I was reading an old thermodynamics textbook and came across this equation describing change in internal energy. What does the (dU/dT)V and (dU/dV)T mean? I think it’s partial derivatives, but I’ve never seen a derivative sub (something). Please help

Answer:

a)   L = 4.75 103 kg m² / s,  b)  K_total = 2.57 10³ J,  

c)   L₀ = L_f =4.75 103 kg m² / s,  d)  K = 1.03 10⁴ J,  K = 1.03 10⁴ J

Explanation:

a) the angular momentum is the sum of the angular momentum of each astronaut

the distance is measured from the center of the circle r = 10/2 = 5.0 m

            L = 2m v r

            L = 2  88.0 5.40 5.0

            L = 4.75 103 kg m² / s

b) rotational kinetic energy

            K = ½ I w²

As there are two astronauts, the total energy is the sum of the energy of each no.

The moment of inertia of a point mass

             I = m r²

             I = 88 5²

             I = 2.2 10³ kg m²

the angular velocity is given by

             v = w r

             w = v / r

             w = 5.40 / 5

             w = 1.08 rad / s

the kinetic energy of the system

             K_total = 2 K

             K_total = 2 (½ I w²)

             K_total = 2.2 10³ 1.08²

             K_total = 2.57 10³ J

c, d) as astronauts are isolated in space, these speeds do not change unless there is an interaction between them, for example they approach each other, suppose they reduce their distance by half

             r = 2.5 m

             I = 88 2.5²

             I = 5.5 10² kg m²

for the change in angular velocity let us use the conservation of moment

            L₀ = L_f

            2Io wo = 2 I w

            w = Io / I wo

            w = 2.2 10³ / 5.5 10² 1.08

            w = 4.32 rad / s

linear velocity is

            v = w r

            v = 4.32 2.5

             K = 1.03 10⁴ J

the kinetic energy of the system is

            K = 5.5 10² 4.32²

            K = 1.03 10⁴ J

Answer:

See annex

Explanation:

By convention potential at ∞    V(∞ ) = 0

As the distance from the sphere decreases the potential increases up to the point d = R  ( R is the radius of the sphere. That potential remains constant while d = R and becomes 0 inside the sphere where there is not free charges and therefore the electric field is 0 and so is the potential.

I am sorry I could not make a better graph

The graph that best  illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere is attached as an image below

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

for r <= R

[tex]V = \frac{KQ}{r}[/tex]

for  r > R  

Therefore the graph will be

For more information on potentials as function of distance

https://brainly.com/question/24146175?referrer=searchResults

Answer:

0.72J

Explanation:

Answer:

29.15 N

Explanation:

Applying,

Pythagoras theorem,

a² = b²+c²................ Equation 1

Where a = resultant of the two forces, b = first force, c = second force.

From the diagram,

Given: b = 15 N, c = 25 N

Substitute these values into equation 1

a² = 15²+25²

a² = 225+625

a² = 850

a = √850

a = 29.15 N

Hence the resultant of the two forces is 29.15 N

Answer:

the calculated ratio to the radius of the sodium [tex]r_{100[/tex] / [tex]r_{Na[/tex] is 2645.0

Explanation:

Given the data in the question;

the calculated ratio to the radius of the sodium = [tex]r_{100[/tex] / [tex]r_{Na[/tex]

so from here we can write the number of energy states as 100

The number of energy states; n = 100

A;

We know that the radius of the sodium atom is;

[tex]r_n[/tex] = n²α₀

Now, the value of the Bohr radius; α₀ = 5.29 × 10⁻¹¹ m

so lets determine the radius of the sodium atom; by substituting in our values;

[tex]r_{100[/tex] = (100)² × (5.29 × 10⁻¹¹ m )

[tex]r_{100[/tex] = 5.29 × 10⁻⁷ m

B

given that, the theoretical value of the radius of the sodium is;

[tex]r_{Na[/tex] = 0.2 nm = 2 × 10⁻¹⁰ m

so we calculate the ratio of the radii of the sodium;

[tex]r_{100[/tex] / [tex]r_{Na[/tex] = ( 5.29 × 10⁻⁷ m ) / ( 2 × 10⁻¹⁰ m )

[tex]r_{100[/tex] / [tex]r_{Na[/tex] = 2645.0

Therefore, the calculated ratio to the radius of the sodium [tex]r_{100[/tex] / [tex]r_{Na[/tex] is 2645.0

Answer:

The Escape Velocity Of Earth is

11.19 km/s

Explanation:

Hope it Helps!

Explanation:

.....................................

Answer:

1 second is defined as 1/86400th part of a mean solar day.

Answer:

I guess it is A. I am not sure

Answer:

48.9 is the answer I think !

Answer:

28.4

Explanation:

Answer:

The velocity of the particle = -1.92 m/s

The speed of the particle = 5.72 m/s

Explanation:

Given equation of motion;

[tex]f(t) = 18 \ + \ \frac{48}{t} \ + \ 1[/tex]

Velocity is defined as the change in displacement with time.

[tex]V = \frac{df(t)}{dt} = -\frac{48}{t^2} \\\\at \ t = 5 \ s\\\\V = -\frac{48}{5^2} = \frac{-48}{25} = - 1.92 \ m/s[/tex]

The distance traveled by the particle in 5 s:

[tex]s = f(5) = 18 + \frac{48}{5} + 1\\\\s= 28.6 \ m[/tex]

The speed of the particle when t = 5s

[tex]Speed = \frac{28.6}{5} = 5.72 \ m/s[/tex]

Answer:

d electric current is the flow of electrons in a circuit

Answer:

the correct answer is B

Explanation:

Let's propose the solution of the problem, for this we form a system formed by the two cars, so that the forces during the collision are internal, the momentum is conserved

instantly starts. Before the crash

         p₀ = M v +0

final instant. After the crash

        m_f = (M + M) v_f

the moment is preserved

        p₀ = p_f

        M v = 2 M v_f

        v_f = v / 2

let's look for kinetic energy

before the crash

       K₀ = ½ M v²

after the crash

       K_f = ½ 2M (v_f)²

       K_f = ½ 2M (v/2)²

       K_f = (½ M v²) ½

       K_f = K₀ / 2

therefore the correct answer is B

Answer:

Thus, [tex]\frac{1 rev}{min} =\frac{2\pi}{60} rad/s[/tex]

Explanation:

The angular speed is defined as the rate of change of angular velocity.

Its SI unit is rad/s and other units are rev/min or rev/s.

[tex]\frac{1 rev}{min } = \frac{1 rev}{60 sec}\\\\1 rev = 2\pi rad\\\\So\\\\\frac{1 rev}{min} = \frac{2\pi}{60} rad/s[/tex]

Explanation:

kinetic energy was converted to potential energy in the spring.

the answer is in the above image

Answer:

K = 0.076 J

Explanation:

The height of the target, h = 0.860  m

The mass of the steel ball, m = 0.0120 kg

Distance moved, d = 1.50 m

We need to find the kinetic energy (in joules) of the target ball just after it is struck. Let t is the time taken by the ball to reach the ground.

[tex]h=ut+\dfrac{1}{2}at^2\\\\t=\sqrt{\dfrac{2h}{g}}[/tex]

Put all the values,

[tex]t=\sqrt{\dfrac{2\times 0.860 }{9.8}} \\\\=0.418\ s[/tex]

The velocity of the ball is :

[tex]v=\dfrac{1.5}{0.418}\\\\= $$3.58\ m/s[/tex]

The kinetic energy of the ball is :

[tex]K=\dfrac{1}{2}mv^2\\\\K=\dfrac{1}{2}\times 0.0120\times 3.58^2\\\\=0.076\ J[/tex]

So, the required kinetic energy is 0.076 J.

Answer:

  T = 9056 K

Explanation:

In the exercise they indicate that the body can be approximated by a black body, for which we can use the Wien displacement relation

                 λ T = 2,898 10⁻³

where lam is the wavelength of the maximum emission

                T = 2,898 10⁻³ /λ

let's calculate

                 T = 2,898 10⁻³ / 320 10⁻⁹

                  T = 9.056 10³ K

                  T = 9056 K

Answer:

  I = ⅓ m L²

Explanation:

They tell us to use the parallel axes theorem

         I = [tex]I_{cm}[/tex] + M d²

The moment of inertia of a rod with respect to the center of mass is

         I_{cm} = [tex]\frac{1}{12}[/tex]  m L²

the distance from the center of mass that coincides with its geometric center to the ends of the rod is

         d = L / 2

we substitute

       I =[tex]\frac{1}{12}[/tex]  m L² + m (L/2)²

       I = m L² (  [tex]\frac{1}{12} + \frac{1}{4}[/tex] )

       I = m L² ( [tex]\frac{1+3}{12}[/tex] )

       I = ⅓ m L²

Answer:

F is non-conservative.

If F were conservative no work would be done in moving back to the original point.       F dot S = W     if the net distance is zero the work done is zero for a conservative force

An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Force, F is non-conservative.

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

Moving back to the initial point wouldn't need any labor if F were a conservative function. Given that F.S = W, a conservative force does not exert any effort if the net distance is zero.

An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Force, F is non-conservative.

To learn more about force refer to the link:

brainly.com/question/13191643

#SPJ2

Answer:

Option b, cosine.

Explanation:

Below you can see an image that illustrates this situation.

Remember that for a triangle rectangle with a given angle θ, we have:

Cos(θ) = (adjacent cathetus)/(hypotenuse)

In the image, you can see a vector of magnitude M, and the angle θ defined between the vector and the positive y-axis.

In this case, the y-component is the adjacent cathetus and the hypotenuse is the magnitude of the vector.

Then we will have:

Cos(θ) = (adjacent cathetus)/(hypotenuse) = y/M

solving that for y, we get:

y = Cos(θ)*M

Then the y-component is the vector's magnitude multiplied by the cosine of the angle between the vector and the y-axis.

The correct option is b.

Answer:

(b) cosine

Explanation:

In a 2-dimensional Cartesian coordinate system, a vector has a x-component and/or a y-component. To get these components, the magnitude of the vector is resolved with respect to the x-axis and the y-axis by multiplying it (the magnitude) by some trigonometric function with respect to the angle between the vector and the x or y axis.

For example, given a vector A of magnitude A which makes an angle α with the x-axis and an angle β with the y-axis, the x and y components of the vector A can be found as follows;

i. x-component is given by [tex]A_{x}[/tex]

[tex]A_{x}[/tex] = A cos α (with respect to the angle between A and the x-axis)  or

[tex]A_{x}[/tex] = A sin β (with respect to the angle between A and the y-axis)

ii. y-component is given by [tex]A_{y}[/tex]

[tex]A_{y}[/tex] = A sin α (with respect to the angle between A and the x-axis)  or

[tex]A_{y}[/tex] = A cos β (with respect to the angle between A and the y-axis)

Therefore, the y-component of a vector in a 2-dimensional Cartesian coordinate is given by the product of the magnitude of the vector and the cosine of the angle between the vector and the y-axis.

Answer:

The metallic conductors

Explanation:

The metallic conductors has more free electrons that are movable, thus they conduct electricity better.

Answer:

16.33°C

Explanation:

Applying,

Heat lost by copper = heat gained by water

cm(t₁-t₃) = c'm'(t₃-t₂).............. Equation 1

Where c = specific heat capacity of copper, m = mass of copper, c' = specific heat capacity of water, m' = mass of water, t₁ = initial temperature of copper, t₂ = initial temperature of water, t₃ = final equilibrium temperature.

From the question,

Given: m = 50 kg, t₁ = 140°C, m' = 90 L = 90 kg, t₂ = 10°C

Constant: c = 385  J/kg°C, c' = 4200J/kg°C

Substitute these values into equation 1

50(385)(140-t₃) = 90(4200)(t₃-10)

(140-t₃) = 378000(t₃-10)/19250

(140-t₃) = 19.64(t₃-10)

140-t₃ = 19.64t₃-196.6

19.64t₃+t₃ = 196.4+140

20.64t₃ = 336,4

t₃ = 336.4/20.6

t₃ = 16.33°C

Answer:

a) True. The battery obeys ohm's law, it is formed by an ideal source with a fixed internal resistance

c) True. Ohm's law is V = iR therefore voltage and current are proportional

Explanation:

In this problem let's analyze the load of the system, when a resistance is placed the current is 80 mA, if we place two resistors in parallel the voltage remains the same, but the current is divided between each resistance (bulb), therefore the current in the battery it must be 160 mA

Let's analyze the answers

a) True. The battery obeys ohm's law, it is formed by an ideal source with a fixed internal resistance

b) false

c) True. Ohm's law is V = iR therefore voltage and current are proportional

d) False

e) False. The current coming out of the battery is proportional to the load placed

Answer: [tex]3.816\ m/s[/tex]

Explanation:

Given

Mass of Henry is 95 kg

Normal weight of Henry is [tex]mg=95\times 9.8=931\ N[/tex]

The scale reads the weight as 830 N for first 3.6 s i.e. less than the normal weight i.e. Elevator is moving downwards

Apparent weight is given by

[tex]\Rightarrow 830=m(g-a)\quad [a=\text{acceleration of elevator}]\\\Rightarrow 830=95(9.8-a)\\\Rightarrow 8.736=9.8-a\\\Rightarrow a=1.06\ m/s^2[/tex]

After 3.6 s weight becomes 930 N which is approximately equal to normal weight. It implies elevator starts moving with constant velocity i.e. no acceleration.

If elevator starts from rest, it velocity after 3.6 s is

[tex]v=u+at\\\Rightarrow v=0+1.06(3.6)\\\Rightarrow v=3.816\ m/s[/tex]

This velocity will remain continues as after 3.6 s, elevator starts moving with constant velocity.

Answer:

Flux is 21 Nm^2/C.

Explanation:

Electric field, E = 6 N/C along X axis

Electric filed vector, E = 6 i N/C

Area, A = 4 square meter

Area vector

[tex]\overrightarrow{A} = 4 (cos30 \widehat{i} + sin 30 \widehat{j})\\\\\overrightarrow{A} = 3.5 \widehat{i} + 2 \widehat{j}\\[/tex]

The flux is given by

[tex]\phi= \overrightarrow{E}.\overrightarrow{A}\\\\\phi = 6 \widehat{i} . \left (3.5 \widehat{i} + 2 \widehat{j} \right )\\\\\phi = 21 Nm^2/C[/tex]

Answer:

a   c

Explanation:

edu 2021

Answer:

V = 240V

Explanation:

V = I*R

V = 15A*16ohms

V = 240V

Answer:

The angle between the wire and the magnetic field is 62.74⁰

Explanation:

Given;

length of the wire, L = 1.2 m

force exerted on the wire, F = 1.6 N

current carried by the wire, I = 3.0 A

magnetic field strength, B = 0.5 T

The magnitude of a magnetic force on a current-carrying conductor is given as;

F = BIL(sinθ)

[tex]sin(\theta) = \frac{F}{BIL} = \frac{1.6}{0.5 \times 3 \times 1.2} = 0.8889 \\\\sin(\theta) =0.8889\\\\\theta = sin^{-1} (0.8889)\\\\\theta = 62.74^0[/tex]

Therefore, the angle between the wire and the magnetic field is 62.74⁰

Answer:

A hypothesis is a limited explanation of a phenomenon; a scientific theory is an in-depth explanation of the observed phenomenon. A law is a statement about an observed phenomenon or a unifying concept

Answer:

Explanation:

will try 2 explain fact, hypothesis, theory n law

fact is the starting pt: e.g. apple falls from tree

hypothesis tries 2 explain a fact: e.g. there is a force pulling down apple

theory is a complete explanation w/ equations n stuff: e.g. Newton came up w/ theory of gravitational attraction force

law is a theory dat has been proven right through tests n experiments: Newton's gravity theory had been proven right in many many tests.

Answer: The weight of the object is 29.4 N

Explanation:

To calculate the weight of the object, we use the equation:

[tex]W=m\times g[/tex]

where,

m = mass of the object = 3 kg

g = acceleration due to gravity = [tex]9.8m/s^2[/tex]

Putting values in above equation, we get:

[tex]W=3kg\times 9.8m/s^2\\\\W=29.4N[/tex]

Hence, the weight of the object is 29.4 N