A toy car having mass m = 1.50 kg collides inelastically with a toy train of mass M = 3.60 kg. Before the collision, the toy train is moving in the positive x-direction with a velocity of Vi = 2.45 m/s and the toy car is also moving in the positive x-direction with a velocity of vi = 4.75 m/s. Immediately after the collision, the toy car is observed moving in the positive x-direction with a velocity of 2.15 m/s.

(a) Determine Vf, the final velocity of the toy train.

Answer:

C) Because it takes less heat to raise the temperature of the metal

Explanation:

A) No. Metals have low specific heats compared to other solids thus they would absorb less heat in order to increase the temperature

B) No. Since they have lower specific heats they are more vulnerable to temperature changes due to variations in the heat rate

C) Yes. It takes less heat to raise the temperature of water due to their lower specific heats

D) No. Because the temperature can be chosen regulating the heat rate to the cookware. Also food burning is related with thermal conduction of cookware and from the cookware to food.

Answer:

C is correct

Explanation:

Answer:

(a) 2.5 cm

(b) Yes

Solution:

As per the question:

Mass of Uranium-235 ion, m = [tex]3.95\times 10^{- 25}\ kg[/tex]

Mass of Uranium- 238, m' = [tex]3.90\times 10^{- 25}\ kg[/tex]

Velocity, v = [tex]3.00\times 10^{5}\ m/s[/tex]

Magnetic field, B = 0.250 T

q = 3e

Now,

To calculate the path separation while traversing a semi-circle:

[tex]\Delta x = 2(R_{U_{35}} - 2R_{U_{38}})[/tex]

The radius of the ion in a magnetic field is given by:

R = [tex]\frac{mv}{qB}[/tex]

[tex]\Delta x = 2(R_{U_{35}} - 2R_{U_{38}})[/tex]

[tex]\Delta x = 2(\frac{mv}{qB} - \frac{m'v}{qB})[/tex]

[tex]\Delta x = 2(\frac{m - m'}{qB}v)[/tex]

Now,

By putting suitable values in the above eqn:

[tex]\Delta x = 2(\frac{3.95\times 10^{- 25} - 3.90\times 10^{- 25}}{3\times 1.6\times 10^{- 19}\times 0.250}\times 3.00\times 10^{5}) = 2.5\ cm[/tex]

[tex]\Delta x = 1.25\ cm[/tex]

(b) Since the order of the distance is in cm, thus clearly this distance is sufficiently large enough in practical for the separation of the two uranium isotopes.

In a mass spectrometer, uranium-235 and uranium-238 ions can be separated based on their masses and velocities. The separation distance between their paths can be determined using the equation: d = mv/(qB). The distance between their paths is practical for the separation of uranium-235 from uranium-238.

In a mass spectrometer, triply charged uranium-235 and uranium-238 ions are separated based on their masses and velocities.

The separation of their paths when they hit a target after traversing a semicircle can be calculated using the equation:

d = mv/(qB)

where d is the separation, m is the mass of the ion, v is the velocity, q is the charge, and B is the magnetic field.

The distance between their paths seems to be big enough to be practical in the separation of uranium-235 from uranium-238, as even a small separation can result in significant enrichment over multiple passes through the mass spectrometer.

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Answer:

[tex]t = 2\ s[/tex]

Explanation:

given,

length of the rope = 16 m

speed of the man = 2 m/s

using the formula of time period

[tex]T =2 \pi \sqrt{\dfrac{L}{g}}[/tex]

[tex]T =2 \pi \sqrt{\dfrac{16}{9.8}}[/tex]

[tex]T = 8.028\ s[/tex]

To cover the maximum distance you need to leave the when the rope is shows maximum displacement.

To reach the displacement time to leave the rope is one fourth of the time period.

[tex]t = \dfrac{T}{4}[/tex]

[tex]t = \dfrac{8.03}{4}[/tex]

[tex]t = 2\ s[/tex]

The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.

The total time taken to hang on if you want to drop into the water at the greatest possible distance from the edge is 2 seconds.

The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.

It can be given as,

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

Here, [tex]g[/tex] is the gravitational force of Earth.

Given information-

Total length of the rope is 16 m.

The speed of the man is 2.0 m/s.

Let the time of to swing by rope both side is [tex]T[/tex]. Thus put the values in the above formula as,

[tex]T=2\pi\sqrt{\dfrac{16}{9.8}}[/tex]

[tex]T=8.028 \rm s[/tex]

Now the greatest possible distance from the edge will be at the greatest displacement.

Thus the time to cove the greatest possible distance will be one forth (1/4) of the total time. Thus,

[tex]t=\dfrac{8.028 }{4}\\t=2\rm s[/tex]

Hence, the total time taken to hang on if you want to drop into the water at the greatest possible distance from the edge is 2 seconds.

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Answer:

2.9744 MW

Explanation:

The air blowing through the wind turbine at 110000kg at speed of 13m/s for every second would have the kinetic energy of

[tex]E_k = 0.5mv^2 = 0.5*110000*13^2 = 9295000J/s[/tex]

If the wind turbine is able to extract only 40% of this kinetic energy, and 80% of this is converted to electricity, then the power output of the generator must be

[tex]E = 80\%*40\%*E_k = 0.8*0.4*9295000= 2974400J/s[/tex]

or 2.9744 MegaWatt

The total power output of the wind turbine is calculated by first finding the kinetic energy of the wind, and then determining the amount of that energy that is harvested and converted into electricity. The wind turbine extracts 40% of the kinetic energy, and 80% of this energy is converted into electricity, resulting in a power output of 2.974 gigawatts.

To calculate the power output of the generator, we'll first need to compute the kinetic energy of the air moving through the turbine. The equation for kinetic energy is given by: KE = 0.5*mass*velocity^2.

So, the kinetic energy of the air per second is KE = 0.5*110,000 kg*(13 m/s)^2 = 9.295 gigajoules per second. Since the wind turbine extracts 40% of this energy, the energy extracted would be 3.718 gigajoules per second.

Of this extracted energy, 80% is converted to electric energy, which corresponds to 2.974 gigajoules per second. Because power is defined as the energy transferred or converted per unit of time, and here the energy is given per second, the power output is therefore 2.974 gigawatts.

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Answer:

The magnetic force on electron 1 by electron 2=[tex]9.22\times 10^{-15} N[/tex]

Explanation:

We are given that

Distance between two electrons=10 nm

Speed of electron 1=[tex]4.5\times 10^7[/tex] m/s

Speed of electron 2=[tex]8.0\times 10^6[/tex] m/s

We have to find the magnitude of the magnetic force exerted  by electron 2 on electron 1.

Magnetic force on electron 1 by electron 2

[tex]F=\frac{\mu_0e^2v_1v_2}{4\pi r^2}[/tex]

[tex]\frac{\mu_0}{4\pi}=10^{-7}[/tex]

[tex]e=1.6\times 10^{-19} C[/tex]

[tex]v_1=4.5\times 10^7 m/s[/tex]

[tex]v_2=8.0\times 10^6 m/s[/tex]

[tex]r=10nm=10\times 10^{-9}m[/tex] [tex](1nm=10^{-9} m[/tex])

Substitute the values in the given formula

The magnetic force on electron 1 by electron 2=[tex]\frac{10^{-7}\times (1.6\times 10^{-19})^2\times 4.5\times 10^7\times 8\times 10^6}{(10\times 10^{-9})^2}[/tex]

The magnetic force on electron 1 by electron 2=[tex]9.22\times 10^{-15} N[/tex]

Hence, the magnetic force on electron 1 by electron 2=[tex]9.22\times 10^{-15} N[/tex]

The magnitude of the magnetic force exerted by electron 2 on electron 1 is [tex]9.22\times10^{-15}[/tex] N.

Magnetic force is the force of attraction of repulsion between two poles of the two magnets. The magnetic force is also appears between two electrically charged bodies.

The magnetic force can be given as,

[tex]F=\dfrac{\mu_oq_1q_2(v_1v_2)}{4\pi r^2}[/tex]

Here, ([tex]\mu_o[/tex]) is the magnetic constant, (q) is the charge on the body, (v) is the speed of the body and (r) is the distance between them.

The distance between the electrons 1 and 2 is 10 nm. As the speed of the electron 1 is [tex]4.5 \times10^7[/tex] m/s and the speed of the electron 2 is [tex]8.0 \times10^6[/tex] m/s.

Thus, put the values in the above formula as,

[tex]F=\dfrac{4\pi \times10^{-7}\times1.6\times10^{-19}\times1.6\times10^{-19}\times4.5\times10^{7}(8.0\times10^6)}{4\pi (10^{-9})^2}[/tex]

[tex]F=9.22\times10^{-15}\rm N[/tex]

Thus the magnitude of the magnetic force exerted by electron 2 on electron 1 is [tex]9.22\times10^{-15}[/tex] N.

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To solve this physics problem involving Young's double-slit experiment, we apply the conditions for constructive interference to determine the angles θ1 and θ2 for the first and second bright fringes. We then use the small angle approximation to determine the distance y between those fringes on the screen. Lastly, we substitute the given values into the formula to compute the numerical value of y.

The topic at hand is Young's double-slit experiment, a foundational experiment in wave optics. Given the slit separation d, the laser light's wavelength λ, and the screen's distance L, we need to find the distance between two bright fringes on the screen. The formulas required here stem from the conditions for constructive interference in double-slit set-ups.

Part a) sin(θ1) = λ/d, which is the condition for the light to interfere constructively at the first bright fringe from the center on the screen.

Part b) sin(θ2) = 2λ/d, which gives us the location of the second bright fringe, as it occurs when the path differential is twice the wavelength.

Part c) The distance y between the two bright fringes on the screen can be found using the small angle approximation, which allows us to express the angles θ1 and θ2 in terms of the fringe order m. Thus, y ≈ L*(θ2 - θ1) = L*(2λ/d - λ/d) = L*λ/d.

Part d) Substituting the given values into the formula from Part c, we find y = 1.6m * (4750Å / 0.038mm), which gives us a numerical value once we make sure to convert the units properly. In this case, we need to convert Å to mm by multiplying 4750Å by 10^-4 mm/Å.

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The question is about Young's double-slit experiment in physics. Both θ1 and θ2 are expressed in terms of d (the separation between the slits) and λ (the wavelength of the laser light). The distance between the fringes on the screen is calculated using these variables, resulting in a numerical value in meters.

The questions refer to the phenomenon of light diffraction and interference, particularly as it relates to Young's double-slit experiment. In this context, we'll use the formulas defined for this experiment:

For parts (a) and (b): we know that the condition for constructive interference, resulting in bright fringes, for a double-slit setup is given by:

d sin θ = mλ

where 'd' is the slit separation, 'θ' is the angle to the fringe from the central maximum, 'm' is the order of the fringe and 'λ' is the wavelength of the light. For the first fringe (m=1), sin(θ1) = λ/d and for the second fringe (m=2), sin(θ2) = 2λ/d.

For part (c): Considering small angles where tan θ is approximately equal to sin θ, the separation of two bright fringes 'y' on the screen is given by:

y = L (θ2 - θ1) = L λ/d.

For part (d): Now, we just need to substitute the values given into the above formula. Substituting the given values of L = 1.6 m, λ = 4750 Å (which is equivalent to 4750 x 10^-10 m), and d = 0.038 mm (or 0.038 x 10^-3 m), you get:

y = L λ/d ≈ 0.02 m.

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Answer:

b. 0.75 mm

Explanation:

The distance between antinodes d is half the wavelength [tex]\lambda[/tex]. We can obtain the wavelength with the formula [tex]v=\lambda f[/tex], where f is the frequency given ([tex]f=1MHz=1\times10^6Hz[/tex]) and v is the speed of sound in body tissues (v=1540m/s), so putting all together we have:

[tex]d=\frac{\lambda}{2}=\frac{v}{2f}=\frac{1540m/s}{2(1\times10^6Hz)}=0.00077m=0.77mm[/tex]

which is very close to the 0.75mm option.

For the development of this problem it is necessary to apply the concepts related to the wavelength depending on the frequency and speed of light.

By definition we know that frequency can be expressed as

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

Where,

v = Velocity

[tex]\lambda =[/tex] Wavelength

Our values are

[tex]v=345m/sec[/tex]

[tex]f=850Hz[/tex]

Re-arrange to find Wavelength

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

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

[tex]\lambda = \frac{345}{850}[/tex]

[tex]\lambda = 0.4058m[/tex]

Converting to centimeters,

[tex]\lambda = 0.4058m(\frac{100cm}{1m})[/tex]

[tex]\lambda = 40.58cm[/tex]

Therefore the wavelength of the sound waves in the tube is 40.58cm

Answer:

D. Entropy is a measure of disorder or randomness

Explanation:

The answer is entropy. It is the method to measure any disorder or randomness of any system. Basically it is concept of physics and chemistry but can also be used in other subject matters as well. In formula terms, it is denoted by S and is measurement value is "Joule per kelvin". The values could be both positive and negative as well.

All the other options are incorrect as heat, energy and temperature are the different concepts of science which do not relates with any measurement.

To solve this problem it is necessary to apply the equations given in Newton's second law as well as Hooke's Law.

Since Newton's second law we have that force is

F = mg

Where,

m = mass

g = gravity

From the hook law, let us know that

F = -kx

Where

k = Spring constant

x = Displacement

Re-arrange to find k,

[tex]k = -\frac{F}{x}[/tex]

PART A ) We can replace the Newton definitions here, then

[tex]k = -\frac{mg}{x}[/tex]

Replacing with our values we have that

[tex]k = \frac{120*9.8}{-0.75*10^{-2}}[/tex]

[tex]k = 1.57*10^5N/m[/tex]

Therefore the required value of the spring constant is [tex]1.57*10^5N/m[/tex]

PART B) We can also equating both equation to find the mass, then

[tex]mg = -kx[/tex]

[tex]m = \frac{-kx}{g}[/tex]

Replacing with tour values we have

[tex]m = \frac{1.568*10^5(-9.48*10^{-2})}{9.8}[/tex]

[tex]m = 76.8Kg[/tex]

Therefore the mass of the player can be of 76.8Kg, then the player is eligible to play because the mass is less than 85Kg

Final answer:

The spring's effective force constant is 156,800 N/m. The player is eligible to play on the under-85-kg team.

Explanation:

Using Hooke's law, the effective force constant of the spring can be calculated by dividing the maximum load by the displacement. In this case, the spring is depressed by 0.75 cm under a maximum load of 120 kg.

To find the effective force constant, we can use the formula:

F = k * x

Where F is the force, k is the force constant, and x is the displacement.

So, the effective force constant of the spring is:

k = F / x = 120 kg * 9.8 N/kg / 0.0075 m = 156,800 N/m

For part (b), we can use the same formula to determine if the player is eligible to play on the under-85-kg team. Given that the player depresses the spring by 0.48 cm, we can plug in the values to calculate the force:

F = k * x = 156,800 N/m * 0.0048 m = 753.6 N

Since the force exerted by the player is less than 85 kg * 9.8 N/kg, the player is eligible to play on the under-85-kg team.

Answer:

The wavelength is 742.7 nm.

Explanation:

Given that,

Grating = 4500 lines/cm

Angle = 42°

Order number =2

We need to calculate the distance

[tex]d=\dfrac{1\times10^{-2}}{4500}[/tex]

[tex]d=2.22\times10^{-6}\ m[/tex]

We need to calculate the wavelength

Using diffraction formula

[tex]d\sin\theta=m\times\lambda[/tex]

[tex]\lambda=\dfrac{d\sin\theta}{m}[/tex]

[tex]\lambda=\dfrac{2.22\times10^{-6}\times\sin42}{2}[/tex]

[tex]\lambda=7.427\times10^{-7}[/tex]

[tex]\lambda=742.7\ nm[/tex]

Hence, The wavelength is 742.7 nm.

The wavelength of this light was found to be 7.08 × 10⁻⁴ m.

To find the wavelength of light that results in a second-order maximum at a 42° angle when striking a diffraction grating with 4500 lines per centimeter, we use the formula for diffraction grating: d sin θ = mλ, where d is the distance between adjacent grating lines, θ is the angle of the maximum, m is the order of the maximum, and λ is the wavelength of the light. First, calculate the distance between grating lines (d) as the reciprocal of the grating's line density (4500 lines/cm or 4.5×105 lines/m), yielding d = 1/4.5×105 m. Then, substituting the given values into the formula with m = 2 and θ = 42°, solve for the wavelength λ.
λ = (1/4.5×105) * sin(42°) / 2
  = 7.08 × 10⁻⁴ m

To solve the problem it is necessary to apply the concepts related to Newton's second law, as well as to the sum of forces in this type of bodies.

According to the description I make a diagram that allows a better understanding of the problem.

Performing sum of forces in the angular direction in which it is inclined we have to

[tex]\sum F = ma_{\theta}[/tex]

[tex]N - W cos\theta = ma_{\theta}[/tex]

[tex]N = ma_{\theta}+Wcos\theta[/tex]

Tangential acceleration can be expressed as

[tex]a_{\theta} = (r\ddot{\theta}+2\dot{r}\dot{\theta})[/tex]

Our values are given by,

[tex]\dot{\theta} = 2.9rad/s[/tex]

[tex]m = 0.15 lb[/tex]

[tex]\theta = 36\°[/tex]

[tex]v = 4.8ft/s[/tex]

Substituting [tex]\ddot{\theta}=0rad/s^2 ,  \dot{r}=-4.8ft/s, \dot{\theta}=2.9 rad/s[/tex]

[tex]a_{\theta} = r*0+2*(4.8*2.9)\\a_{\theta}=27.84ft/s^2[/tex]

At the same time we acan calculate the mass of the particle, then

W = mg

Where,

W = Weight of the particle

m = mass

g = acceleration due to gravity

[tex]0.15lb = m(32.2ft/s^2)[/tex]

[tex]m = 4.66*10^{-3}Lb[/tex]

Now using our first equation we have that

[tex]N = ma_{\theta}+Wcos\theta[/tex]

[tex]N = (4.66*10^{-3})(27.84)+0.2cos36[/tex]

[tex]N = 0.2914Lb[/tex]

Therefore the normal force exerted by the wall of the tube on the particle at this instant is 0.2914Lb

The magnitude of the normal force [tex]\( N \)[/tex] exerted by the wall of the tube on the particle at the instant when the angle [tex]\( \theta = 36^\circ \)[/tex] is approximately 0.249 lb

To determine the normal force [tex]\( N \)[/tex]exerted by the wall of the tube on the particle, we analyze the forces acting on the particle in a rotating reference frame. Here’s the step-by-step process:

1. Identify the given data:

  - Angular velocity [tex]\( \omega = 2.9 \)[/tex] rad/sec

  - Particle weight [tex]\( W = 0.15 \)[/tex] lb

  - Relative velocity towards O [tex]\( v_r = 4.8 \)[/tex] ft/sec

  - Angle [tex]\( \theta = 36^\circ \)[/tex]

2. **Convert the weight to mass:**

  -[tex]\( W = mg \)[/tex]

  -[tex]\( m = \frac{W}{g} \)[/tex]

  - Using[tex]\( g = 32.2 \text{ ft/sec}^2 \)[/tex]:

  - [tex]\( m = \frac{0.15 \text{ lb}}{32.2 \text{ ft/sec}^2} = 0.00466 \text{ slugs} \)[/tex]

3. Calculate the distance ( r ):

  - Since [tex]\( v_r = 4.8 \)[/tex] ft/sec is towards O and the tube is rotating with [tex]\( \omega \),[/tex] the distance [tex]\( r \)[/tex] can be found using [tex]\( r = \frac{v_r}{\omega} \)[/tex]:

  - [tex]\( r = \frac{4.8 \text{ ft/sec}}{2.9 \text{ rad/sec}} = 1.655 \text{ ft} \)[/tex]

4. **Determine the forces:**

  - Centrifugal force [tex]\( F_c = m \omega^2 r \)[/tex]:

   [tex]\[ F_c = 0.00466 \text{ slugs} \times (2.9 \text{ rad/sec})^2 \times 1.655 \text{ ft} = 0.0638 \text{ lb} \][/tex]

  - Component of gravitational force in the radial direction [tex]\( F_{g, r} = W \cos \theta \)[/tex]:

 [tex]\[ F_{g, r} = 0.15 \text{ lb} \times \cos 36^\circ = 0.1214 \text{ lb} \][/tex]

5. Calculate the normal force [tex]\( N \)[/tex]:

  - Normal force [tex]\( N \)[/tex] must balance the radial forces:

[tex]\[ N = F_c + F_{g, r} + m \cdot (\omega^2 r) \][/tex]

[tex]\[ N = 0.0638 \text{ lb} + 0.1214 \text{ lb} + 0.0638 \text{ lb} \][/tex]

 [tex]\[ N = 0.249 \text{ lb} \][/tex]

Answer:

Explanation:

Given

Radius of A is twice of B i.e.

[tex]R_A=2R_B[/tex]

Also Potential of both sphere is same

[tex]V_A=V_B[/tex]

[tex]V=\frac{kQ}{R}[/tex]

thus

[tex]k\frac{Q_A}{R_A}=K\frac{Q_B}{R_B}[/tex]

[tex]\frac{Q_A}{Q_B}=\frac{R_A}{R_B}[/tex]

[tex]\frac{Q_A}{Q_B}=\frac{2}{1}=2[/tex]

[tex]\frac{Q_B}{Q_A}=\frac{1}{2}[/tex]

(b)Ratio of [tex]\frac{E_B}{E_A}[/tex]

Electric Field is given by [tex]E=\frac{kQ}{R^2}[/tex]

thus [tex]E_A=\frac{kQ_A}{R_A^2}[/tex]----1

[tex]E_B=\frac{kQ_B}{R_B^2}[/tex]----2

Divide 2 by 1

[tex]\frac{E_B}{E_A}=\frac{Q_B}{R_B^2}\times \frac{R_A^2}{Q_A}[/tex]

[tex]\frac{E_B}{E_A}=\frac{1}{2}\times 4=2[/tex]

The ratio QB/QA for the charges on the spheres is 2, and the ratio EB/EA for the magnitudes of the electric field at the surfaces of the spheres is 1/2.

The question revolves around the principles of electric fields and electric charges on two spherical objects. The spheres in question here are metal and have different sizes, but they hold the same electric potential at their surfaces. This situation is governed by the principles of physics, specifically electrostatics.

To solve this, we begin by noting that the electric potential (V) at the surface of a charged sphere is given by the equation V = KQ/r, where K is Coulomb's constant, Q is the charge on the sphere, and r is the radius of the sphere. Since the potential is the same for both spheres, we get that QA/2R = QB/R. Simplifying, we get the ratio QB/QA = 2.

Next, we calculate the electric field. The electric field (E) at the surface of a charged sphere is given by E = KQ/r^2. Therefore, EA = K×QA/(2R)^2 and EB = K×QB/R^2. Inserting the earlier found ratio of QB/QA = 2, the ratio EB/EA simplifies to 1/2.

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Answer:

Thus, if field were sampled at same distance, the field due to short wire is greater than field due to long wire.

Explanation:

The magnetic field, B of long straight wire can be obtained by applying ampere's law

[tex]B= \frac{\mu_0 I}{2\pi r}[/tex]

I is here current, and r's the distance from the wire to the field of measurement.

The magnetic field is obviously directly proportional to the current wire. From this expression.

As the resistance of the long cable is proportional to the cable length, the short cable becomes less resilient than the long cable, so going through the short cable (where filled with the same material) is a bigger amount of currents. If the field is measured at the same time, the field is therefore larger than the long wire because of the short wire.

Answer:

W = 0.384 J

Explanation:

Work and energy in the rotational movement are related

    W = ΔK = [tex]K_{f}[/tex] - K₀

    W = ½ I [tex]w_{f}[/tex]² - 1 /2 I w₀²

where W isthe work, I is the moment of inertia and w angular velocity

With the system part of the rest the initial angular speed is zero (w₀ = 0)

The angular and linear quantities are related

    v = w r

    w = v / r

Let's replace

    W = ½ I (v / r)²

Let's calculate

    W = ½  1.2 10⁻⁴ 1.2² / (1.5 10⁻²)²

    W = 0.384 J

    W = 38.4 J

Answer:[tex]\alpha =10.66 rad/s^2[/tex]

Explanation:

Given

mass of disk [tex]m=5 kg[/tex]

diameter of disc [tex]d=30 cm[/tex]

Force applied [tex]F=4 N[/tex]

Now this force will Produce  a  torque of magnitude

[tex]T=F\cdot r[/tex]

[tex]T=4\dot 0.15[/tex]

[tex]T=0.6 N-m[/tex]

And Torque is given Product of moment of inertia and angular acceleration [tex](\alpha )[/tex]

[tex]T=I\cdot \alpha [/tex]

Moment of inertia for Disc [tex]I= \frac{Mr^2}{2}[/tex]

[tex]I=0.05625 kg-m^2[/tex]

[tex]0.6=0.05625\cdot \alpha [/tex]

[tex]\alpha =10.66 rad/s^2[/tex]

Question is Incomplete, Complete question is given below.

Current flowing in a circuit depends on two variables. Identify these variables and their relationship to current.

A) Current is proportionate to the conductance of the circuit and precisely proportional to the voltage applied across the circuit.

B) Current is conversely proportional to the electrical tension of the circuit and corresponds to the resistance across the circuit.

C) Current is inversely proportional to the resistance of the circuit and directly proportional to the voltage applied across the circuit.

D) Current is commensurate to the resistance of the circuit and directly proportional to the electric pressure applied across the circuit.

Answer:

C) Current is inversely proportional to the resistance of the circuit and directly proportional to the voltage applied across the circuit.

Explanation:

Now Ohms Law states that, "So long as a physical state of a conductor remains the potential difference applied to the conductor is directly proportional to current flowing through it."

I ∝ V

V=IR also I=V/R

where R is the Resistance

Hence, From above equation we can say that Current increases when there is increase in Voltage but Current decreases as the resistance decreases.

Hence,Current is inversely proportional to the resistance of the circuit and directly proportional to the voltage applied across the circuit.

Answer:

29J

Explanation:

Please see attachment .

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

According to the information, the magnetic field INSIDE the plates is,

[tex]B=\frac{1}{2} \mu \epsilon_0 r[/tex]

Where,

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

[tex]\epsilon_0 =[/tex]Electromotive force

r = Radius

From this deduction we can verify that the distance is proportional to the field

[tex]B \propto r[/tex]

Then the distance relationship would be given by

[tex]\frac{r}{R} = \frac{B}{B_{max}}[/tex]

[tex]r =\frac{B}{B_{max}} R[/tex]

[tex]r = \frac{0.5B_{max}}{B_{max}}R[/tex]

[tex]r = 0.5R[/tex]

On the outside, however, it is defined by

[tex]B = \frac{\mu_0 i_d}{2\pi r}[/tex]

Here the magnetic field is inversely proportional to the distance, that is

[tex]B \not\propto r[/tex]

Then,

[tex]\frac{r}{R} = \frac{B_{max}{B}}[/tex]

[tex]r = \frac{B_{max}{B}}R[/tex]

[tex]r = \frac{B_{max}{0.5B_{max}}}R[/tex]

[tex]r = 2R[/tex]

Answer:

Impulse = 18.53 kg m / s

Net force = 1853N

Explanation:

Mass of the ball, m = 0.4 kg

Initial velocity = 20 m/s horizontally left

Final velocity = 30 m/s at 45 degrees from horizontal

Time of collision = 0.010 s

Check attachment to see full explanation

The impulse and the average net force is 16.484 Ns and 1648.4 N respectively.

To calculate the impulse of the ball, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

To calculate the average force, we use the formula below.

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The impulse and the average net force is 16.484 Ns and 1648.4 N respectively.

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The gravitational potential energy is 2526 J

Explanation:

The gravitational potential energy (GPE) of an object is the energy possessed by the object due to its position in the gravitational field. Near the Earth's surface, it can be calculated as

[tex]GPE=mgh[/tex]

where

m is the mass of the body

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

h is the height of the object

In this problem, we have

m = 84.8 kg

h = 3.04 m

Substituting,

[tex]GPE=(84.8)(9.8)(3.04)=2526 J[/tex]

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Explanation:

Given that,

(a) Speed, [tex]v=6.66\times 10^6\ m/s[/tex]

Mass of the electron, [tex]m_e=9.11\times 10^{-31}\ kg[/tex]

Mass of the proton, [tex]m_p=1.67\times 10^{-27}\ kg[/tex]

The wavelength of the electron is given by :

[tex]\lambda_e=\dfrac{h}{m_ev}[/tex]

[tex]\lambda_e=\dfrac{6.63\times 10^{-34}}{9.11\times 10^{-31}\times 6.66\times 10^6}[/tex]

[tex]\lambda_e=1.09\times 10^{-10}\ m[/tex]

The wavelength of the proton is given by :

[tex]\lambda_p=\dfrac{h}{m_p v}[/tex]

[tex]\lambda_p=\dfrac{6.63\times 10^{-34}}{1.67\times 10^{-27}\times 6.66\times 10^6}[/tex]

[tex]\lambda_p=5.96\times 10^{-14}\ m[/tex]

(b) Kinetic energy, [tex]K=1.71\times 10^{-15}\ J[/tex]

The relation between the kinetic energy and the wavelength is given by :

[tex]\lambda_e=\dfrac{h}{\sqrt{2m_eK}}[/tex]

[tex]\lambda_e=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 9.11\times 10^{-31}\times 1.71\times 10^{-15}}}[/tex]

[tex]\lambda_e=1.18\times 10^{-11}\ m[/tex]

[tex]\lambda_p=\dfrac{h}{\sqrt{2m_pK}}[/tex]

[tex]\lambda_p=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 1.67\times 10^{-27}\times 1.71\times 10^{-15}}}[/tex]

[tex]\lambda_p=2.77\times 10^{-13}\ m[/tex]

Hence, this is the required solution.

Answer:

T=5797.8  K

Explanation:

Given that

Power P = 3.9 x 10²⁶ W

Radius ,r= 6.96 x 10⁸ m

We know that ,From Plank's law

P = σ A T⁴

σ = 5.67 x 10 ⁻⁸

A= Area ,T= Temperature ( in Kelvin)

[tex]T=\left (\dfrac{P}{\sigma A} \right )^{\dfrac{1}{4}}[/tex]

Now by putting the values

[tex]T=\left (\dfrac{P}{\sigma A}\right )^{\dfrac{1}{4}}[/tex]

[tex]T=\left (\dfrac{3.9\times 10^{26}}{5.67\times 10^{-8}\times 4\times \pi \times (6.96\times 10^8)^2} \right )^{\dfrac{1}{4}}[/tex]

T=5797.8  K

The temperature of surface will be 5797.8 K

The surface temperature of the sun can be calculated using the Stefan-Boltzmann law, which describes how the energy a perfect blackbody emits is related to its temperature. Knowing the radiant power and the surface area of the sun, we can use this law to find the surface temperature in kelvins.

To calculate the surface temperature of the sun, we can make use of the Stefan-Boltzmann law ( radiant power, surface area of the object, and temperature in kelvins), a principle in Physics that describes how the total energy a perfect blackbody like the sun emits is related to its temperature. The law is represented mathematically as P = σ A T^4, where P is the radiant power, A is the surface area, T is the temperature, and σ is Stefan-Boltzmann constant (5.67 x 10^-8 J/(s.m².K^4)). Given that the sun's radiant power is approximately 3.9 x 10^26 W and its radius is 6.96 x 10^8 m (meaning its surface area is 4πr^2), we can rearrange the equation and solve for T to find the sun's surface temperature in kelvins: T = (P/ σA) ^ (1/4).

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Answer:

(a) Current will be [tex]17.857\times 10^{-12}A[/tex]

(b) Number of ions will be [tex]8.258\times 10^6[/tex]

Explanation:

We have given that resistance of the biological cell [tex]R=4.2\times 10^9ohm[/tex]

(a) We have given potential difference of 75 mV

So [tex]V=75\times 10^{-3}volt[/tex]

From ohm's law we know that current is given by

[tex]i=\frac{V}{R}=\frac{75\times 10^{-3}}{4.2\times 10^9}=17.857\times 10^{-12}A[/tex]

(b) We have given time t = 0.74 sec

We have to find the charge

We know that charge is given by Q = it, here i is current and t is time  

So charge will be [tex]Q=17.857\times 10^{-12}\times 0.74=13.214\times 10^{-12}C[/tex]

So number of ions will be [tex]n=\frac{13.214\times 10^{-12}}{1.6\times 10^{-19}}=8.258\times 10^6[/tex]

Answer:

Explanation:

Inductance L = 1.4 x 10⁻³ H

Capacitance C = 1 x 10⁻⁶ F

a )

current I = 14 .0 t

dI / dt  = 14

voltage across inductor

= L dI / dt

= 1.4 x 10⁻³ x 14

= 19.6 x 10⁻³ V

= 19.6 mV

It does not depend upon time because it is constant at 19.6 mV.

b )

Voltage across capacitor

V = ∫ dq / C

= 1 / C ∫ I dt  

= 1 / C ∫ 14 t dt

1 / C x 14 t² / 2

= 7 t² / C

= 7 t² / 1 x 10⁻⁶

c ) Let after time t energy stored in capacitor becomes equal the energy stored in capacitance

energy stored in inductor

= 1/2 L I²

energy stored in capacitor

= 1/2 CV²

After time t

1/2 L I² = 1/2 CV²

L I² =  CV²

L x ( 14 t )² = C x  ( 7 t² / C )²

L x 196 t² = 49 t⁴ / C

t² = CL x 196 / 49

t = 74.8 μ s

After 74.8 μ s energy stored in capacitor exceeds that of inductor.

Answer:

 τ = 166.67 N m

Explanation:

The torque is related to the angular momentum

        τ = dL / dt

Bold indicates vectors, where tau is the torque and L is the angular momentum

In this case we put the variations, It's like looking for middle values

      τ = ΔL / Δt

Let's calculate

     τ = 50.00 / 0.30

     τ = 166.67 N m

Applied in the direction of rotation at the end of the wheel

Answer: entropy

Explanation: entropy is the degree of disorderliness or randomness in a system

Answer:

(d) Less than or equal to the magnitude of vector

Explanation:

The magnitude of any vector is vector sum of magnitude of its component

As magnitude of vector is sum of its component so magnitude of its component never be greater than the magnitude of vector

It can be equal to the magnitude of vector in one case when the magnitude of other component of the vector is zero

So it can be less or equal to the magnitude of vector  

The magnitude of a component of a vector must be less than or equal to the magnitude of the vector.

The magnitude of a component of a vector must be less than or equal to the magnitude of the vector.

When a vector is resolved into its components, the magnitude of each component represents the projection of the vector onto that specific axis. The maximum magnitude of any component can be equal to the magnitude of the vector itself, but it cannot exceed it.

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Answer:

v = 3.7 m/s

Explanation:

As the swing starts from rest, if we choose the lowest point of the trajectory to be the zero reference level for gravitational potential energy, and if we neglect air resistance, we can apply energy conservation as follows:

m. g. h = 1/2 m v²

The only unknown (let alone the speed) in the equation , is the height from which the swing is released.

At this point, the ropes make a 30⁰ angle with the vertical, so we can obtain the vertical length at this point as L cos 30⁰, appying simply cos definition.

As the height we are looking for is the difference respect from the vertical length L, we can simply write as follows:

h = L - Lcos 30⁰ = 5m -5m. 0.866 = 4.3 m

Replacing in the energy conservation equation, and solving for v, we get:

v = √2.g.(L-Lcos30⁰) = √2.9.8 m/s². 4.3 m =3.7 m/s

Answer:

[tex]7.7549\times 10{19}\ J[/tex]

[tex]1.17037\times 10^{15}\ Hz[/tex]

[tex]2.56329\times 10^{-7}\ m[/tex]

Explanation:

c = Speed of light = [tex]3\times 10^8\ m/s[/tex]

[tex]N_A[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]

[tex]\nu[/tex] = Frequency

[tex]\lambda[/tex] = Wavelength

The minimum energy is given by

[tex]E=\frac{1\ mol}{N_A}\\\Rightarrow E=467\times 10^{3}\times \frac{1}{6.022\times 10^{23}}\\\Rightarrow E=7.7549\times 10{19}\ J[/tex]

The minimum energy is [tex]7.7549\times 10{19}\ J[/tex]

The energy of a photon is given by

[tex]E=h\nu\\\Rightarrow \nu=\frac{E}{h}\\\Rightarrow \nu=\frac{467\times 10^{3}\frac{1}{6.022\times 10^{23}}}{6.626\times 10^{-34}}\\\Rightarrow \nu=1.17037\times 10^{15}\ Hz[/tex]

The frequency of the photon is [tex]1.17037\times 10^{15}\ Hz[/tex]

Wavelength is given by

[tex]\lambda=\frac{c}{\nu}\\\Rightarrow \lambda=\frac{3\times 10^8}{1.17037\times 10^{15}}\\\Rightarrow \lambda=2.56329\times 10^{-7}\ m[/tex]

The wavelength is [tex]2.56329\times 10^{-7}\ m[/tex]