Calculate the hoop stress at rupture if the burst (maximum internal) pressure is 136.4 MPa. The PV has a nominal thickness of 4 mm.

A) 1 Year, if the Earth is larger in mass, but still the same distance from the sun, it will orbit at the same rate.

The Earth will continue to orbit at the same rate even if its mass increases but its distance from the sun stays the same, or 1 year. Hence, option A is correct.

A huge, spherical celestial object that is not a star nor a remnant is called a planet. The emission nebula hypothesis, which holds that a cosmic cloud collapses out of a supernova to produce a young primitive orbited by a planetary system, is the best theory currently available for explaining planet formation. The slow accumulation of matter propelled by gravity—a process known as accretion—leads to the formation of planets in this disk.

The planetary systems Mercury, Venus, Earth, and Mars, as well as the giant planets Jupiter, Saturn, Uranus, and Neptune, make up the Solar System's minimum number of eight planets. Each of these planets revolves around an axis that is inclined with regard to its orbit pole.

Hence, option A is correct.

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(a) The uncertainty principle reveals that the position of a flying mosquito can be known with an extremely high precision that doesn't affect the application of classical mechanics. (b) The inherent uncertainty calculated is extremely small.

(a) The Heisenberg principle states that the more precisely the position (Δx) of a particle is known, the less precisely its momentum (Δp) can be known, and vice versa. This is quantitatively expressed as ΔxΔp ≥ ħ/2, where ħ is the reduced Planck's constant (approximately 1.055 × 10⁻³⁴ J⋅s).

Given the speed (v) of the mosquito is 50 cm/s with an uncertainty in velocity (Δv) of 0.5 mm/s, and the mass (m) of the mosquito is 0.15 mg, we first convert these to SI units: v = 0.5 m/s, Δv = 5 × 10⁻⁴ m/s, and m = 0.15 × 10⁻⁶ kg. The uncertainty in momentum, Δp, is mΔv = (0.15 × 10⁻⁶ kg)(5 × 10⁻⁴ m/s) = 7.5 × 10⁻¹¹ kg⋅m/s.

Using the uncertainty principle, Δx ≥ ħ / (2Δp), where Δp is the momentum uncertainty calculated above. Plugging in values, Δx ≥ (1.055 × 10⁻³⁴ J⋅s) / (2 × 7.5 × 10⁻¹¹ kg⋅m/s) ≈ 7.033 × 10⁻²⁵ meters. This calculation shows how precisely the mosquito's position can be known.

(b) The inherent uncertainty calculated is extremely small, particularly when dealing with macroscopic objects like a mosquito. Therefore, this uncertainty does not present any hindrance to the application of classical mechanics, which comfortably applies at the scale of everyday objects.

Answer:

[tex]23851.35840\ lbft^2/s^2[/tex]

Explanation:

[tex]1\ Btu=1.0051\ kJ\\\Rightarrow 1\ Btu=1.0051\times 1000 kgm^2/s^2[/tex]

The English units that are to be used here are pounds (lb) and feet (ft)

[tex]1\ kg=2.20462\ lb[/tex]

[tex]1\ m=3.28084\ ft[/tex]

[tex]1005.1\times 2.20462\times 3.28084^2=23851.35840\ lbft^2/s^2[/tex]

The answer is [tex]1\ Btu=23851.35840\ lbft^2/s^2[/tex]

Answer:

(a)There are no magnetic monopoles. true

(c) There must be a vector potential. true

(d) Charges create electric fields.2. true

Explanation:

a) there are no magnetic monopoles because magnetic field is created by charges (electrons) and these electrons have dipole field so it is not possible to have magnetic dipoles, more ever Gauss's law always explained that there are not magnetic dipoles. furthermore magnetic monopoles aree caused by magnetic charges and we have electric charges.

c)vector potential is a vector field which serves as a potential for magnetic field so, the magnetic field B by Faraday and Gauss's law is also known as vector potential.

d) electric field is solely generated by charges be it static charges or moving charges if there are no charges it is not possible to have an electric field.

Final answer:

The question from the student involves the concept of thermal expansion in physics, where the goal is to determine at what temperature a copper cylinder's volume becomes 0.163% larger than its original volume at 21.1°C.

Explanation:

The student's question is about thermal expansion, which is a concept in physics specifically relating to how the volume of a solid changes with temperature. This falls under the broader subject of thermodynamics. The student is given the initial volume and temperature of the copper cylinder and is asked to find the temperature at which its volume is 0.163% larger. To solve this, we need to use the linear expansion formula for solids.
The formula for the volume expansion of solids is
V = V₀(1 + βΔT), where V is the final volume, V₀ is the initial volume, β is the coefficient of volume expansion for copper, and ΔT is the change in temperature. To find the new temperature, we first need to express the 0.163% increase in volume as a decimal, which gives us 0.00163. We can then rearrange the formula to solve for ΔT. After finding ΔT, we add it to the initial temperature of 21.1°C to find the final temperature.

Plugging in the numbers:

0.00163 = 3(16.5 x 10⁻⁶)ΔT

ΔT = 21.3 °C

Therefore, T2 = T1 + ΔT = 21.1 °C + 21.3 °C = 42.4 °C

The temperature at which the copper cylinder's volume will be 0.163% larger than at 21.1 °C is 42.4 °C.

Answer:

There are [tex]4.89\times 10^{20}\ electrons[/tex] flowing in the lighting bolt.

Explanation:

Given that,

Charge on certain lighting bolt, q = 78.3 C

We need to find the number of charge flowing in that bolt. Let there are n number of electrons. It is a case of quantization of electric charge. It is given by :

q = ne

[tex]n=\dfrac{q}{e}[/tex]

e is the charge on an electron

[tex]n=\dfrac{78.3\ C}{1.6\times 10^{-19}\ C}[/tex]

[tex]n=4.89\times 10^{20}\ electrons[/tex]

So, there are [tex]4.89\times 10^{20}\ electrons[/tex] flowing in the lighting bolt.

Answer: The truck has a greater kinetic energy

Explanation:

The initial velocities of both the truck and car are the same. Likewise, the final velocity is the same. The change in kinetic energy is dependent only on mass. The truck has a greater mass, therefore, the change in its kinetic energy is greater.

Answer:

Net force is zero

Explanation:

According to the Newton's second law, the net force on the body is equal to the product of mas of body and the acceleration.

here acceleration is equal to zero so net force is also zero because mass of an object can never be zero.

Answer:

Conservation of angular momentum

Explanation:

When the objects spread in universe after big bang, because of the tremendous force , they gained angular momentum and started to rotate. Since, then the object continue to rotate on their axis because of conservation of angular momentum. In vacuum of space there no other forces that can stop these rotation, therefore, they continue to rotate.  

To solve this problem we will apply the concepts related to Hooke's law for which the force exerted on a spring is described as the product between the spring constant and its displacement, that is

[tex]F = kx[/tex]

Where k is the spring's constant and x is the elongation,

Rearranging to find the elongation we have

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

Replacing,

[tex]x = \frac{100}{500}[/tex]

[tex]x = 0.2in[/tex]

[tex]x = 5.08mm[/tex]

Therefore the elongation produced in the rope from its original length is 0.2in or 5.08mm

Answer:

If a negatively charged balloon is brought near one end of the rod but not in direct contact, then the negative charges on the balloon repel the same amount of negative charges on the end of the rod that is close to the balloon, and the positive charges stay at the balloon-side of the rod. The total charge of the rod is still zero, but the distribution of the charges are now non-uniform.

Answer:

12.5 m.

Explanation:

Speed: This can be defined as the rate of change of distance. The S.I unit of speed is m/s. Mathematically it can be expressed as,

Speed = distance/time

S = d/t......................... Equation 1

d = S×t ...................... Equation 2.

Where S = speed of the car, d = distance, t = time taken to shut the eye during sneezing

Given: S = 90 km/h, t = 0.50 s.

Conversion: 90 km/h ⇒ m/s = 90(1000/3600) = 25 m/s.

S = 25 m/s.

Substitute into equation 2.

d = 25×0.50

d = 12.5 m.

Hence the car will move 12.5 m during that time

Final answer:

To find out the distance a car covers during a sneeze while driving at 90 km/h, we first convert the speed to meters per second (25 m/s) and then multiply by the sneeze duration (0.50 s), resulting in a distance of 12.5 meters.

Explanation:

To calculate the distance a car moves during a sneeze, we can use the formula for distance traveled at a constant speed, which is distance = speed imes time. Given that the car's speed is 90 km/h, we first need to convert this speed into meters per second. Since 1 km = 1000 meters and 1 hour = 3600 seconds, the conversion yields:

90 km/h imes (1000 meters/km) imes (1 hour/3600 seconds) = 25 m/s.

Now, using the time duration of the sneeze, which is 0.50 seconds, the distance traveled during the sneeze can be calculated as:

Distance = 25 m/s imes 0.50 s = 12.5 meters.

Therefore, the car travels 12.5 meters during a sneeze lasting 0.50 seconds.

Answer:

a. position function of the coin:

    [tex]s=-16t^2+1344[/tex]

    Now the velocity function:

    [tex]v=-32t[/tex]

b. [tex]v_{avg}=-112\ m.s^{-1}[/tex]

c. [tex]v_3=-96\ m.s^{-1}[/tex]        &   [tex]v_4=-128\ m.s^{-1}[/tex]

d. [tex]t=9.165\ s[/tex]

e. [tex]v_f=293.285\ m.s^{-1}[/tex]

Explanation:

Given:

Given position function associated with free falling objects:

[tex]s=-16t^2+v_0t+s_0[/tex]

here:

[tex]s_0=[/tex] initial height

[tex]v_0=[/tex]initial velocity

[tex]t=[/tex] time of observation

a)

position function of the coin:

[tex]s=-16t^2+1344[/tex]

∵the object is dropped it was initially at rest

Now the velocity function:

[tex]v=\frac{d}{dt} s[/tex]

[tex]v=-32t[/tex]

b)

we know average velocity is given as:

[tex]\rm v_{avg}=\frac{total\ displacement}{total\ time}[/tex]

Displacement in the given interval:

[tex]s_{_{3-4}}=s_4-s_3[/tex]

[tex]s_{_{3-4}}=(-16\times 4^2+1344)-(-16\times 3^2+1344)[/tex]

[tex]s_{_{3-4}}=-112\ ft[/tex]

Now,

[tex]v_{avg}=\frac{-112}{4-3}[/tex]

[tex]v_{avg}=-112\ m.s^{-1}[/tex]

c)

Instantaneous velocity at t = 3 s:

[tex]v_3=-32\times 3[/tex]

[tex]v_3=-96\ m.s^{-1}[/tex]

Instantaneous velocity at t = 4 s:

[tex]v_4=-32\times 4[/tex]

[tex]v_4=-128\ m.s^{-1}[/tex]

d)

At ground we  have s=0:

Put this in position function:

[tex]0=-16t^2+1344[/tex]

[tex]t=9.165\ s[/tex]

e)

Velocity of the coin at impact:

[tex]v_f=-32\times 9.165[/tex]

[tex]v_f=293.285\ m.s^{-1}[/tex]

The position and velocity functions of the silver dollar are s(t) = -16t^2 + 1344 and v(t) = -32t, respectively. After a time of 9.6 seconds, the coin hits the ground with a velocity of -307.2 ft/s. The average speed between 3 and 4 seconds is -224 ft/s.

In this particular problem, we know that the silver dollar is dropped from rest from a height (s0) of 1344 feet. Thus, the initial velocity (v0) is 0.

(a) The position function with these initial conditions becomes s(t) = -16t^2 + 1344 and the velocity function is derived from the position function as v(t) = -32t.

(b) The average velocity on the interval [3,4] can be found by taking the change in position divided by the change in time in that interval and is calculated by [s(4)-s(3)]/[4-3] = -224 ft/s.

(c) The instantaneous velocities at t = 3 s and t = 4 s are found by substituting these times into the velocity function, yielding v(3) = -96 ft/s and v(4) = -128 ft/s.

(d) The time required for the coin to reach the ground level can be found by solving the position function s(t) = 0 for t: t = sqrt(1344/16) = 9.6 s.

(e) The velocity of the coin at impact is found by evaluating the velocity function at t = 9.6 s: vf = -32*9.6 = -307.2 ft/s.

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Answer:

(a) x=157 m

(b) No

Explanation:

Given Data

Mass of proton m=1.67×10⁻²⁷kg

Charge of proton e=1.6×10⁻¹⁹C

Electric field E=3.00×10⁶ N/C

Speed of light c=3×10⁸ m/s

For part (a) distance would proton travel

Apply the third equation of motion

[tex](v_{f})^{2} =(v_{i})^{2}+2ax[/tex]

In this case vi=0 m/s and vf=c

so

[tex]c^{2}=(0)^{2}+2ax\\ c^{2}=2ax\\x=\frac{c^{2} }{2a}[/tex]

[tex]x=\frac{c^{2}}{2a}--------Equation (i)[/tex]

From the electric force on proton

[tex]F=qE\\where\\ F=ma\\so\\ma=qE\\a=\frac{qE}{m}\\[/tex]

put this a(acceleration) in Equation (i)

So

[tex]x=\frac{c^{2} }{2(qE/m)}\\ x=\frac{mc^{2}}{2qE} \\x=\frac{(1.67*10^{-27})*(3*10^{8})^{2} }{2*(1.6*10^{-19})*(3*10^{6})}\\ x=157m[/tex]

For part (b)

No the proton would collide with air molecule

The energy absorbed by a hydrogen atom to transition an electron from n = 3 to n = 5 can be calculated using the Rydberg formula. The resulting value, given in Joules, can be converted to electron volts for ease of comparison.

The energy of light absorbed by a hydrogen atom to transition an electron from n = 3 to n = 5 can be calculated using the Rydberg formula, which describes the energies of the orbits of electrons in a hydrogen atom. The formula uses Rydberg's constant (RH = 2.18 × 10^-18 J) and the principal quantum numbers of the initial (ni) and final (nf) states:

ΔE = RH . ((1/ni²) - (1/nf²))  

In this case, ni = 3 (the initial energy level) and nf = 5 (the final energy level). Therefore, to find the energy involved in this transition, we substitute these values into the formula:

ΔE = 2.18 × 10^-18 . ((1/3²) - (1/5²))

The result you get from this calculation is in Joules, and to convert it to electron volts (eV), divide by 1.6 × 10^-19 (since 1 eV = 1.6 × 10^-19 J).

This numerical calculation will represent the energy absorbed by the atom as the electron transitions from n = 3 to n = 5, mentioned in the question.

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Answer:

6.42 s

Explanation:

Period: This can be defined as the time taken for a wave or an oscillating body to complete on oscillation. The S.I unit of period is Second (s).

The period of a simple pendulum is represented as,

T = 2π√(L/g)....................................... Equation 1.

Where T = period, L = length of the pendulum, g = acceleration due to gravity. π = pie.

Given: L = 1.7 m, g = 1.624 m/s² and π = 3.14

T = 2(3.14)√(1.7/1.624)

T = 6.28√(1.047)

T = 6.28×1.023

T = 6.42 s.

Thus, the period of the pendulum = 6.42 s

The period of a 1.7-m-long pendulum on the Moon, where the free-fall acceleration is 1.624 m/s² is 6.425 secs

The formula for calculating the period of a simple pendulum is expressed using the formula:

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

l is the length of the pendulum

g is the acceleration due to gravity

Given the following parameters

g =  1.624 m/s²

l = 1.7m

Substitute the given values into the formula:

[tex]T=2(3.14)\sqrt{\frac{1.7}{1.624} } \\T=6.28\sqrt{1.0468}\\T=6.28(1.0231)\\T = 6.425secs[/tex]

Hence the period of a 1.7-m-long pendulum on the Moon, where the free-fall acceleration is 1.624 m/s² is 6.425 secs.

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Answer:

The wavelength of the first harmonic is 155.4 cm.

Explanation:

Given that,

The separation between a stretched string that is fixed at both ends, l = 77.7 cm

The density of the string, [tex]d=0.014\ g/cm^3[/tex]

Tension in the string, T = 600 N

We need to find the wavelength of the first harmonic. The wavelength of the nth harmonic on the string that is fixed at both ends is given by :

[tex]\lambda=\dfrac{2l}{n}[/tex]

Here, n = 1

[tex]\lambda=2l[/tex]

[tex]\lambda=2\times 77.7[/tex]

[tex]\lambda=155.4\ cm[/tex]

So, the wavelength of the first harmonic is 155.4 cm. Hence, this is the required solution.                                                              

The wavelength of the first harmonic will be "155.4 cm".

According to the question,

Separation between stretched string, I = 77.7 cm

String's density, d = 0.014 g/cm³

String's tension, T = 600 N

We know the relation,

Wavelength, λ = [tex]\frac{2l}{n}[/tex]

here, n = 1

then, λ = 2l

By substituting the values,

           = 2 × 77.7

           = 155.4 cm

Thus the above answer is appropriate.  

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Answer:

v = 620.17 m/s

Explanation:

There are different formulas for calculating the speed of a wave. Based on the given parameters, the speed of the wave can be estimated as:

v = sqrt(breaking tensile strength/density)

Where:

The breaking tensile strength = 3*10^9 N/m^2

Density = 7800 kg/m^3

Therefore, we can estimate the speed of the wave as shown below:

v = sqrt(3*10^9/7800) = sqrt(384615.3846) = 620.17 m/s

The speed of a wave in a wire at its breaking point depends on the maximum tension the wire can sustain and its linear mass density, calculated with the formula v = (T/μ)¹⁄².

The speed v of a wave traveling down a wire at its breaking point would be determined by the tension in the wire just before breaking and the wire's linear mass density. The formula for the speed of a wave on a stretched string is v = (T/μ)¹⁄², where T is the tension in the wire and μ is the linear mass density. For a wire stretched to its breaking point, the tension T would be at its maximum value that the wire can sustain without breaking.

Answer:

q₁ = q₂ = Q = 14.8 pC

Explanation:

Given that

q₁ = q₂ = Q = ?

Distance between charges = r =7.3 cm = 0.073 m

Combined electric field = E₁ + E₂ = E = 50 N/C

Using formula

[tex]E=2\frac{kQ}{r^2}[/tex]

Rearranging for Q

[tex]Q= \frac{Er^2}{2k}\\\\Q=\frac{(50)(.005329)}{2\times 9\times 10^9}[/tex]

[tex]Q=14.8\times 10^{-12}\, C\\\\Q=14.8\, pC[/tex]

Answer:

Speed of the glacier, [tex]v=1.0148\times 10^{-6}\ m/s[/tex]

Explanation:

Given that,

The average speed of Hubbard Glacier, [tex]v=105\ feet/year[/tex]

We need to find speed of advance of the glacier in  m/s. As we know that,

1 meter = 3.28 feet

And

[tex]1\ year=3.154\times 10^7\ second[/tex]

Using the above conversions, we can write the value of average speed is :

[tex]v=1.0148\times 10^{-6}\ m/s[/tex]

So, the speed of advance of the glacier is [tex]1.0148\times 10^{-6}\ m/s[/tex]. Hence, this is the required solution.

Answer:

[tex]P=1.44*10^{-2}Pa[/tex]

Explanation:

The pressure amplitude is given by:

[tex]P=\sqrt{2I\rho v[/tex]

Here, I is the sound intensity, [tex]\rho[/tex] the density of the air and v the speed of air.

The sound intensity can be calculated from:

[tex]I=10^\beta I_0[/tex]

Where [tex]\beta[/tex] is the sound intensity level in bels and [tex]I_0[/tex] is the reference sound intensity. So, replacing (2) in (1):

[tex]P=\sqrt{2(10^\beta) I_o \rho v}\\P=\sqrt{2(10^{5.4})(10^{-14}\frac{W}{m^2})(1.2\frac{kg}{m^3})(344\frac{m}{s})}\\P=1.44*10^{-2}Pa[/tex]

The pressure amplitude is found using the formulas for pressure amplitude and sound intensity. Once the sound intensity is found, the pressure amplitude can be calculated, given the speed and density of air. The pressure amplitude at the given distance is approximately 0.0143 Pa.

The pressure amplitude can be found with the formula p = √(2*ρ*v*I), where p is the pressure amplitude, ρ is the density of the medium (air), v is the speed of sound in the medium, and I is sound intensity. The sound intensity level (dB) can be converted to sound intensity (W/m^2) by using the formula I = I0 * 10^(L/10), where I0 is the reference intensity (10^-12 W/m^2) and L is the sound intensity level in decibels.

So, calculating the sound intensity I = (10^-12 W/m^2) * 10^(54/10) = 0.002 W/m^2. Once we have the sound intensity, we can calculate the pressure amplitude using the speeds of sound in air at 20°C (343 m/s), and the density of air at sea level (1.225 kg/m^3). Substituting these values into our formula results in a pressure amplitude of about 0.0143 Pa.

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To develop this problem we will apply the concepts related to the conservation of momentum. For this purpose we will define that the initial moment must be preserved and be equal to the final moment. Since the system was at a stationary moment, the moment before the bullet is fired will be 0, while the moment after the bullet is fired will be equivalent to the sum of the products of the mass and the velocity of each object. , this is,

[tex]m_1u_1+m_2u_2 = m_1v_1+m_2v_2[/tex]

Here,

m = mass of each object

u = Initial velocity of each object

v = Final velocity of each object

Our values are,

[tex]\text{Mass of hunter} ) m_1 = 75 kg = 75000 g[/tex]

[tex]\text{Mass of bullet} = m_2 = 42 g[/tex]

[tex]\text{Speed of bullet} = v_2 = 6200 m/s[/tex]

[tex]\text{Recoil speed of hunter} =v_1 = ?[/tex]

Applying our considerations we have that the above formula would become,

[tex]m_1v_1 + m_2v_2 = 0[/tex]

Solving for speed 1,

[tex]v_1 = - \frac{m_2v_2}{m_1 }[/tex]

[tex]v_1 = - \frac{42 * 620}{75000 }[/tex]

[tex]v_1 = - 0.3472 m/s[/tex]

Therefore  the recoil speed of the hunter is -0.3472m/s, said speed being opposite to the movement of the bullet.

The recoil speed of the hunter standing on the frictionless ice is 0.35m/s².

Given the data in the question;

Recoil speed of the hunter; [tex]v_1 =\ ?[/tex]

From the law of conservation of momentum:

[tex]MV = mv[/tex]

Where m is mass and v is velocity

So

[tex]m_1v_1 = m_2v_2\\\\v_1 = \frac{m_2v_2}{m_1}[/tex]

We substitute our given values into the equation

[tex]v_1 = \frac{ 0.042kg \ *\ 620m/s^2}{75kg} \\\\v_1 = \frac{26.04kg.m/s^2}{75kg} \\\\v_1 = 0.35m/s^2[/tex]

Therefore, the recoil speed of the hunter standing on the frictionless ice is 0.35m/s².

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Answer:

Jill average velocity is  0

Jack  average velocity is 0.159337

Jill average speed = 1.593372

Jack average speed = 1.434034

Explanation:

given data

long swimming pool = 25.0 m

9 lengths of the pool = 156.9 s ( 2 min and 36.9 s )

10 lengths = same time interval

to find out

average velocity and average speed

solution

we know that average velocity that is express as

average velocity = [tex]\frac{displacement}{time}[/tex]    .....................1

Jill come back where she start

so here velocity will be = 0

and

Jack ends up on the other end of pool

so average velocity =  [tex]\frac{25}{156.9}[/tex]

average velocity = 0.159337

now we get here average speed that is express as

average speed = [tex]\frac{distance}{time}[/tex]      .............2

jack speed = 9 × [tex]\frac{25}{156.9}[/tex]

jack speed = 1.434034

and

Jill speed = 10 × [tex]\frac{25}{156.9}[/tex]

Jill speed = 1.593372

Answer:

Explanation:

Given

mass of water [tex]m_1=0.27\ kg[/tex]

Temperature of water [tex]T_{wi}=82.5^{\circ}C[/tex]

Initial Temperature of ice[tex]=-22.3^{\circ}C[/tex]

Final temperature of system [tex]T=34^{\circ}C[/tex]

specific heat of water [tex]c=4.18\ kJ/kg-K[/tex]

specific heat of ice [tex]c_i=2.108\ kJ/kg-K[/tex]

Latent heat of ice [tex]L=336\ kJ/kg[/tex]

Heat loss by Water is equal to heat gained by ice

Heat loss by water [tex]Q_1=m_w\times c\times \Delta T[/tex]

[tex]Q_1=0.27\times 4.18\times (82.5-34)=54.7371\ kJ[/tex]

Heat gained by ice [tex]Q_1=x\times c_i(0-(-22.3))+x\times L+x\times c\times (T-0)[/tex]

[tex]Q_2=x\times 2.108\times (22.3)+x\times 336+x\times 4.18\times 34[/tex]

[tex]Q_2=525.1284x\ kJ[/tex]

[tex]Q_1=Q_2[/tex]

[tex]x=\frac{54.73}{525.1284}[/tex]

[tex]x=0.104\ kg[/tex]  

Answer:

0.000230144 N

Explanation:

n = Number of electrons = [tex]10\times 10^{23}[/tex]

q = Charge of electron = [tex]1.6\times 10^{-19}\ C[/tex]

k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]

r = Distance between obects = 1 m

The force would be

[tex]F=\dfrac{nkq^2}{r^2}\\\Rightarrow F=\dfrac{10\times 10^{23}\times 8.99\times 10^9\times (1.6\times 10^{-19})^2}{1^2}\\\Rightarrow F=0.000230144[/tex]

The force would be 0.000230144 N

Answer:

During the 3 s interval, the average velocity was 4 m/s.

Explanation:

Hi there!

The average velocity (AV) is calculated as follows:

AV = Δx / Δt

Where:

Δx = traveled distance.

Δt = elapsed time.

The traveled distance (x) is calculated as follows:

x = x0 + v0 · t + 1/2 · a · t²

Where:

x0 = initial position.

v0 = initial velocity.

t = time.

a = acceleration.

Since x0 and v0 are equal to zero, the equation gets reduced to:

x = 1/2 · a · t²

Since the acceleration is constant, it can be calculated with this equation:

a = v/t

a = 8 m/s / 3 s

a = 8/3 m/s²

Then, the traveled distance will be:

x = 1/2 · a · t²

x = 1/2 · 8/3 m/s² · (3 s)²

x = 12 m

And the average velocity will be:

AV = Δx / Δt

AV = 12 m / 3 s = 4 m/s

During the 3 s interval, the average velocity was 4 m/s.

The smaller charge is approximately **3.37 x 10⁻⁷ C** and the larger charge is approximately **1.35 x 10⁻⁶ C**.

These are approximate values due to rounding during calculations.

Solving for the Charges on the Spheres:

Case (a): Equal Charges

1. **Apply Coulomb's Law:** The force between two charged objects is given by Coulomb's Law:

[tex]$$F = k \cdot \frac{q_1 \cdot q_2}{r^2}$$[/tex]

where:

* F is the force (0.200 N)

* k is Coulomb's constant (8.99 x 10^9 N m²/C²)

* q₁ and q₂ are the charges on the spheres (which are equal in this case)

* r is the distance between the spheres (0.16 m)

2. **Plug in the values and solve for q₁:**

[tex]$$0.200 = 8.99 \times 10^9 \cdot \frac{q_1^2}{(0.16)^2}$$$$q_1^2 = \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9}$$$$q_1 = \sqrt{ \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9}} \approx 7.54 \times 10^{-7} \text{ C}$$[/tex]

Therefore, the charge on each sphere is approximately **7.54 x 10⁻⁷ C**.

Case (b): One Sphere has Four Times the Charge

1. **Let q₁ be the smaller charge and q₂ be the larger charge:** We know q₂ = 4q₁.

2. **Apply Coulomb's Law again:

[tex]$$0.200 = 8.99 \times 10^9 \cdot \frac{q_1 \cdot q_2}{(0.16)^2}$$$$0.200 = 8.99 \times 10^9 \cdot \frac{q_1 \cdot (4q_1)}{(0.16)^2}$$3. **Substitute and solve for q₁:**$$0.200 = 8.99 \times 10^9 \cdot \frac{16q_1^2}{(0.16)^2}$$$$q_1^2 = \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9 \cdot 16}$$$$q_1 = \sqrt{ \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9 \cdot 16}} \approx 3.37 \times 10^{-7} \text{ C}$$4. **Find the larger charge (q₂):**$$q_2 = 4q_1 = 4 \cdot (3.37 \times 10^{-7} \text{ C}[/tex]

Final answer:

The temperature of the patch is approximately 1387 Kelvin, and the rate of heat loss through the patch is approximately 0.07 Watts.

Explanation:

The temperature of the patch can be calculated using the Stefan-Boltzmann law of thermal radiation, which states that the power radiated by an object is proportional to the fourth power of its temperature. The equation to calculate the temperature is:

T = sqrt((P / (A * sigma * e))

Where T is the temperature, P is the power, A is the surface area, sigma is the Stefan-Boltzmann constant, and e is the emissivity. Substituting the given values:

T = sqrt((1850 W / (1 m2 * 5.67×10–8 W/m2·K4 * 1.0)))

T = sqrt((1850 W / 5.67×10–8 W/m2·K4))

Calculating the square root:

T = 1387 K

The temperature of the patch is approximately 1387 Kelvin.

The rate of heat loss through the patch can be calculated using the Stefan-Boltzmann law:

P = A * e * sigma * T4

Substituting the known values:

P = (0.05 m * 0.08 m * 5.67×10–8 W/m2·K4 * 0.300 * (1387 K)4)

Calculating the power:

P = 0.07 W

The rate of heat loss through the patch is approximately 0.07 Watts.

Answer:

[tex]Q_x=60\ J[/tex]

[tex]T_L=-23\ ^{\circ}C[/tex] is the lowest possible temperature of the cold reservoir.

Explanation:

Given:

Coefficient of performance of refrigerator, [tex]COP=5[/tex]

A)

We know that for a refrigerator:

[tex]\rm COP=\frac{ desired\ effect }{\: energy\ supplied }[/tex]

Given that 10 J of energy is consumed by the compressor:

[tex]5=\frac{desired\ effect}{10}[/tex]

[tex]\rm Desired\ effect=50\ J[/tex]

Now the by the conservation of energy the heat exhausted :

[tex]Q_x=50+10[/tex]

[tex]Q_x=60\ J[/tex]

B)

Also

[tex]COP=\frac{T_L}{T_H-T_L}[/tex]

where:

[tex]T_H\ \&\ T_L[/tex] are the absolute temperatures of high and low temperature reservoirs respectively.

[tex]5=\frac{T_L}{(273+27)-T_L}[/tex]

[tex]1500-5\times T_L=T_L[/tex]

[tex]T_L=250\ K[/tex]

[tex]T_L=-23\ ^{\circ}C[/tex] is the lowest possible temperature of the cold reservoir.

Final answer:

The coefficient of performance (COP) of a refrigerator is the ratio of heat removed from the cold reservoir to the work done by the compressor. Using this definition, we can solve for the amount of heat exhausted to the hot reservoir and the temperature of the cold reservoir.

Explanation:

The coefficient of performance (COP) of a refrigerator is a measure of its efficiency. It is defined as the ratio of heat removed from the cold reservoir to the work done by the compressor:

COP = heat removed / work done

(A) To find the amount of heat exhausted to the hot reservoir, we can use the formula:

heat removed = COP x work done

Substituting the given values, we get:

heat removed = 5.0 x 10 J = 50 J

(B) To find the lowest possible temperature of the cold reservoir, we can use the Carnot efficiency formula:

COP = hot temperature / (hot temperature - cold temperature)

Substituting the given values and rearranging the formula, we get:

cold temperature = hot temperature - (hot temperature / COP)

cold temperature = 27°C - (27°C / 5.0) = 21.6°C

Answer:

Option c is correct

Explanation:

There are two types of collisions-elastic collision and inelastic collision.

In elastic collision, both kinetic energy and total momentum are conserved. On the other hand, in inelastic collision, total momentum is conserved but kinetic energy is not conserved. Thus, option b and d are incorrect.

Total energy is always conserved in both types. Thus, option a is incorrect.

In a perfectly inelastic collision, objects stick together. This happens because maximum kinetic energy is dissipated and used in bonding of the two objects. Thus, correct option is c.

Answer:

i believe its a?

Explanation:

In an inelastic collision, momentum is conserved