Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Write a differential equation that expresses Newton's Law of Cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant.)

To determine the distance between the slits and the screen, we can use the formula for the separation between fringes in a double-slit interference pattern. Applying the small angle approximation, we find that the screen must be placed approximately 1.065 km away from the slits.

To determine the distance between the slits and the screen, we can use the formula for the separation between fringes in a double-slit interference pattern:

d*sin(theta) = m*lambda

Where d is the separation between the slits (65.0 µm), lambda is the wavelength of light (693 nm), m is the order of the fringe (in this case, m = 21), and theta is the angle of the fringe from the central maximum. Since we want the central maximum to be at the center of the screen, we can consider the angle to be very small, and therefore sin(theta) ≈ theta. Rearranging the formula, we have:

theta = m*lambda / d = 21 * (693e-9 m) / (65.0e-6 m) = 2.241e-3 radians

Next, we can use the small angle approximation to find the distance from the slits to the screen. This approximation states that tan(theta) ≈ theta for small angles. Therefore, tan(theta) = y / L, where y is the distance between the center of the screen and the fringe, and L is the distance between the slits and the screen. Solving for L, we have:

L = y / tan(theta) = (4.75 m / 2) / tan(2.241e-3 radians) ≈ 1.065 km

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Answer: I think that you are asking about an interactive reader which talks about an exercise which asked for the person's velocity who were on the bus.

The answer is 14 m/s

Explanation: When you have to do an exercise about velocity, you can do this exercise knowing the velocity from the bus in relative the street and you ALWAYS have to define your positive or negative motion about the direction in which the person were walking to know if you have to add or subtract

In this case, the bus were travelling east at 15 m/s and the person walked toward the back of the bus at 1 m/s.

It doesn't matter if the positive is the west or the east. While you only know the positive and knowing that the person was walking toward back the bus you can deduce this:

The person's total velocity is (+15 m/s) - (+1 m/s) = +14 m/s

If positive motion is defined as motion westward, the total velocity would be the individual's speed in the westward direction. It includes both the speed and the direction, which makes velocity a vector quantity.

In the context of the question, if positive motion is defined as motion westward, then the individual's total velocity would be their speed in the westward direction with the magnitude and direction incorporated. Velocity is a vector quantity because it encompasses both magnitude (how fast an object is moving) and direction (where it is going). So if the person is walking at a speed of 3 km/h, in the westward (positive) direction, then we can say the person's total velocity is 3 km/h west.

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Answer:

1355 days

Explanation:

Find the given attachment

Andre will not be able to use the fan at all during his working hours.

To estimate how many hot days Andre will be able to use the fan, we need to calculate the number of rotations the fan will make during his working hours and subtract the number of rotations it takes for the fan to stop once turned off. We know that the fan reaches a speed of 700 rpm in 4.0 s from rest. This means its angular velocity is 700 * 2π/60 = 73.33 rad/s. So, in 8 hours (Andre's working hours), the fan will rotate for 73.33 * 3600 * 8 = 210,624 rotations. Subtracting the rotations it takes for the fan to stop (700 * 11 = 7700 rotations), Andre will be able to use the fan for approximately 210,624 - 7700 = 202,924 rotations. Since the fan is specified to operate up to 1 billion rotations, Andre will be able to use the fan for approximately 202,924 / 1,000,000,000 = 0.0002029 (or about 0.02%) of its lifespan. Rounded to the nearest day, this is 0 days. 

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The gravitational force on a particle due to a sphere can be calculated using Newton's Law of gravitation. Different distances result in different force magnitudes.

The magnitude of the gravitational force (F) on a particle due to a sphere can be calculated by using Newton's Law of Gravitation, F = G*(m1*m2)/r², where G is the gravitational constant (6.67 × 10-¹¹ N·m²/kg²), m1 and m2 are the masses of the two bodies, and r is the distance between their centers.

(a) For a distance of 1.4 m, F = G*(3.0 × 10⁴ kg*9.3 kg) / (1.4 m)².

(b) For a distance of 0.21 m, F = G*(3.0 × 10⁴ kg*9.3 kg) / (0.21 m)².

(c) For a general expression for the magnitude of the gravitational force on the particle at a distance r ≤ 1.0 m from the center of the sphere, the formula changes to F = G*(m1*m2)/r², where r ≤ 1.0 m.

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Answer:

Decrease the amount of carbon dioxide in the ecosystem.

Explanation:

becaus egthy

To increase the number of energy storage molecules that producers can make, Jaime should:

1. Increase the amount of sunlight in the ecosystem: Sunlight is a vital source of energy for photosynthesis, the process by which producers convert carbon dioxide and water into energy-rich molecules such as glucose. More sunlight can potentially increase the rate of photosynthesis, leading to more energy storage molecules being produced.

2. Decrease the amount of carbon dioxide in the ecosystem: While carbon dioxide is essential for photosynthesis, excessive levels can inhibit the process. By decreasing the amount of carbon dioxide in the ecosystem to an optimal level, Jaime can ensure that producers can efficiently utilize available resources to produce energy storage molecules.

So, both increasing sunlight and decreasing carbon dioxide can contribute to increasing the number of energy storage molecules that producers can make.

Given Information:

Resistance = R = 14 Ω

Inductance = L = 2.3 H

voltage = V = 100 V

time = t = 0.13 s

Required Information:

(a) energy is being stored in the magnetic field

(b) thermal energy is appearing in the resistance

(c) energy is being delivered by the battery?

Answer:

(a) energy is being stored in the magnetic field ≈ 219 watts

(b) thermal energy is appearing in the resistance ≈ 267 watts

(c) energy is being delivered by the battery ≈ 481 watts

Explanation:

The energy stored in the inductor is given by

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

The rate at which the energy is being stored in the inductor is given by

[tex]\frac{dU}{dt} = Li\frac{di}{dt} \: \: \: \: eq. 1[/tex]

The current through the RL circuit is given by

[tex]i = \frac{V}{R} (1-e^{-\frac{t}{ \tau} })[/tex]

Where τ is the the time constant and is given by

[tex]\tau = \frac{L}{R}\\ \tau = \frac{2.3}{14}\\ \tau = 0.16[/tex]

[tex]i = \frac{110}{14} (1-e^{-\frac{t}{ 0.16} })\\i = 7.86(1-e^{-6.25t})\\\frac{di}{dt} = 49.125e^{-6.25t}[/tex]

Therefore, eq. 1 becomes

[tex]\frac{dU}{dt} = (2.3)(7.86(1-e^{-6.25t}))(49.125e^{-6.25t})[/tex]

At t = 0.13 seconds

[tex]\frac{dU}{dt} = (2.3) (4.37) (21.8)\\\frac{dU}{dt} = 219.11 \: watts[/tex]

(b) thermal energy is appearing in the resistance

The thermal energy is given by

[tex]P = i^{2}R\\P = (7.86(1-e^{-6.25t}))^{2} \cdot 14\\P = (4.37)^{2}\cdot 14\\P = 267.35 \: watts[/tex]

(c) energy is being delivered by the battery?

The energy delivered by battery is

[tex]P = Vi\\P = 110\cdot 4.37\\P = 481 \: watts[/tex]

Given Information:

Velocity = v = 150 m/s

angle = θ = 12°

Required Information:

Radius of curvature = R = ?

Answer:

Radius of curvature = [tex]R = 1.079 \times 10^{4} \: m[/tex]

Explanation:

Please refer to the attached diagram,

[tex]Fcos(\theta) = m \cdot g\\Fcos(12^{\circ}) = m \cdot g \:\:\:\:\:\:eq. 1[/tex]

Where m is the mass of the plane and g is the gravitational acceleration.

[tex]Fsin(\theta) = \frac{mv^{2}}{R}\\Fsin(12^{\circ}) = \frac{m \cdot v^{2}}{R}\:\:\:\:\:\:eq. 2[/tex]

Where v is the velocity of the plane and R is the radius of curvature of the curved path of the airplane.

Dividing eq. 2 by eq. 1 yields,

[tex]tan(12^{\circ}) = \frac{v^{2}}{R\cdot g }[/tex]

[tex]since \: \frac{sin(\theta)}{cos(\theta)} = tan(\theta)[/tex]

[tex]tan(12^{\circ}) = \frac{v^{2}}{R\cdot g }\\\\R = \frac{v^{2}}{g\cdot tan(12^{\circ}) }\\\\R = \frac{150^{2}}{9.81\cdot 0.212 }\\\\R = 10793\\R = 1.079 \times 10^{4} \: m[/tex]

Therefore, the radius of curvature of the curved path of the airplane is 1.079×10⁴ m

Final answer:

The radius of curvature of an airplane's horizontal circular path can be determined by the centripetal force, provided by the horizontal component of lift when the airplane is banked at a specific angle.

Explanation:

The question involves an airplane traveling in a horizontal curved path and banking at an angle to achieve this motion. To find the radius of curvature for the airplane's path, we need to consider the centripetal force necessary for circular motion, which is supplied by the horizontal component of the lift force when the airplane is banked. The lift force itself acts perpendicular to the wings. By using trigonometry and the principles of circular motion, we can relate the banking angle, the airplane's velocity, and the force required for level flight to find the radius of curvature. Notably, this type of problem is a common application of Newton's laws of motion in a circular motion context.

Answer:

1. FB; 2. SF; 3, 4. FF and OF are simultaneous; 5, 6. BB and SB are simultaneous; 7. OB; 8 BF

Explanation:

According to the report the listed below are what Dan saw in the exact chronological order.

1. FB; 2. SF; 3, 4. FF and OF are simultaneous; 5, 6. BB and SB are simultaneous; 7. OB; 8 BF

These represents the series of events as described in the question.

Answer:

Option A is correct - While a guitar string is vibrating, you gently touch the midpoint of the string to ensure that the string does not vibrate at that point. The lowest-frequency standing wave that could be present on the string vibrates at twice the fundamental frequency.

Explanation:

Before touching the midpoint of the string, the string vibrates with one loop.

Fundamental frequency, f1 = v/(2*L)

Now, when the midpoint of the guitar string was touched, the string vibrates with two loops.

Hence, f2 = 2*v/(2*L)

f2 = 2*f1

Therefore, compared to the fundamental frequency the frequency would be double.

Option A is correct - While a guitar string is vibrating, you gently touch the midpoint of the string to ensure that the string does not vibrate at that point. The lowest-frequency standing wave that could be present on the string vibrates at twice the fundamental frequency.

D                                                                     _____________________________________________________

Answer:

The voltage across the capacitor = 0.8723 V

Explanation:

From the question, it is said that the coil is quickly pulled out of the magnetic field. Therefore , the final magnetic flux linked to the coil is zero.

The change in magnetic flux linked to this coil is:

[tex]\delta \phi = \phi _f - \phi _i[/tex]

    = 0 - BA cos 0°

[tex]\delta \phi =-BA \\ \\ \delta \phi =-B( \pi r^2) \\ \\ \delta \phi =(1.0 \ mT)[ \pi ( \frac{d}{2} )^2][/tex]

[tex]\delta \phi =(1.0 \ mT)[ \pi ( \frac{0.01}{2} )^2][/tex]

[tex]\delta \phi = -7.85*10^8 \ Wb[/tex]

Using Faraday's Law; the induced emf on N turns of coil is;

[tex]\epsilon = N |\frac{ \delta \phi}{\delta t} |[/tex]

Also; the induced current I = [tex]\frac{ \epsilon}{R}[/tex]

[tex]\frac{ \delta q}{ \delta t} = \frac{1}{R} (N|\frac{\delta \phi}{\delta t } |)[/tex]

[tex]\delta q = \frac{1}{R} N|\delta \phi |[/tex]

[tex]\delta q = \frac{1}{0.30} (10)| -7.85*10^8 \ Wb |[/tex]

[tex]\delta q = 2.617*10^{-6} \ C[/tex]

The voltage across the capacitor can now be determined as:

[tex]\delta \ V =\frac{ \delta q}{C}[/tex]

= [tex]\frac{ 2.617*10^{-6} \ C}{3.0 \ *10^{-6} F}[/tex]

= 0.8723 V

Answer:

5026.55 m/s

Explanation:

Gravitation potential of a body in orbit from the center of the earth is given as

Pg = -GM/R

Where G is the gravitational constant 6.67x10^-11 N-m^2kg^-2

M is the mass of the earth = 5.98x10^24 kg

R is the distance from that point to the center of the earth = r + Re

r is the distance above earth surface, Re is the earth's radius.

R = 1610 km + 6370 km = 7980 km

Pg = -(6.67x10^-11 x 5.98x10^24)/7980x10^3

Pg = -49983208.02 J/kg

The negative sign means that the gravitational potential is higher away from earth than it is at the earth's surface (it shows convention).

This indicates the kinetic energy per kilogram that the chest of jewel will fall with to earth.

Gravitation Potential on earth's surface is

Pg = -GM/Re

= -(6.67x10^-11 x 5.98x10^24)/6370x10^3 = -62616326.53 J/kg

Difference in gravity potential = -49983208.02 - (-62616326.53)

= 12633118.51 J/kg

The velocity V of the jewel chest will be

0.5v^2 = 12633118.51

V^2 = 25266237.02

V = 5026.55 m/s

Answer:

0.106

Explanation:

For 1 liter of diesel the car can get 19 km, if it takes 0.2 MJ for each km then it would take the total energy of 19*0.2 = 3.8 MJ to move an aerodynamic car 19 km. Since 1 liter of of diesel also contains 36 MJ in internal energy, then the efficiency of the diesel engine is the ratio of its output energy over its input energy:

[tex]\frac{3.8}{36} = 0.106[/tex]

The efficiency of a diesel engine, in the given scenario, is found to be 10.56%. This is determined by considering the energy content of diesel fuel and the amount of work done by the engine.

Firstly, the energy content for a liter of diesel fuel is 36 MJ, and the car can travel 19 km with one liter of fuel. Thus, the total energy to travel 19 km is 19 km * 0.20 MJ/km = 3.8 MJ. The useful outcome is therefore 3.8 MJ from the total of 36 MJ. Therefore, applying the formula for efficiency which is Output Energy/Input Energy * 100%, gives a result of (3.8 MJ / 36 MJ) * 100% = 10.56%.

This indicates that the diesel engine is 10.56% efficient at converting the energy in diesel fuel into work to move the car, whereas the remaining energy is lost mainly due to heat, sound etc.

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Answer:

The frequency of the beat is  [tex]f_t = 8Hz[/tex]    

Explanation:

From the question we are told that

   The speed of the ride [tex]v = 6,2 m/s[/tex]

   The frequency of the oboe is  [tex]f = 440Hz[/tex]

    The temperature outside is  [tex]T = 27^oC[/tex]

Generally the speed of sound generated in air is mathematically evaluated as

             [tex]v_s = 331 + 0.61 T[/tex]

Substituting value

           [tex]v_s = 331 + 0.61 *27[/tex]

           [tex]v_s = 347.47 \ m/s[/tex]

The frequency of sound(generated by the musician on he park) getting to the musicians on the unicycle is mathematically evaluated as

                 [tex]f_a = \frac{v_s }{v_s - v} f[/tex]

substituting values

                [tex]f_a = \frac{347.47 }{347.47 - 6.2} * 440[/tex]                

               [tex]f_a = 448Hz[/tex]

Since the musician on the park is not moving the frequency of sound (from the musicians riding the unicycle )getting to him is  = 440Hz

    The beat frequency these musician here is mathematically evaluated as

                  [tex]f_t = f_a - f[/tex]  

So               [tex]f_t = 448 - 440[/tex]  

                  [tex]f_t = 8Hz[/tex]    

Answer:

23.5 mV

Explanation:

number of turn coil  'N' =22

radius 'r' =3.00 cm=> 0.03m

resistance = 1.00 Ω

B= 0.0100t + 0.0400t²

Time 't'= 4.60s

Note that Area'A' = πr²

The magnitude of induced EMF is given by,

lƩl =ΔφB/Δt = N (dB/dt)A

    =N[d/dt (0.0100t + 0.0400 t²)A        

    =22(0.0100 + 0.0800(4.60))[π(0.03)²]

     =0.0235

     =23.5 mV

Thus, the induced emf in the coil at t = 4.60 s is 23.5 mV

Answer:

Because all organisms are  

adapted

to their native habitat, human activities that result in  

habitat destruction

are the major reason for their extinction.

Explanation:

Answer:

Adapted

and

habitat destruction

Answer:

9

Explanation:

9×9 is 81, i hope this helpes

Answer:

9

Explanation:

Answer:

The period of the pendulum is  [tex]T = 1.68 \ sec[/tex]

Explanation:

The diagram illustrating this setup is shown on the first uploaded image

From the question we are told that

     The length of the rod is [tex]L = 80 \ cm[/tex]

       The diameter of the ring is [tex]d = 10 \ cm[/tex]

       The distance of the hole from the one end  [tex]D = 15cm[/tex]

From the diagram we see that point A is the center of the brass ring

 So the length from the axis of  rotation is mathematically evaluated as

          [tex]AP = 80 + 10 -5 -15[/tex]  

          [tex]AP = 70 \ cm = \frac{70}{100} = 0.7 \ m[/tex]

Now the period of the pendulum is mathematically represented as

             [tex]T = 2 \pi \sqrt{\frac{AP}{g} }[/tex]

             [tex]T = 2 \pi \sqrt{\frac{0.7}{9.8 } }[/tex]

             [tex]T = 1.68 \ sec[/tex]

Answer:

[tex]\phi=1.55 [eV][/tex]

Explanation:

We can use the work function equation for a photoelectric experiment:

[tex]\phi=\frac{hc}{\lambda}-K_{max}[/tex]

So we will have:

[tex]\phi=\frac{hc}{\lambda}-e\Delta V[/tex]

[tex]\phi=\frac{6.63*10^{-34}*3*10^{8}}{546.1*10^{-9}}-0.728eV[/tex]    

[tex]\phi=3.64*10^{-19}[J]-0.728 [eV][/tex]

[tex]\phi=(3.64*10^{-19}[J]*\frac{1eV}{1.6*10^{-19}[J]})-0.728 [eV][/tex]

[tex]\phi=2.28 [eV] - 0.728 [eV][/tex]

[tex]\phi=1.55 [eV][/tex]

I hope it helps you!

Answer:

The work function is [tex]\phi = 1.544eV[/tex]

Explanation:

   From the question we are told that

        The wavelength of the green light is [tex]\lambda = 546.1nm[/tex]

        The stopping potential   is  [tex]V= 0.728V[/tex]  

At  stopping potential the kinetic is also maximum because this where the electron(causing the current ) would flow at it highest speed before return to zero

   So the maximum  kinetic energy of this electron in term of electron volt is  

           [tex]KE_{max} = 0.728 eV[/tex]

This maximum kinetic energy is mathematically represented as

          [tex]KE_{max} = \frac{hc}{\lambda} - \phi[/tex]

Where h is the planck's constant with a value [tex]h = 4.1357 *10^{-15} eV[/tex]

            c is the speed of light [tex]c = 3.0 *10^8 m/s[/tex]

            [tex]\phi[/tex] is the work function

Making [tex]\phi[/tex] the subject of the formula

            [tex]\phi = \frac{hc}{\lambda} - KE_{max}[/tex]

Substituting values

           [tex]\phi = \frac{4.1357 *10^{-15} * (3.0 *10^8)}{546.1 *10^{-9}} - 0.728[/tex]

            [tex]\phi = 1.544eV[/tex]

From largest to smallest they are: Universe, galaxy, solar system, star, planet, moon and asteroid.

Explanation:Let's describe them from smallest to largest. In fact the size order is not exact as there are exceptions.An asteroid is a rocky body which lies in the asteroid belt between Mars and Jupiter. They are typically quite small object. The largest asteroid Ceres has been reclassified as a dwarf planet.A moon is typically a rocky body which is in orbit around a planet. Some moons such as our Moon are quite large and are typically bigger than asteroid. Some moons can actually be smaller than some asteroids.A planet is a nearly spherical body which is in orbit around the Sun. Planets are larger than moons.A star is what planets orbit around. It is the source of light and heat. Our Sun is a star which is many times bigger than all of the planets.A solar system is a star and all of its planets, asteroids, comets and other bodies. It is significantly bigger than a star.A galaxy, such as our Milky Way Galaxy, is a collection of solar systems orbiting around a central core. Most galaxies have a supermassive black hole at their centres.Galaxies also form clusters which are large scale structures.The universe is everything. It contains billions of galaxies. Lots of information RIGHT!!!!

YOUR VERY WelCoMe!!!!           :) :) :) :) :0 :)

Answer:

Universe, galaxy, solar system, star, planet, moon and asteroid. Hope this helped!

Answer:6 joules

Explanation:

Mass(m)=3kg

Velocity(v)=2m/s

Kinetic energy=0.5 x m x v^2

Kinetic energy=0.5 x 3 x 2^2

Kinetic energy=0.5 x 3 x 2 x 2

Kinetic energy=6

Answer:

33.4 litres/sec

Explanation:

Given:

hole area A = 0.0048 m²

Velocity is given by:

V =√2gh = √(2 x 9.8 x 2.5) = 7 m/sec

flow = A x V = (0.0048)(7) = 0.0334 m³/sec

0.0334 m³/sec => 33.4 litres/sec

No water leaks into the ship because the velocity of the water entering the hole is 0 m/s.

The volume of water leaking into the ship can be calculated using Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The volume of water displaced is equal to the volume of water leaking into the ship. The formula to calculate the volume of water leaking per second is: V = A * h * v, where V is the volume, A is the area of the hole, h is the height of the water above the hole, and v is the velocity of the water entering the hole. In this case, the area of the hole is given as 4.8 × 10-3 m2, the height of the water above the hole is 2.5 m, and we can assume the velocity of the water entering the hole is 0 m/s since the ship is floating on a lake and there is no external force pushing the water into the hole.

Using the formula, we can calculate the volume of water leaking per second:

V = (4.8 × 10-3 m2) * (2.5 m) * 0 m/s = 0 m3/s

Therefore, no water is leaking into the ship because the velocity of the water entering the hole is 0 m/s.

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Answer:

p₀ = (- 20,000 i - 17,000 j) kg m / s

vₓ = -10.81 m / s ,   v_{y} = - 9,189 m / s  

Explanation:

This exercise can be solved with the conservation of the moment.

The system is formed by the two cars, so the forces during the crash are internal and the moment is conserved

initial moment. Just before the crash

      p₀ = M v₁ + m v₂

where the masses M = 1000 kg with a velocity of v₁ = - 20 i m / s for traveling west, the second vehicle has a mass m = 850 kg and a velocity of v₂ = - 20 i m / s, we substitute

     p₀ = - 1000 20 i - 850 20 j

     p₀ = (- 20,000 i - 17,000 j) kg m / s

final moment. Right after the crash

how the cars fit together

      [tex]p_{f}[/tex] = (M + m) [tex]v_{f}[/tex]

the final speed is shaped

      v_{f} = vₓ i + v_{y} j

  we substitute

     p_{f} = (M + m) (vₓ i + v_{y} j)

     p_{f} = (1000 + 850) (vₓ i + [tex]v_{y}[/tex]j)

     p₀ = p_{f}

      (- 20000 i - 17000 j) = 1850 (vₓ i + v_{y} j)

we solve for each component

    vₓ = -20000/1850

    vₓ = -10.81 m / s

    v_{y} = -17000/1850

    v_{y} = - 9,189 m / s

Answer:

Explanation:

Initial kinetic energy = 29 J

work done against gravity = mgsin33 x d  , m is mass of the block

= 1.2 x 9.8 sin 33 x .9

= 5.76 J

potential energy stored in compressed spring

= 1/2 k x², k is spring constant and x is compression

= .5 x 200 x .3²

= 9

energy left = 29 - ( 5.76 + 9 )

= 14.24 J

b )

energy stored in spring when compression is .4 m

= 1/2 x 200 x .4²

= 16 J

required kinetic energy = 16 + 5.76

= 21.76 J

Block must be projected with energy of 21.76 J .

Answer:

See explaination

Explanation:

Please kindly check attachment for the step by step solution of the given problem.

The attached file has a detailed solution of the given problem.

Newton's second law allows us to find the average force for the impact of a particle against the wall of a container is:

        [tex]F = \frac{m v_x^2}{L_x}[/tex]  

Newton's second law is the change of the momentum with respect to time and the momentum is defined as the product of the mass and the velocity of the body.

           [tex]F = \frac{dp}{dt} \\p = m v[/tex]

where F is the force, p the moment, m the mass, t the time and v is the velocity.

Ask for the average force, therefore we change the differentials for variations.

           [tex]<F> = m \frac{\Delta v}{\Delta t}[/tex]  

They indicate that the velocity in the direction of the wall is vₓ and the mass of the container is much greater than the mass of the particle, they also indicate that the collision is elastic, therefore the speed of the particle before and after the collision is equal , but its address changes.

      Δv = vₓ - (-vₓ)

      Δv = 2 vₓ

The change in velocity occurs during the collision, in the rest of the motion the particle has a constant velocity, using the uniform motion relation.

         [tex]v = \frac{d}{t} \\t = \frac{d}{v}[/tex]  

The particle travels a distance Lₓ from inside the container to the wall and bounces, we can find the total time for the particle where the distance of the entire route is:

          d = 2 Lₓ

          t = [tex]\frac{2L_x}{v_x}[/tex]

Let's substitute in Newton's second law.

     [tex]<F>= \frac{m \ 2v_x}{ \frac{2L_x}{v_x} } \\<F>= \frac{m v_x^2}{L_x}[/tex]

In conclusion, using Newton's second law we can find the average force for the collision of a particle against the wall of a container is:

         [tex]<F> = \frac{m \ v_x^2}{L_x}[/tex]  

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Answer:

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Explanation:

Answer:

plants depend on animals for CO2 (to use during photosynthesis) while animals depend on plants for food (consumation)

Explanation:

Answer:

plants depend on animals for CO2 (to use during photosynthesis) while animals depend on plants for food (consumation)

Explanation:

Answer:

a) 750W

b) 800W

  1018.9W

c) the circular frame

Explanation:

a) To find the electric flux you use the following formula:

[tex]\Phi_E=EAcos\theta=EA[/tex]

where you have assumed that the plane of the loop and B are perpendicular between them.

By replacing you obtain:

[tex]\Phi_E=(2*10^4N/C)(0.25m)(0.15m)=750W[/tex]

b) In order to calculate the electric flux in a square frame you first calculate the perimeter of the rectangular frame of wire:

P = 0.25m+0.25m+0.15m+0.15m=0.8m

A square with this length will have sides of 0.2m

Hence. you have that the electric flux is:

[tex]\Phi_E=(2*10^4N/C)(0.2m)^2=800W[/tex]

for a circular frame you have that the radius is:

[tex]s=2\pi r\\\\r=\frac{s}{2\pi}=\frac{0.8m}{2\pi}=0.127m[/tex]

Then, the electric flux will be:

[tex]\Phi_E=(2*10^4N/C)(\pi)(0.127m)^2=1018.9W[/tex]

c) The electric flux is maximum in the circular frame.

Answer:

Energy density, [tex]E=3.11\times 10^4\ J[/tex]

Explanation:

It is given that,

Magnetic field in a solenoid is 0.28 T

We need to find the energy density of the field. The energy density of the magnetic field is given by below formula as follows :

[tex]E=\dfrac{B^2}{2\mu_o}\\\\E=\dfrac{(0.28)^2}{2\times 4\pi \times 10^{-7}}\\\\E=3.11\times 10^4\ J[/tex]

So, the energy density of this field is [tex]3.11\times 10^4\ J[/tex].

Answer:

1.25 kgm²/sec

Explanation:

Disk inertia, Jd =

Jd = 1/2 * 3.7 * 0.40² = 0.2960 kgm²

Disk angular speed =

ωd = 0.1047 * 30 = 3.1416 rad/sec

Hollow cylinder inertia =

Jc = 3.7 * 0.40² = 0.592 kgm²

Initial Kinetic Energy of the disk

Ekd = 1/2 * Jd * ωd²

Ekd = 0.148 * 9.87

Ekd = 1.4607 joule

Ekd = (Jc + 1/2*Jd) * ω²

Final angular speed =

ω² = Ekd/(Jc+1/2*Jd)

ω² = 1.4607/(0.592+0.148)

ω² = 1.4607/0.74

ω² = 1.974

ω = √1.974

ω = 1.405 rad/sec

Final angular momentum =

L = (Jd+Jc) * ω

L = 0.888 * 1.405

L = 1.25 kgm²/sec

To find the final angular momentum of the system, we can apply the principle of conservation of angular momentum. The initial angular momentum of the turntable is equal to its final angular momentum, which can be determined using the moment of inertia and final angular velocity of the system.

The final angular momentum of the system can be determined by applying the principle of conservation of angular momentum. Since no external torques act on the system, the angular momentum of the system remains constant. Initially, the turntable has an angular momentum given by L1 = I1ω1, where I1 is the moment of inertia of the turntable and ω1 is its initial angular velocity. After the hollow cylinder slips on the turntable and acquires the same final angular velocity, the system's angular momentum becomes L2 = I1ω2. Setting L1 = L2 and solving for ω2 gives us the final angular velocity of the system. Finally, we can use the moment of inertia of the turntable to calculate its final angular momentum, Lf = I1ω2.

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