/tex]

[tex]\mu_{s}\geq \dfrac{\omega^2 A}{g}[/tex]

[tex]\mu_{s} \geq (\dfrac{2\pi}{T})^2\times\dfrac{A}{g}[/tex]

Put the value into the formula

[tex]\mu_{s} \geq (\dfrac{2\pi}{0.66})^2\times\dfrac{0.067}{9.8}[/tex]

[tex]\mu_{s} \geq 0.62[/tex]

Hence, The minimum coefficient of static friction should be 0.62.

To solve this problem it is necessary to apply the concepts related to the magnetic flow of a coil and take into account the angles for each case.

It is also necessary to delve into part C, the concept of electromotive force (emf) which is defined as the variation of the magnetic flux as a function of time.

By definition the magnetic flux is determined as:

[tex]\phi = NBA cos\theta[/tex]

Where

N = Number of loops [tex]\rightarrow[/tex] We will calculate the value for each of the spins

B = Magnetic Field

A = Cross-sectional Area

[tex]\theta =[/tex] Angle between the perpendicular cross-sectional area and the magnetic field.

PART A) The magnetic flux through the coil after it is rotated is as follows:

[tex]\phi_i = NBA cos\theta[/tex]

[tex]\phi_i = (1turns)(6*10^{-5}T)(12*10^{-4}m^2)cos(0)[/tex]

[tex]\phi_i = 7.2*10^{-8}T\cdot m^2[/tex]

PART B) For the second case the angle formed is perpendicular therefore:

[tex]\phi_f = NBA cos\theta[/tex]

[tex]\phi_f = (1turns)(6*10^{-5}T)(12*10^{-4}m^2)cos(90)[/tex]

[tex]\phi_f = 0[/tex]

PART C) The average induced emf of the coil is as follows:

[tex]\epsilon = - (\frac{\phi_f-\phi_i}{dt})[/tex]

[tex]\epsilon = -(\frac{0-7.2*10^{-8}}{0.04})[/tex]

[tex]\epsilon = 1.8*10^{-6}V[/tex]

Answer:

The series A test tube has some left amount of glucose left in it.

Explanation:

Let's assume that a fixed amount of glucose is synthesized, for the fixed quantity the bacteria produced in A and B be x and y respectively,

Therefore, the condition on x and y is,    y > x  as the no. of bacteria present in B is greater.

As a result B would require a greater amount of energy for its functioning, these energy would be derived from the already fixed amount of glucose present.

A test tube would also require the energy for its x number of bacteria, but it is less than that of B.

Therefore, there would be some unused glucose left in Test Tube Series A which has unused energy.