If an astronaut can throw a certain wrench 15.0 m vertically upward on earth, how high could he throw it on our moon if he gives it the same starting speed in both places?

Answer:

1.2 A of current will send (3.744 × 10¹⁸) ions to the cathode per second.

Explanation:

According to Faraday's second law of electrolysis, the amount of ions/mass of substance deposited at an electrode depends on its equivalent weight.

For a divalent ion, it will require 2F of electricity per mole.

1 F = 96500 C

Amount of electricity that passes through the electrolyte per second = (magnitude of current) × (time) = It = (1.2 × 1) = 1.2 C

2F (2×96500C) of electricity will deposit 1 mole of Copper ions

That is,

193000 C of electricity will deposit 1 mole of Copper.

1.2 C will deposit (1.2×1/193000); 0.0000062176 mole of Copper.

1 mole of Copper contains (6.022 × 10²³) ions according to the Avogadro's constant.

0.0000062176 mole of Copper will contain (0.0000062176 × 6.022 × 10²³) ions = (3.744 × 10¹⁸) ions.

Therefore, 1.2 A of current will send (3.744 × 10¹⁸) ions to the cathode per second.

Hope this Helps!!!

Answer:

[tex]3.2\times 10^{-7}\ m[/tex] or 0.32 μm.

Explanation:

Given:

The radiations are UV radiation.

The frequency of the radiations absorbed (f) = [tex]9.38\times 10^{14}\ Hz[/tex]

The wavelength of the radiations absorbed (λ) = ?

We know that, the speed of ultraviolet radiations is same as speed of light.

So, speed of UV radiation (v) = [tex]3\times 10^8\ m/s[/tex]

Now, we also know that, the speed of the electromagnetic radiation is related to its frequency and wavelength and is given as:

[tex]v=f\lambda[/tex]

Now, expressing the above equation in terms of wavelength 'λ', we have:

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

Now, plug in the given values and solve for 'λ'. This gives,

[tex]\lambda=\frac{3\times 10^8\ m/s}{9.38\times 10^{14}\ Hz}\\\\\lambda=3.2\times 10^{-7}\ m\\\\\lambda=3.2\times 10^{-7}\times 10^{6}\ \mu m\ [1\ m=10^6\ \mu m]\\\\\lambda=3.2\times 10^{-1}=0.32\ \mu m[/tex]

Therefore, the wavelength of the radiations absorbed by the ozone is nearly [tex]3.2\times 10^{-7}\ m[/tex] or 0.32 μm.

Explanation:

The give data is as follows.

             C = 6 [tex]\mu F[/tex] = [tex]6 \times 10^{-6} F[/tex]

             V = 6 V

Now, we know that the relation between charge, voltage and capacitor for series combination is as follows.

              Q = CV

                  = [tex]6 \times 10^{-6} F \times 6 V[/tex]

                  = [tex]36 \times 10^{-6} C[/tex]

or,               = 36 [tex]\mu C[/tex]

Thus, we can conclude that maximum charge of the given capacitor is 36 [tex]\mu C[/tex].

Answer:

Explanation:

capacitance, C = 6 μF

Voltage, V =  6 V

Let the maximum charge is Q.

Q = C x V

Q = 6 x 6 = 36 μC

Answer:

The force exerted on an electron is [tex]7.2\times10^{-18}\ N[/tex]

Explanation:

Given that,

Charge = 3 μC

Radius a=1 m

Distance  = 5 m

We need to calculate the electric field at any point on the axis of a charged ring

Using formula of electric field

[tex]E=\dfrac{kqx}{(a^2+x^2)^{\frac{3}{2}}}\hat{x}[/tex]

[tex]E_{1}=\dfrac{kqx}{(a^2+x^2)^{\frac{3}{2}}}\hat{x}[/tex]

Put the value into the formula

[tex]E_{1}=\dfrac{9\times10^{9}\times3\times10^{-6}\times5}{(1^2+5^2)^{\frac{3}{2}}}[/tex]

[tex]E_{1}=1.0183\times10^{3}\ N/C[/tex]

Using formula of electric field again

[tex]E_{2}=\dfrac{kqx}{(a^2+x^2)^{\frac{3}{2}}}\hat{x}[/tex]

Put the value into the formula

[tex]E_{2}=\dfrac{9\times10^{9}\times(-3\times10^{-6})\times5}{((0.5)^2+5^2)^{\frac{3}{2}}}[/tex]

[tex]E_{2}=-1.064\times10^{3}\ N/C[/tex]

We need to calculate the resultant electric field

Using formula of electric field

[tex]E=E_{1}+E_{2}[/tex]

Put the value into the formula

[tex]E=1.0183\times10^{3}-1.064\times10^{3}[/tex]

[tex]E=-0.045\times10^{3}\ N/C[/tex]

We need to calculate the force exerted on an electron

Using formula of electric field

[tex]E = \dfrac{F}{q}[/tex]

[tex]F=E\times q[/tex]

Put the value into the formula

[tex]F=-0.045\times10^{3}\times(-1.6\times10^{-19})[/tex]

[tex]F=7.2\times10^{-18}\ N[/tex]

Hence, The force exerted on an electron is [tex]7.2\times10^{-18}\ N[/tex]

Explanation:

Below is an attachment containing the solution.

(a) In a parallel circuit, each bulb receives the full voltage of the household circuit. Therefore, the current running through each bulb is 1.2A.

(a) In a parallel circuit, the voltage across each component remains the same. Therefore, each bulb in the circuit will receive the full 120V supplied by the household circuit.

Using Ohm's Law (V = IR), we can calculate the current running through each bulb. The resistance of each bulb is given as 100 Ω. Therefore, the current through each bulb is:

I = V/R = 120V / 100 Ω = 1.2A

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Explanation:

It is given that mass at the right side of the pulley weighs 9 kg, mass at the center weighs 8 kg and mass at the left side weighs 5 kg.

Hence, starting from the right side

              [tex]T_{1}[/tex] = 9 kg

Now,  [tex]T_{2} = 2 \times 9 kg[/tex]

                      = 18 g

Hence, the force balance on 8 kg mass is as follows.

            [tex]T_{2} + mg = T_{3}[/tex]

     [tex]T_{3}[/tex] = [tex](18 + 8) \times g[/tex]

                 = 26 g

Now, force balance on 5 kg mass is as follows.

              5 g + T = [tex]2 \times 26 g[/tex]

                 T = 47 g

                   = [tex]47 \times 9.8[/tex]

                   = 460.6 N

Therefore, we can conclude that value of force T is 460.6 N.

The value of force T is 460.6N

Tension is a force developed by a rope, string, or cable when stretched under an applied force.

Given:

Mass (m₁) = 9 kg, m₂ = 8 kg, m₃ = 5kg, g = acceleration due to gravity = 9.8 m/s².

T₁ = 9 kg * 9.8 m/s² = 88.2N

T₂ = 2 * m₁ * g = 2 * 9 kg * 9.8 = 176.4N

T₂ + m₂g = T₃

176.4 + 8*9.8 = T₃

T₃ = 254.8N

Force balance on 5 kg mass:

T + 5(9.8) = 2 * T₃

T + 5(9.8) = 2 * 254.8

T = 460.6N

The value of force T is 460.6N

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Explanation:

Lets consider

Circumference of orbit = T

as it is mentioned in the question that a satellite is in orbit that is very close to the surface of planet. so

circumference of orbit = circumference of planet

Time period = T

radius of planet = R

orbital velocity = V

gravitational constant = G

mass of planet = m

Solution:

Time period for a uniform circular motion of orbit is,

T = [tex]\frac{2\pi R}{V}[/tex]

[tex]T = \frac{2\pi R }{\sqrt{\frac{GM}{R} } }[/tex]

[tex]T= 2\pi \sqrt{(\frac{R^3}{GM} )}[/tex]

[tex]M = \frac{4}{3} \pi R^{3}p[/tex]

where p = density

[tex]T = 2\pi \sqrt{\frac{R^{3} }{G\frac{4}{3}\pi R^{3} p } }[/tex]

[tex]T = \sqrt{\frac{3\pi }{Gp} }[/tex]

T = 2.17 hours = 7812 sec

(7812)² = [( 3×3.14)/6.67×[tex]10^{-11}[/tex]×ρ)]

ρ = 6.28/6.67×[tex]10^{-11}[/tex]×6.10×[tex]10^{-7}[/tex]

ρ = 6.28/40.687×[tex]10^{-18}[/tex]

ρ = 0.1543×[tex]10^{18}[/tex]kg/m³

ρ = 15.43×[tex]10^{16}[/tex]kg/m³

Final answer:

Calculating a planet's density based on a satellite's orbital period involves physics concepts like gravitational laws and Kepler's third law, applying them to given data about the satellite's orbit. Direct calculation requires additional information that is not provided in the question.

Explanation:

One can use Kepler's third law in combination with the formula for gravitational force to find the planet's density based on the period of a satellite in a circular orbit close to the planet's surface.

The key relationship to use is T^2 = (4π^2/GM)r^3, where T is the period of the satellite, G is the gravitational constant, M is the mass of the planet, and r is the radius of the orbit, which is approximately the radius of the planet if the satellite is very close to the surface. However, to find the density (ρ) of the planet, we use the formula ρ = M/(4/3πr^3).

Given that we do not have the mass (M) or radius (r) of the planet explicitly, we cannot directly calculate the density without additional information such as the gravitational constant (G) and the exact radius of the planet's orbit.

The solution involves using the period (T) given to manipulate these equations to express mass in terms of the period and then apply it to the density formula. This complex physics problem requires an understanding of orbital mechanics and gravitational laws.

I think your question should be:

An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is

[tex] S = 1.23*10^9 W/m^2 [/tex]

What is the rms value of (a) the electric field and

(b) the magnetic field in the electromagnetic wave emitted by the laser

Answer:

a) [tex] 6.81*10^5 N/c [/tex]

b) [tex] 2.27*10^3 T [/tex]

Explanation:

To find the RMS value of the electric field, let's use the formula:

[tex] E_r_m_s = sqrt*(S / CE_o)[/tex]

Where

[tex] C = 3.00 * 10^-^8 m/s [/tex];

[tex] E_o = 8.85*10^-^1^2 C^2/N.m^2 [/tex];

[tex] S = 1.23*10^9 W/m^2 [/tex]

Therefore

[tex] E_r_m_s = sqrt*{(1.239*10^9W/m^2) / [(3.00*10^8m/s)*(8.85*10^-^1^2C^2/N.m^2)]} [/tex]

[tex] E_r_m_s= 6.81 *10^5N/c [/tex]

b) to find the magnetic field in the electromagnetic wave emitted by the laser we use:

[tex] B_r_m_s = E_r_m_s / C [/tex];

[tex] = 6.81*10^5 N/c / 3*10^8m/s [/tex];

[tex] B_r_m_s = 2.27*10^3 T [/tex]

Complete Question:

An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is 1.38 * 10⁹ W/m². What is the rms value of the electric field in the electromagnetic wave emitted by the laser?

Answer:

E = 7.21 * 10⁶ N/C

Explanation:

S = 1.38 * 10⁹ W/m²..............(1)

The formula for the average intensity of light can be given by:

S = c∈₀E²

The speed of light, c = 3 * 10⁸ m/s²

Permittivity of air, ∈₀ = 8.85 * 10⁻¹²m-3 kg⁻¹s⁴ A²

Substituting these parameters into equation (1)

1.38 * 10⁹ = 3 * 10⁸ * 8.85 * 10⁻¹² * E²

E² = (1.38 * 10⁹)/(3 * 10⁸ * 8.85 * 10⁻¹²)

E² = 0.052 * 10¹⁷

E = 7.21 * 10⁶ N/C

Answer:

[tex]q = 2.067 \times 10^{-5}\ C[/tex]

Explanation:

Given,

mass = 1.41 g = 0.00141 Kg

Electric field,E = 670 N/C.

We know,

Force in charge due to Electric field.

F = E q

And also we know

F = m g

Equating both the equation of motion

m g = E q

[tex]q =\dfrac{mg}{E}[/tex]

[tex]q =\dfrac{0.00141 \times 9.81}{670}[/tex]

[tex]q = 2.067 \times 10^{-5}\ C[/tex]

Charge of the particle is equal to [tex]q = 2.067 \times 10^{-5}\ C[/tex]

Answer:

(a) the current in the coil is 12.03 A

(b) the maximum magnitude of the torque is 0.0854 N.m

Explanation:

Given;

number of turns, N = 185

radius of the coil, r = 1.6 cm = 0.016 m

magnetic dipole moment, μ = 1.79 A·m²

Part (a) current in the coil

μ = NIA

Where;

I is the current in the coil

A is the of the coil = πr² = π(0.016)² = 0.000804 m²

I = μ / (NA)

I = 1.79 / (185 x 0.000804)

I = 1.79 / 0.14874

I = 12.03 A

Part (b) the maximum magnitude of the torque

τ = μB

Where;

τ is the maximum magnitude of the torque

B is the magnetic field strength = 47.7 mT

τ = 1.79 x 0.0477 = 0.0854 N.m

Given Information:

Number of turns = N = 185 turns

Radius of circular coil = r = 1.60 cm = 0.0160 m

Magnetic field = B =  47.7 mT

Magnetic dipole moment = µ =1.79 A.m

Required Information:

(a) Current = I = ?

(b) Maximum Torque = τ = ?

Answer:

(a) Current = 12.03 A

(b) Maximum Torque = 0.0853 N.m

Explanation:

(a) The magnetic dipole moment µ is given by

µ = NIAsin(θ)

I = µ/NAsin(θ)

Where µ is the magnetic dipole moment, N is the number of turns, I is the current flowing through the circular loop, A is the area of circular loop and is given by

A = πr²

A = π(0.0160)²

A = 0.000804 m²

I = 1.79/185*0.000804*sin(90)

I = 12.03 A

(b) The toque τ is given by

τ = NIABsin(θ)

The maximum torque occurs at θ = 90°

τ = 185*12.03*0.00804*0.0477*sin(90°)

τ = 0.0853 N.m

Answer:

-26.1111

Explanation:

Hello!

The formula for converting Fahrenheit to Celsius can be written as follows:

C = [tex]\frac{(F-32)(5)}{9}[/tex]

Now let’s insert the value provided for Fahrenheit:

C = [tex]\frac{((-15)-32)(5)}{9}[/tex]

Now simplify the numerator:

C = [tex]\frac{(-235)}{9}[/tex]

Now divide:

C = -26.111

We have now proven that -15 degrees Fahrenheit is equal to -26.111 degrees Celsius.

I hope this helps!

Answer: No

Explanation:

The force F required is equal to the Force exerted in stretching the first material since conditions are the same

Answer:

No.

Explanation:

Both wires are made up of the same material which means they will have the same young modulus.

Y = F/A × L/ΔL

From the equation above, the force applied per cross sectional (same diameter) are is the same for both materials and is constant.

So

L1/ΔL1 = L2/ΔL2

Or L2/L1 = ΔL2/ΔL1

So the force needed to bring about a stretching the the breaking point is the same. The only difference is in by how much the longer wire would have to stretch before reaching its breaking point.

The time the projectile (or 'turd') takes to hit the ground can be calculated using the formula (T = 2u*sin(θ)/g). This formula uses the initial velocity, the projection angle, and gravitational acceleration.

This question relates to the physics concept of projectile motion. Given the launch speed, in this case, 72 m/s, and the angle of projection, 12 degrees, you can calculate the time of flight, i.e., the time taken by the projectile (in this humorous context, a 'turd') to hit the ground.

The time of flight (T) for a projectile can be calculated using the formula: T = 2u*sin(θ)/g, where u is the initial velocity, θ is the projection angle, and g is the gravitational acceleration (approximately 9.81 m/s² on Earth). Substituting the given values, we get T = 2*72*sin(12)/9.81, which gives the time after which the ground should be covered by a hypothetical 'portal' to intercept the turd just before it hits the ground.

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Answer:

Option A

498 Hz

Explanation:

Beat frequency is given by F1-F2 where F is the frequency of source while F2 is frequency that disappear as one moves towards the source. when a source moves towards observer the frequency increases

Substituting 500 for F1 and 2 for F2 then

Beat frequency is 500-2=498 Hz

Option A

Answer:

Gain in kinetic energy is [tex]1.6 \times 10^{-11} J[/tex]

or [tex]10^{8} eV[/tex]

Explanation:

The potential difference between the cloud and ground  is 100 MV (million volts)

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

Kinetic energy of an electron accelerated through this potential difference is the work done to move the electron.

hence kinetic energy gained is

[tex]KE= \Delta V \times q\\KE= 100 \times 10^6 \times 1.6 \times 10^{-19}\\KE=1.6 \times 10^{-11} J[/tex]

In terms of electron volts, the conversion factor is 1 electron volt (eV) =

[tex]1.6 \times 10^{-19} J[/tex]

So,

[tex]\frac{1.6 \times 10^{-11} J}{1.6 \times 10^{-19} J} \\= 10^8 eV[/tex]

Answer:

a) Magnitude of maximum emf induced = 0.0714 V = 71.4 mv

b) Maximum current through the bulb = 0.00793 A = 7.93 mA

Explanation:

a) The induced emf from Faraday's law of electromagnetic induction is related to angular velocity through

E = NABw sin wt

The maximum emf occurs when (sin wt) = 1

Maximum Emf = NABw

N = 1

A = 4 cm² = 0.0004 m²

B = 6 T

w = (284/60) × 2π = 29.75 rad/s

E(max) = 1×0.0004×6×29.75 = 0.0714 V = 71.4 mV

Note that: since we're after only the magnitude of the induced emf, the minus sign that indicates that the induced emf is 8n the direction opposite to the change in magnetic flux, is ignored for this question.

b) Maximum current through the bulb

E(max) = I(max) × R

R = 9 ohms

E(max) = 0.0714 V

I(max) = ?

0.0714 = I(max) × 9

I(max) = (0.0714/9) = 0.00793 A = 7.93 mA

Hope this Helps!!

Answer:

Explanation:

Energy stored in a capacitor is given by the expression

E = Q² / 2C , where Q is charge on it and C  is its capacitance . As we put dielectric slab between the plates , capacitance increases , Due to it energy decreases as capacitance form the denominator in the formula above and Q is constant .

Hence energy decreases.

The distance between the orbits of two satellites is 7.97 m.

Explanation:

Johannes Kepler was the first to propose three laws for the planetary motion. According to him, the orbits in which planets are rotating are elliptical in nature and Sun is at the focus of the ellipse. Also the area of sweeping is same.

So based on these three assumptions, Kepler postulated three laws. One among them is Kepler's third law of planetary motion. According to the third law, the square of the time taken by a planet to cover a specified region is directly proportional to the cube of the major elliptical axis or the radius of the ellipse.

So, [tex]T^{2} = r^{3}[/tex]

Thus, for the geosynchornous satellite, as the time taken is 24 hours, then the radius or the major axis of this satellite is

[tex](24)^{2}= r^{3} \\(2*2*2*3)^{2} = r^{3}\\r = \sqrt[\frac{2}{3} ]{2*2*2*3} =(2)^{2} * (6)^{\frac{2}{3} } =13.21 m[/tex]

Similarly, for the another satellite orbiting in time period of 12 hours, the major axis of this satellite is

[tex](12)^{2}= r^{3} \\(2*2*3)^{2} = r^{3}\\r = \sqrt[\frac{2}{3} ]{12} =5.24 m[/tex]

So, the difference between the two radius will give the distance between the two orbits, 13.21-5.24 = 7.97 m.

So the distance between the orbits of two satellites is 7.97 m.

Answer:

(a) 11.3 L

(b) 10 M

Explanation:

The mass-luminosity relationship states that:

Luminosity ∝ Mass^3.5

Luminosity = (Constant)(Mass)^3.5

So, in order to find the values of luminosity or mass of different stars, we take the luminosity or mass of sun as reference. Therefore, write the equation for a star and Sun, and divide them to get:

Luminosity of a star/L = (Mass of Star/M)^3.5 ______ eqn(1)

where,

L = Luminosity of Sun

M = mass of Sun

(a)

It is given that:

Mass of Star = 2M

Therefore, eqn (1) implies that:

Luminosity of star/L = (2M/M)^3.5

Luminosity of Star = (2)^3.5 L

Luminosity of Star =  11.3 L

(b)

It is given that:

Luminosity of star = 3160 L

Therefore, eqn (1) implies that:

3160L/L = (Mass of Star/M)^3.5

taking ln on both sides:

ln (3160) = 3.5 ln(Mass of Star/M)

8.0583/3.5 = ln(Mass of Star/M)

Mass of Star/M = e^2.302

Mass of Star = 10 M

Answer:

1. 11

2. 10

Explanation:

1. Using the formula L=M^3.5, and the fact that we were given the Mass,

L=2^3.5

L=11.3137085

L=11

Thus, the luminosity of the star would be 11 solar lumen

2. If we invert the formula, M=L^(2/7)

M=3160^(2/7)

M=9.99794159

M=10

Thus, the mass of the starwould be 10 solar masses.

Answer:

The force developed in the link is 6.36 N.

Explanation:

Given that,

Mass of block A = 10 kg

Mass of block B = 6 kg

Coefficients of kinetic friction [tex]\mu_{A}= 0.1[/tex]

Coefficients of kinetic friction [tex]\mu_{B}= 0.3[/tex]

Suppose the angle is 30°

We need to calculate the acceleration

Using formula of acceleration

[tex]a=\dfrac{m_{A}g\sin\theta+m_{B}g\sin\theta-\mu_{A}m_{A}g\cos\theta-\mu_{A}m_{A}g\cos\theta}{m_{A}+m_{B}}[/tex]

Put the value into the formula

[tex]a=\dfrac{10\times9.8\sin30+6\times9.8\sin30-0.1\times10\times9.8\times\cos30-0.3\times6\times9.8\times\cos30}{16}[/tex]

[tex]a=3.415\ m/s^2[/tex]

We need to calculate the force developed in the link

For block A,

Using balance equation

[tex]ma=m_{A}g\sin\theta-\mu m_{A}g\cos\theta-T[/tex]

[tex]T=ma+\mu m_{A}g\cos\theta-m_{A}g\sin\theta[/tex]

Put the value into the formula

[tex]T=10\times3.415+0.1\times10\times9.8\times\cos30-10\times9.8\times\sin30[/tex]

[tex]T=-6.36\ N[/tex]

Negative sign shows the opposite direction of the force.

Hence, The force developed in the link is 6.36 N.

Answer:

n = 1.7*10²² electrons.

Explanation:

       [tex]I =\frac{\Delta q}{\Delta t} \\ \\ \Delta q = I* \Delta t \\ \\ \Delta t = 5hs*\frac{3600s}{1h} = 18000 s[/tex]

       ⇒ Δq = I * Δt = 0.151 A * 18000 s = 2718 C

         Δq = n*e

        [tex]n = \frac{\Delta q}{e} =\frac{2718C}{1.6-19C} = 1.7e22 electrons.[/tex]

Explanation:

Below is an attachment containing the solution.

Answer:

(A) Fo = 72 Hz

(B) The pipe is open at both ends

(C) The length of the pipe is 2.38m

This problem involves the application of the knowledge of standing waves in pipes.

Explanation:

The full solution can be found in the attachment below.

For pipes open at both ends the frequency of the pipe is given by

F = nFo = nv/2L where n = 1, 2, 3, 4.....

For pipes closed at one end the frequency of the pipe is given by

F = nFo = nv/4L where n = 1, 3, 5, 7...

The full solution can be found in the attachment below.

Full Question:

Consider an automobile with a mass of 5510 lbm braking to a stop from a speed of 60.0 mph.

How much energy (Btu) is dissipated as heat by the friction of the braking process?

______Entry field with incorrect answer Btu

Suppose that throughout the United States, 350.0 x 10^6 such braking processes occur in the course of a given day.   Calculate the average rate (megawatts) at which energy is being dissipated by the resulting friction.

______Entry field with incorrect answer MW

Answer:

Energy dissipated as heat = 852.10 Btu

Average rate of energy dissipation = 3.64 MW

Explanation:

1 lb = 0.453592 Kg

Mass = 5510 lb = 0.453592 * 5510 Kg = 2499.29 Kg

1 mph = 0.44704 m/s

Velocity = 60 mph = 60 * 0.44704 m/s = 26.82 m/s

Let E be equal to energy acquired

[tex]E = 1/2 MV^{2}[/tex]

[tex]E = 0.5 * 2499.29 * 26.88^{2} \\E = 899.01 * 10^{3} Joules[/tex]

Energy dissipated as heat:

[tex]E= 8.99*10^{3} = 0.0009478 * 8.99*10^{3}\\E = 852.10 tu[/tex]

E = 852.10 Btu

Energy dissipated throughout the United States

[tex]E = 350 * 10^{6} * 899.01 *10^{3} \\E=3.1466 * 10^1^4 Joules\\[/tex]

Average power rate in MW, P

[tex]P = (3.1466*10^{14} )/(24*60*60)\\P=3.64*10^{9} \\P=3.64MW[/tex]

Answer:

[tex]a. m_i_c_e=54.6g\\b. m_i_c_e=48.7g\\m_c_o_l_d_w_a_t_e_r=900g[/tex]

Explanation:

First we need to state our assumptions:

Thermal properties of ice and water are constant, heat transfer to the glass is negligible, Heat of ice [tex]h_i_f=333.7KJkg[/tex]

Mass of water,[tex]m_w=\rho V =1\times0.3=0.3Kg[/tex].

Energy balance for the ice-water system is defined as

[tex]E_i_n-E_o_u_t=\bigtriangleup E_s_y_s\\0=\bigtriangleup U=\bigtriangleup U_i_c_e+\bigtriangleup U_w[/tex]

a.The mass of ice at [tex]0\textdegree C[/tex] is defined as:

[tex][mc(0-T_1)+mh_i_f+mc(T_2-0)]_i_c_e+[mc(T_2-T_1)]_w=0\\\\m_i_c_e[0+333.7+418\times(5-0)]+0.3\times4.18\times(5-20)=0\\m_i_c_e=0.0546Kg=54.6g[/tex]

b.Mass of ice at [tex]20\textdegree C[/tex] is defined as:

[tex][mc(0-T_1)+mh_i_f+mc(T_2-0)]_i_c_e+[mc(T_2-T_1)]_w=0\\\\m_i_c_e[2.11\times(0-(20))+333.7+4.18\times(5-0)]+0.3\times4.18\times(5-20)=0\\\\m_i_c_e=0.0487Kg=48.7g[/tex]

c.Mass of cooled water at [tex]T_c_w=0\textdegree C[/tex]

[tex]\bigtriangleup U_c_w+\bigtriangleup U_w=0[/tex]

[tex][mc(T_2-T_1)]_c_w+[mc(T_2-T_1)]_w=0\\m_c_w\times4.18\times(5-0)+0.3\times4.18\times(5-20)\\m_c_w=0.9kg=900g[/tex]

(a) The mass of ice needed if the ice is at 0°C is [tex]\( 56.4 \, \text{g} \).[/tex]

(b) The mass of ice needed if the ice is at -20°C is [tex]\( 50.1 \, \text{g} \).[/tex]

(c) The mass of cold water needed if the cooling is done with water at 0°C is [tex]\( 900 \, \text{g} \).[/tex]

To determine how much ice needs to be added to the water to cool it from 20°C to 5°C, we need to consider the heat transfer involved. We'll use the principles of heat balance, assuming no heat is lost to the surroundings.

Given Data:

Calculations:

(a) Ice at 0°C:

1. Heat required to cool the water from 20°C to 5°C:

[tex]\[ Q_{\text{water}} = m_w \cdot c_w \cdot (T_i - T_f) \][/tex]

  where:

  So,

[tex]\[ m_w = 1 \, \text{kg/L} \times 0.3 \, \text{L} = 0.3 \, \text{kg} \][/tex]

[tex]\[ Q_{\text{water}} = 0.3 \, \text{kg} \times 4.18 \, \text{kJ/kg}^\circ \text{C} \times (20^\circ \text{C} - 5^\circ \text{C}) \][/tex]

[tex]\[ Q_{\text{water}} = 0.3 \times 4.18 \times 15 \][/tex]

[tex]\[ Q_{\text{ice}} = m_{\text{ice}} \cdot L_f \][/tex]

2. Heat absorbed by ice to melt at 0°C:

[tex]\[ Q_{\text{ice}} = m_{\text{ice}} \cdot L_f \][/tex]

  To find the mass of ice needed:

[tex]\[ m_{\text{ice}} = \frac{Q_{\text{water}}}{L_f} \][/tex]

[tex]\[ m_{\text{ice}} = \frac{18.81 \, \text{kJ}}{333.7 \, \text{kJ/kg}} \][/tex]

[tex]\[ m_{\text{ice}} = 0.0564 \, \text{kg} = 56.4 \, \text{g} \][/tex]

(b) Ice at -20°C:

1. Heat required to cool ice from -20°C to 0°C:

[tex]\[ Q_{\text{cool}} = m_{\text{ice}} \cdot c_i \cdot (0^\circ \text{C} - (-20^\circ \text{C})) \][/tex]

[tex]\[ Q_{\text{cool}} = m_{\text{ice}} \cdot 2.1 \, \text{kJ/kg}^\circ \text{C} \cdot 20 \][/tex]

[tex]\[ Q_{\text{cool}} = m_{\text{ice}} \cdot 42 \, \text{kJ/kg} \][/tex]

2. Heat absorbed by ice to melt at 0°C:

[tex]\[ Q_{\text{melt}} = m_{\text{ice}} \cdot L_f = m_{\text{ice}} \cdot 333.7 \, \text{kJ/kg} \][/tex]

3. Total heat absorbed by the ice:

[tex]\[ Q_{\text{total}} = Q_{\text{cool}} + Q_{\text{melt}} \][/tex]

[tex]\[ Q_{\text{total}} = m_{\text{ice}} \cdot 42 \, \text{kJ/kg} + m_{\text{ice}} \cdot 333.7 \, \text{kJ/kg} \][/tex]

[tex]\[ Q_{\text{total}} = m_{\text{ice}} \cdot (42 + 333.7) \, \text{kJ/kg} \][/tex]

[tex]\[ Q_{\text{total}} = m_{\text{ice}} \cdot 375.7 \, \text{kJ/kg} \][/tex]

Using the heat required to cool the water:

[tex]\[ m_{\text{ice}} = \frac{Q_{\text{water}}}{Q_{\text{total}}} \][/tex]

[tex]\[ m_{\text{ice}} = \frac{18.81 \, \text{kJ}}{375.7 \, \text{kJ/kg}} \][/tex]

[tex]\[ m_{\text{ice}} = 0.0501 \, \text{kg} = 50.1 \, \text{g} \][/tex]

(c) Cooling with Water at 0°C:

1. Heat required to cool the water from 20°C to 5°C:

[tex]\[ Q_{\text{water}} = 18.81 \, \text{kJ} \][/tex]

2. Heat absorbed by the cold water to warm from 0°C to 5°C:

[tex]\[ Q_{\text{cold water}} = m_{\text{cold water}} \cdot c_w \cdot (5^\circ \text{C} - 0^\circ \text{C}) \][/tex]

[tex]\[ 18.81 \, \text{kJ} = m_{\text{cold water}} \cdot 4.18 \, \text{kJ/kg}^\circ \text{C} \cdot 5 \][/tex]

[tex]\[ m_{\text{cold water}} = \frac{18.81 \, \text{kJ}}{4.18 \, \text{kJ/kg}^\circ \text{C} \times 5} \][/tex]

[tex]\[ m_{\text{cold water}} = \frac{18.81}{20.9} \][/tex]

[tex]\[ m_{\text{cold water}} \approx 0.900 \, \text{kg} = 900 \, \text{g} \][/tex]

Answer:

2.51 m/s

Explanation:

Parameters given:

Angle, A = 33°

Mass, m = 90kg

Inclined distance, D = 2m

Force, F = 600N

Initial speed, u = 2.3m/s

From the relationship between work and kinetic energy, we know that:

Work done = change in kinetic energy

W = 0.5m(v² - u²)

We also know that work done is tẹ product of force and distance, hence, net work done will be the sum of the total work done by the force from the students and gravity.

Hence,

W = F*D*cosA - w*D*sinA

w = m*9.8 = weight

=> W = 600*2*cos33 - 90*9.8*2*sin33

W = 45.7J

=> 45.7 = 0.5*m*(v² - u²)

45.7 = 0.5*90*(v² - 2.3²)

45.7 = 45(v² - 5.29)

=> v² - 5.29 = 1.016

v² = 6.306

v = 2.51 m/s

The final velocity is 2.51 m/s

Answer: v = 3.26 m/s

Explanation:

Force applied (F) = 900 N,

mass of professor and chair (m) = 90kg,

g = acceleration due to gravity = 9.8 m/s²,

Fr = frictional force = 0 ( since from the question, the rollers the chair and professor are moving is frictionless),

θ = angle of inclination = 33°

a = acceleration of object =?

From newton's second law of motion, we have that

F - (mg sinθ +Fr) = ma

Where mg sinθ is the horizontal component of the weight of the mass of professor and chair due to the inclination of the ramp.

But Fr = 0

Hence, we have that

F - mg sinθ = ma

600 - (90×9.8×sin30) = 90 (a)

600 - 480.371= 90a

119.629 = 90a

a = 119.629/ 90

a = 1.33 m/s².

But the body started the morning (at the bottom of the ramp) with a velocity of 2.30 m/s²

Hence u = initial velocity = 2.30 m/s², a = acceleration = 1.33m/s², v = final velocity =?, s = distance covered = 2m

By using equation of motion for a constant acceleration, we have that

v² = u² + 2as

v ² = (2.3)² +2(1.33)×(2)

v² = 5.29 + 5.32

v² = 10.61

v = √10.61

v = 3.26 m/s

Answer:

P =1156mmHg

Explanation:

Given

Ptriple = 846mmHg

Ttriple = 273.16K

T = temperature of boiling water = 100°C = (273.16 +100)K = 373.16K

P/Ptriple = T/Ttriple

P = T/Ttriple × Ptriple

P = 373.16/×273.6 × 846

P = 1156mmHg.

The temperature used in this solution is the absolute temperature because the gas thermometer use the absolute temperature scale. On this scale (Kelvin temperature scale) the zero point, Absolute zero is 273.16K.

Answer:

Explanation:

Ideal gas obeys the law , [tex]PV = RT[/tex]

When volume remains constant

[tex]\frac{P2}{P1} = \frac{T2}{T1}[/tex]

Temperature of triple point of water is [tex]T1 = 273.16K[/tex]

Temperature of normal boiling point of water is [tex]T2 = 373.15 K[/tex]

therefore,

[tex]P2 = 846 * \frac{373.15}{273.16}\\\\P2 = 1155.68 mm[/tex]

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The solution is in the attachment

Answer:

80 - 32t

Explanation:

The height, h, in terms of time, t, is given as:

h(t) = 650 + 80t − 16t²

Velocity is the derivative of distance with respect to time:

v(t) = dh(t)/dt = 80 - 32t

The velocity of the object as a function of time is given by the derivative of the height function, which is v(t) = 80 - 32t.

The height h(t) of an object is given by the equation h(t) = 650 + 80t − 16t2. To find the velocity v(t), we need to take the derivative of h(t) with respect to time t. Using the power rule, we get:

v(t) = dh/dt = 0 + 80 - 32t.

So, the velocity of the object as a function of time t is v(t) = 80 - 32t.

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Answer: x, y (0, 1)

Explanation:

the X coordinate of the center mass is

X(c) = Σm(i)*x(i) / Σx(i)

X(c) = (0 + 0 + 0 + 0) / (1.93 + 3.06 + 2.41 + 3.96)

X(c) = 0 / 11.36

X(c) = 0

The y coordinate of the center mass is

Y(c) = Σm(i)y(i) / Σm(i)

Y(c) = [(1.93)(2.93) + (3.06)(2.58) + (2.41)(0) + (3.96)(-0.498)] / (1.93 + 3.06 + 2.41 + 3.96)

Y(c) = (5.6549 + 7.8948 + 0 - 1.97208) / 11.36

Y(c) = 11.57762 / 11.36

Y(c) = 1.02

Therefore, the center of masses is at x, y (0, 1)

Answer:

Explanation:

mass of elephant, m1 = 5240 kg

mass of ball, m2 = 0.150 kg

initial velocity of elephant, u1 = - 4.55 m/s

initial velocity of ball, u2 = 7.81 m/s

Let the final velocity of ball is v2.

Use the formula of collision

[tex]v_{2}=\left ( \frac{2m_{1}}{m_{1}+m_{2}} \right )u_{1}+\left ( \frac{m_{2}-m_{1}}{m_{1}+m_{2}} \right )u_{2}[/tex]

[tex]v_{2}=\left ( \frac{2\times 5240}{5240+0.150} \right )(-4.55)+\left ( \frac{0.15-5240}{5240+0.150} \right )(7.81)[/tex]

v2 = - 16.9 m/s

The negative sign shows that the ball bounces back towards you.

(b) It is clear that the velocity of ball increases and hence the kinetic energy of the ball increases. This gain in energy is due to the energy from elephant.