A motorist drives north for 35.0 min at 85.0 km/h and then stops for 15.0 min. He then continues north, traveling 130 km in 2.00 h. (a) what is his total displacement? b) what is his average velocity?

Answer:

(a) 62.57 L

(b) 801.94 kPa

Explanation:

Given:

[tex]n[/tex] = number of moles of gas = 10.3 mol

[tex]P_1[/tex] = initial pressure of the gas = [tex]519\ kPa = 5.19\times 10^5\ Pa[/tex]

[tex]T_1[/tex] = initial temperature of the gas = [tex]361.38^\circ C = (361.38+273)\K = 598.38\ K[/tex]

[tex]T_2[/tex] = final temperature of the gas = [tex]651.6^\circ C = (651.6+273)\K = 924.6\ K[/tex]

[tex]V[/tex] = volume of the tank

R = universal gas constant = [tex]8.314 J/mol K[/tex]

Part (a):

Using Ideal gas equation, we have

[tex]PV=nRT\\\Rightarrow V = \dfrac{nRT}{P}\\\Rightarrow V = \dfrac{10.3\times 8.314\times 598.38}{5.19\times 10^{5}}\\\Rightarrow V = 6.2567\times10^{-2}\ m^3\\\Rightarrow V = 62.567\ L[/tex]

Hence, the volume of the container is 62.567 L.

Part (b):

As the volume of the container remains constant.

Again using ideal gas equation,

[tex]PV=nRT\\\because V,\ n, R\ are\ constant\\\therefore \dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}\\\Rightarrow P_2 = \dfrac{T_2}{T_1}P_1\\\Rightarrow P_2 = \dfrac{924.6}{598.38}\times 519\\\Rightarrow P_2 = 801.94\ kPa[/tex]

Hence, the final pressure of the gas is now 801.94 kPa.

Answer:

a) 12.528 m/s

b) 15.344 m/s

Explanation:

Given:

Mass of the child, m = 34.9 kg

Height of the water slide, h = 16.0 m

Now,

a) By the conservation of energy,

loss in potential energy = gain in kinetic energy

mgh = [tex]\frac{\textup{1}}{\textup{2}}\textup{m}\times\textup{v}^2[/tex]

where,

g is the acceleration due to the gravity

v is the velocity of the child

thus,

at halfway down, h = [tex]\frac{\textup{16}}{\textup{2}}[/tex]= 8 m

therefore,

34.9 × 9.81 × 8 = [tex]\frac{\textup{1}}{\textup{2}}\textup{34.9}\times\textup{v}^2[/tex]

or

v = 12.528 m/s

b)

at three-fourth way down

height = [tex]\frac{\textup{3}}{\textup{4}}\times16[/tex] = 12 m

thus,

loss in potential energy = gain in kinetic energy

34.9 × 9.81 × 12 = [tex]\frac{\textup{1}}{\textup{2}}\textup{34.9}\times\textup{v}^2[/tex]

or

v = 15.344 m/s

Answer:

(a) 12.52 m/s

(b) 15.34 m/s

Explanation:

mass, m = 34.9 kg

h = 16 m

(a) Initial velocity, u = 0

height = h / 2 = 16 / 2 = - 8 m (downward)

let the speed of child is v.

acceleration, a = - 9.8 m/s^2 (downward)

Use third equation of motion

[tex]v^{2}=u^{2}+2as[/tex]

[tex]v^{2}=0^{2}+2\times 9.8\times 8[/tex]

v = 12.52 m/s

(b) Initial velocity, u = 0

height = 3 h / 4 = 12 m = - 12 m (downward)

let the speed of child is v.

acceleration, a = - 9.8 m/s^2 (downward)

Use third equation of motion

[tex]v^{2}=u^{2}+2as[/tex]

[tex]v^{2}=0^{2}+2\times 9.8\times 12[/tex]

v = 15.34 m/s

Answer:

3.75s

Explanation:

We can use the equations for constant acceleration motion. Let's call x, the total length of the path, then x/2 will be half of path. After falling from rest and reaching the half of its total path, the velocity of the body will be:

[tex]v_f^2 =v_0^2 + 2a(x/2)[/tex]

vf is the final velocity, v0 is the initial velocity, 0m/s because the body starts from rest. a is the acceleration, gravity = 9.81m/s^2 in this case. Now, clearing vf we get:

[tex]v_f=\sqrt{(0m/s)^2 + 2g(x/2)}\\v_f = \sqrt{g*x}

In the second half:

[tex]x/2 = \frac{1}{2}gtx^{2}  + v_ot[/tex]

[tex]x/2 = \frac{1}{2}g*(t)^2 + \sqrt{g*x}*(t)[/tex]

[tex](\frac{1}{2}\frac{(x-gt^2)}{\sqrt{g}t})^2 = x\\\\\frac{1}{4gt^2}(x^2 - 2xgt^2 + g^2t^4) = x\\\\\frac{1}{4gt^2}x^2 - (\frac{2gt^2}{4gt^2}+1)x + \frac{g^2t^4}{4gt^2} = 0\\ \frac{1}{4gt^2}x^2 - \frac{3}{2}x + \frac{gt^2}{4} = 0\\[/tex]

[tex]0.0211 x^2 - 1.5x + 2.97 = 0\\[/tex]

Solving for x, you get that x is equal to 69.2 m or 2.03m. The total time of the fall would be:

[tex]x = \frac{1}{2}gt^2\\t=\sqrt{(2x/g)}[/tex]

Trying both possible values of x:

[tex]t_1 = 3.75 s\\t_2 = 0.64 s[/tex]

t2  is lower than 1.1s, therefore is not a real solution.

Therefore, the path traveled will be 69.2m and the total time 3.75s

Answer:

2.97m

Explanation:

Hi!

To solve this problem we must consider the directions of the electric fields, since both charges are positive each field will point outwards form the sources meaning that the field will point yo the -x direction formpoints along the x-axis to the left of the charges and the field will point to the +x direction for points along the x-axis to the rigth of the sources, having said this, the only place where the fields point to oposite ditections is between them:

In the following diagram X is the 17nC charge and O the 8nC charge, the arrows represent the direction of their respective electric fields and d is an arbitrary distance measured from the origin.

|-------d------|-----5-d------|

X-----------> | <------------O

|---------------5--------------|

At d the electric fields of the charges are:

[tex]E_{X}=k\frac{17nC}{d^{2}} \\E_{O}=-k\frac{8nC}{(5-d)^{2}}[/tex]

And the total field is the sum of both. Since we are looking for a position d at which the total or net electric field is zero we must solve the following equation:

[tex]0=k(\frac{17}{d^{2}} - \frac{8}{(5-d)^2} )[/tex]

Reorganizing terms:

17*(5-d)^2-8*d^2=0

17*25-170d+9d^2=0

Solving for d, we find two solutions

  d1 = 2.9655     d2=15.923

The second solution implies a distance outside the region between the charges for which the equations are no longer valid, since the direction of the 8nC field would be wrong.

So the solution is

 d=2.97 m

The rate of heat loss by radiation is equal to -207.5kW

Why?

To calculate the heat loss rate (or heat transfer rate) by radiation, from the given situation, we can use the following formula:

[tex]HeatLossRate=E*S*A*((T_{cold})^{4} -(T_{hot})^{4} )[/tex]

Where,

E, is the emissivity of the body.

A, is the area of the body.

T, are the temperatures.

S, is the Stefan-Boltzmann constant, which is equal to:

[tex]5.67x10^{-8}\frac{W}{m^{2}*K^{-4} }[/tex]

Now, before substitute the given information, we must remember that the given formula works with absolute temperatures (Kelvin), so,  we need to convert the given values of temperature from Celsius degrees to Kelvin.

We know that:

[tex]K=Celsius+273.15[/tex]

So, converting we have:

[tex]T_{1}=1110\°C+273.15=1383.15K\\\\T_{2}=36.2\°C+273.15=309.35K[/tex]

Therefore, substituting the given information and calculating, we have:

[tex]HeatLossRate=E*S*A*((T_{cold})^{4} -(T_{hot})^{4} )[/tex]

[tex]HeatLossRate=1*5.67x10^{-8}\frac{W}{m^{2}*K^{-4} }*1m^{2} *((309.35K)^{4} -(1383.15})^{4} )\\\\HeatLossRate=5.67x10^{-8}\frac{W}{K^{-4} }*(95697.42K^{4} -3.66x10^{12}K^{4})\\ \\HeatLossRate=5.67x10^{-8}\frac{W}{K^{-4} }*(-3.66x10^{12} K^{4})=-207522W=-207.5kW[/tex]

Hence, we have that the rate of heat loss is equal to -207.5kW.

Answer:

3.825*10^-6 N

Explanation:

As particle 1 and particle 3 has opposite types of charge, particle 3 will be attracted to particle 1. And as particle 2 and 3 has the same sign, they will repel each other. Due to the position of the particles, both the Force that 1 exerts on 3 and the force that 2 exerts on 3, will have the same direction. Now, you need the magnitude. You can use the following expression:

[tex]F_e = K\frac{q_1*q_3}{r^2}[/tex]

K is the Coulomb constant equal to 9*10^9 N*m^2/C^2, q1 and q2 is the charge of the particles, and r is the distance.

Force 1 on 3 is equal to:

[tex]F_e = K\frac{q_1*q_3}{r^2} = 9*10^9 \frac{Nm^2}{C^2} * \frac{2.3*10^{-9}C * 7.5*10^{-9}C}{(-0.6m - (-0.3m))^2} = 1.725 * 10^{-6} N[/tex]

Force 2 on 3:

[tex]F_e = K\frac{q_2*q_3}{r^2} = 9*10^9 \frac{Nm^2}{C^2} * \frac{2.8*10^{-9}C * 7.5*10^{-9}C}{(0m - (-0.3m))^2} = 2.1 * 10^{-6} N[/tex]

The magnitude of the resultant force is the addition of both forces:

[tex]F_e = 1.725*10^{-6} N + 2.1*10^{-6} N= 3.825 * 10^{-6} N[/tex]

The magnitude of the net force exerted by the two charges on the third charge is 1.38 N.

The magnitude of the net force exerted by q1 and q2 on q3 can be found using Coulomb's Law. Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:

F = k(q1 * q2) / r^2

Where F is the force, k is Coulomb's constant (k = 9 x 10^9 N * m^2 / C^2), q1 and q2 are the charges, and r is the distance between them.

In this case, q1 = -2.30 nC, q2 = 2.80 nC, q3 = 7.50 nC, y1 = -0.600 m, y3 = -0.300 m, and y2 = 0 m.

Using the formula and substituting the values, we can calculate the force:

F = (9 x 10^9 N * m^2 / C^2) * (q1 * q3) / ((y3 - y1)^2)

F = (9 x 10^9 N * m^2 / C^2) * (-2.30 nC * 7.50 nC) / ((-0.300 m + 0.600 m)^2)

F = -1.38 N

Therefore, the magnitude of the net force exerted by the two charges on the third charge is 1.38 N.

We have that for the Question "What is the minimum charge required to pick up the tissue paper?" it can be said that minimum charge is

From the question we are told

Generally the equation for the Electro static force  is mathematically given as

[tex]\frac{kqq'}{r^2}=mg\\\\Therefore\\\\q=\frac{5*10^{-3}*9.8*(0.06^)^2}{9*10^{9}*14*10^{-6}}\\\\q=1.4*10^{-9}C\\\\q=1.4mc\\\\[/tex]

q=0.0014\muC

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Answer:

The answer is  a=b=c=3.833 cm

Explanation:

Lets call the variables a=side a b=side b c=side c

We have that the formula of the equilateral triangle for its height is:

1)h=(1/2)*root(3)*a

2) If we resolve the equation we have

 2.1)2h=root(3)*a

 2.2)(2h/root(3))=a

3) After the replacement of each value we have that

a=2*3.32/1.73205

a=3.833 cm

And we know that the equilateral triangle has the same value for each side so a=b=c=3.833 cm

Answer:

a) 10.2 eV

b) 122 nm

Explanation:

a) First we must obtain the energy for each of the states, which is given by the following formula:

[tex]E_{n}=\frac{-13.6 eV}{n^2}[/tex]

So, we have:

[tex]E_{1}=\frac{-13.6 eV}{1^2}=-13.6 eV\\E_{2}=\frac{-13.6 eV}{2^2}=-3.4 eV[/tex]

Now we find the energy that the electron loses when it falls from state 2 to state 1, this is the energy carried away by the emitted photon.

[tex]E_{2}-E_{1}=-3.4eV-(-13.6eV)=10.2eV[/tex]

b) Using the Planck – Einstein relation, we can calculate the wavelength of the photon:

[tex]E=h\nu[/tex]

Where E is the photon energy, h the Planck constant and  [tex]\nu[/tex] the frequency.

Recall that [tex]\nu=\frac{c}{\lambda}[/tex], Rewriting for [tex]\lambda[/tex]:

[tex]E=\frac{hc}{\lambda}\\\lambda=\frac{hc}{E}\\\lambda=\frac{(4.13*10^{-15}eV)(3*10^8\frac{m}{s})}{10.2eV}=1.22*10^{-7}m[/tex]

Recall that [tex]1 m=10^9nm[/tex], So:

[tex]1.22*10^{-7}m*\frac{10^9nm}{1m}=122nm[/tex]

Answer:

45°

Explanation:

λ = 600 nm = 600 x 10^-9 m

d = 1.7 x 10^-6 m

For second order, N = 2

Use the equation

d Sinθ = N λ

1.7 x 10^-6 x Sinθ = 2 x 600 x 10^-9

Sinθ = 0.706

θ = 45°

Thus, the angle of diffraction is 45°.

The diffraction angle of the second-order line is approximately 44.22°.

The diffraction angle of the second order line can be found using the formula:

dsinθ = mλ

Where d is the ruling separation of the diffraction grating, θ is the diffraction angle, m is the order of the line, and λ is the wavelength of light. Plugging in the values given in the question:

1.7 × 10-6 m × sinθ = 2 × 600 × 10-9 m

Simplifying the equation:

sinθ = 2 × 600 × 10-9 m / (1.7 × 10-6 m)

Calculating the value of sinθ, we find:

sinθ ≈ 0.7059

Finally, taking the inverse sine of 0.7059, we find:

θ ≈ 44.22°

The second-order line occurs at a diffraction angle of approximately 44.22°.

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Answer:197.504 N

Explanation:

Given

Two Charges with magnitude Q experience a  force of 12.344 N

at distance r

and we know Electrostatic force is given

[tex]F=\frac{kq_1q_2}{r^2}[/tex]

[tex]F=\frac{kQ\cdot Q}{r^2}[/tex]

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

Now the magnitude of charge is 2Q and is at a distance of [tex]\frac{r}{2}[/tex]

[tex]F'=\frac{k2Q\cdot 2Q}{\frac{r^2}{2^2}}[/tex]

F'=16F

F'=197.504 N

Answer:

[tex]r=6.72\times 10^{-13}\ m[/tex]

Explanation:

Let r is the radius of the n = 1 orbit of the gold. According to Bohr's model, the radius of orbit is given by :

[tex]r=\dfrac{n^2h^2\epsilon_o}{Z\pi me^2}[/tex]

Where

n = number of orbit

h = Planck's constant

Z = atomic number (for gold, Z = 79)

m = mass of electron

e = charge on electron

[tex]r=\dfrac{(6.63\times 10^{-34})^2 \times 8.85\times 10^{-12}}{79\pi \times 9.1\times 10^{-31}\times (1.6\times 10^{-19})^2}[/tex]

[tex]r=6.72\times 10^{-13}\ m[/tex]

So, the radius of the n = 1 orbit of gold is [tex]6.72\times 10^{-13}\ m[/tex]. Hence, this is the required solution.

Final answer:

In a tug-of-war where forces are exerted in opposite directions (10 N south and 17 N north), the net force is calculated by subtracting the smaller force from the larger, resulting in a 7 N force towards the north. The correct answer is D.

Explanation:

The net force in a tug of war scenario is the vector sum of all the forces acting on the object. Since force is a vector quantity, it has both magnitude and direction. In this case, the force exerted by one team (17 N north) and the force exerted by the other team (10 N south) are in opposite directions along the same line, so we subtract the smaller force from the larger one to find the net force.

|17 N| - |10 N| = 17 N - 10 N = 7 N north.

Answer with Explanation:

We know from newton's second law that acceleration produced by a force 'F' in a body of mass 'm' is given by

[tex]a=\frac{Force}{Mass}=\farc{F}{m}[/tex]

In the given case the acceleration equals

[tex]a=\frac{F_{o}cos^{2}(\omega t)}{m}[/tex]

Now by definition of acceleration we have

[tex]a=\frac{dv}{dt}\\\\\int dv=\int adt\\\\v=\int adt\\\\v=\int \frac{F_{o}cos^{2}(\omega t)}{m}\cdot dt\\\\v=\frac{F_{o}}{m}\int cos^{2}(\omega t)dt\\\\v=\frac{F_{o}}{\omega m}\cdot (\frac{\omega t}{2}+\frac{sin(2\omega t)}{4}+c)[/tex]

Similarly by definition of position we have

[tex]v=\frac{dx}{dt}\\\\\int dx=\int vdt\\\\x=\int vdt[/tex]

Upon further solving we get

[tex]x=\int [\frac{F_{o}}{\omega m}\cdot (\frac{\omega t}{2}+\frac{sin(2\omega t)}{4}+c)]dt\\\\x=\frac{F_{o}}{\omega m}\cdot ((\int \frac{\omega t}{2}+\frac{sin(2\omega t)}{4}+c)dt)\\\\x(t)=\frac{F_{o}}{\omega m}\cdot (\frac{\omega t^{2}}{4}-\frac{cos(2\omega  t)}{8\omega }+ct+d)[/tex]

The plots can be obtained depending upon the values of the constants.

Answer:

net electrostatic force = 46.76 N

and direction is vertical downward

Explanation:

given data

charge =  +5μC

corners identical charges = -6 μC

length of side = 0.10 m

to find out

What is the net electrostatic force

solution

here apex is the vertex where the two sides of equal length meet

so upper point A have charge +5μC and lower both point B and C have charge -6 μC

so

force between +5μC and -6 μC is express as

force  = [tex]k \frac{q1q2}{r^2}[/tex]       ..............1

put here electrostatic constant  k = 9 × [tex]10^{9}[/tex] Nm²/C² and q1 q2 is charge given and r is distance 0.10 m

so

force  = [tex]9*10^{9} \frac{5*6*10^(-12)}{0.10^2}[/tex]

force = 27 N

so net force is vector addition of both force

force = [tex]\sqrt{x^{2}+x^{2}+2x^{2}cos60}[/tex]

here x is force 27 N

force = [tex]\sqrt{27^{2}+27^{2}+2(27)^{2}cos60}[/tex]

net electrostatic force = 46.76 N

and direction is vertical downward

Answer:

Distance, d = 6.75 meters

Explanation:

Given that,

Time taken by the eyes to shut during a hard sneeze, t = 0.32 s

Speed of the car, v = 76 km/h = 21.11 m/s

We need to find the distance covered by the car during this time. The product of speed and the time taken by the car is called the distance covered by the it. Mathematically,

[tex]d=v\times t[/tex]

[tex]d=21.11\times 0.32[/tex]

d = 6.75 meters

So, the car will cover 6.75 meters during that time. Hence, this is the required solution.

Final answer:

The final momentum of the car pushed by two men with a net force of 690 N for 6.6 seconds is 4554 N·s. This is calculated using the formula for impulse, which is the product of the net force and the time over which the force is applied.

Explanation:

The question is asking to calculate the final momentum of a car after two men have pushed it with a net force of 690 N for 6.6 seconds. According to Newton's second law of motion, the change in momentum (also known as impulse) is equal to the net force multiplied by the time over which the force is applied. The formula for impulse is:

Impulse (J) = Force (F) × Time (t)

By applying this formula, we can find the final momentum:

Therefore, the impulse is:

J = 690 N × 6.6 s = 4554 N·s

Since the car was initially at rest and assuming there is no external resistance, the final momentum of the car will be equal to the impulse given to it:

Final momentum = 4554 N·s

The final momentum of the car, with an applied force of +690 N for 6.6 seconds, is 4554 Ns.  The initial momentum is zero since the car starts from rest.

To determine the final momentum of the car, we will utilize the relationship between force, time, and momentum. According to the impulse-momentum theorem, the impulse applied to an object is equal to the change in its momentum.

Impulse is given by the formula:

Impulse (J) = Force (F) × Time (t)

Given:

Now, calculate the impulse:

J = 690 N × 6.6 s = 4554 Ns

In this scenario, the car starts from rest, which means its initial momentum (p_initial) is 0. Hence, the final momentum ([tex]p_{final}[/tex]) after 6.6 seconds is equal to the impulse:

[tex]p_{final}[/tex] = 4554 Ns

The final momentum of the car is 4554 Ns.

That statement is false.

Angular velocity is the rate at which that angle changes. As long as the reference line doesn't move, it doesn't matter where it is. The rate at which the angle changes is still the same, constant number.

The angular velocity of a rigid body that undergoes plane motion depends on the reference line from which its angle of rotation is measured is False.

When anything is moving, its velocity tells us how quickly that something's location is changing from a certain vantage point and as measured by a particular unit of time.

When a point travels down a path and completes a certain distance in a predetermined amount of time, its average speed over that time is equal to the distance covered divided by the travel time. A train traveling 100 kilometers in two hours, for instance, is doing it at an average speed of 50 km/h.

The pace at which that angle change is known as the angular velocity. It doesn't matter where the reference line is, as long as it stays put. The rate of change of the angle remains constant and the same.

Therefore, the angular velocity of a rigid body that undergoes plane motion depends on the reference line from which its angle of rotation is measured is False.

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Answer:

4.66 x 10^7 N/C

Explanation:

radius of drop, r = 35 micro meter = 35 x 10^-6 m

number of electrons, n = 26

density of water, d = 1000 kg / m^3

The gravitational force is equal to the product of mass of drop and the acceleration due to gravity.

Mass of drop, m = Volume of drop x density of water

[tex]m = \frac{4}{3}\times 3.14 \times r^{3}\times d[/tex]

[tex]m = \frac{4}{3}\times 3.14 \times \left ( 35\times10^{-6} \right )^{3}\times 1000[/tex]

m = 1.795 x 10^-10 kg

Gravitational force, Fg = m x g = 1.795 x 10^-10 x 9.8 = 1.759 x 10^-9 N

Charge,q = number of electrons x charge of one electron

q = 236 x 1.6 x 10^-19 = 3.776 x 10^-17 C

Electrostatic force, Fe = q E

Where, E is the strength of electric field.

here electrostatic force is balanced by the gravitational force

Fe = Fg

3.776 x 106-17 x E = 1.759 x 10^-9

E = 4.66 x 10^7 N/C

Answer:

The amount of charge at the center is -132.7 nC

Solution:

As per the question:

Electric flux from one face of cube, [tex]\phi_{E} = - 2.5 kN.m^{2}/C[/tex]

Edge, a = 19cm

Since, a cube has six faces, thus total flux from all the 6 faces = [tex]6\times (-2.5) = - 15 kN.m^{2}/C[/tex]

Also, from Gauss' law:

[tex]\phi_{E,net} = \frac{1}{\epsilon_{o}}Q_{enc}[/tex]

[tex]Q_{enc} = 8.85\times 10^{- 12}\times - 15\times 10^{3}[/tex]

[tex]Q_{enc} = - 132.7 nC[/tex]

Final answer:

To change 350 g of ice at -20 degrees Celsius to water at 20 Celsius, you need to calculate the heat required for two processes: warming the ice and melting the ice. The heat needed to warm the ice can be calculated using the equation: Q = mcΔT, and the specific heat capacity of ice is 2.09 J/g°C. The heat needed to melt the ice can be calculated using the equation: Q = mL, where L is the heat of fusion, which is 334 J/g for ice.

Explanation:

To calculate the heat necessary to change 350 g of ice at -20 degrees Celsius to water at 20 degrees Celsius, we need to consider the energy required for two processes: warming the ice from -20°C to 0°C and then melting the ice at 0°C to form water at 0°C.

The heat needed to warm the ice can be calculated using the equation: Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. The specific heat capacity of ice is 2.09 J/g°C.

The heat needed to melt the ice can be calculated using the equation: Q = mL, where L is the heat of fusion, which is 334 J/g for ice.

Let's calculate the heat needed for each process and add them together:

Finally, add both values to find the total heat required.

Answer:

−5.0  

Explanation:

Answer:

The squirrel's initial velocity is 5 m/s.

Explanation:

It is given that,

Distance covered by the squirrel, d = 5 m

Time taken, t = 0.5 s

Final speed of the squirrel, v = 15 m/s

To find,

The squirrel's initial velocity.

Solution,

Let a is the acceleration of the squirrel. Using the first equation of motion to find it :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{15-u}{0.5}[/tex]..............(1)

Let u is the initial speed of the squirrel. Using again third equation of kinematics to find it :

[tex]v^2-u^2=2ad[/tex]

Use equation (1) to put value of a

[tex](15)^2-u^2=2\times \dfrac{15-u}{0.5}\times 5[/tex]

[tex]225-u^2=20(15-u)[/tex]

On solving the above quadratic equation, we get the value of u as :

u = 5 m/s

Therefore, the squirrel's initial velocity before getting started is 5 m/s.

Answer:

[tex]y_{o}=v_{o}*sin(\alpha )*t + 1/2*gt^{2}[/tex]

Explanation:

Kinematics equation, with gravity as deceleration

[tex]y =y_{o}-v_{o}*sin(\alpha )*t - 1/2*gt^{2}[/tex]

If the base of the building is taken to be the origin of the coordinates, then :

[tex]y_{o} [/tex] is the initial coordinates of the ball

for t=5.00, the ball strikes the ground ⇒ y=0m

then:

[tex]y_{o}=v_{o}*sin(\alpha )*t + 1/2*gt^{2}[/tex]

Final answer:

The initial coordinates of the ball below the horizontal are (0, y0), with y0 representing the height from which the ball was tossed and 0 representing the horizontal origin.

Explanation:

The student's question asks for the initial coordinates of a ball tossed from a window with a given initial velocity and angle relative to the horizontal. Since we're dealing with projectile motion, we need to resolve the initial velocity into its horizontal (x-direction) and vertical (y-direction) components.

The initial horizontal velocity (vx0) can be found using trigonometry: vx0 = v0 × cos(θ), where v0 is the initial velocity of 8.40 m/s and θ is the launch angle of 15.0°. However, since the angle is below the horizontal, the vertical component of the initial velocity (vy0) will be negative: vy0 = v0 × sin(θ), pointing downward.

Given the vertical direction is positive upwards, and taking the base of the building to be at the origin (0,0), the initial coordinates of the ball will be (0, y0), where y0 represents the height of the window from which the ball was tossed.

Answer:

- 273.77 rad/s^2

Explanation:

fo = 3800 rev/min = 3800 / 60 rps = 63.33 rps

f = 0

ωo = 2 π fo = 2 x 3.14 x 63.33 = 397.71 rad/s

ω = 2 π f = 0

θ = 46 revolutions = 46 x 2π radian = 288.88 radian

Let α be the angular acceleration of the centrifuge

Use third equation of motion for rotational motion

[tex]\omega^{2}=\omega _{0}^{2}+2\alpha \theta[/tex]

[tex]0^{2}=397.71^{2}+2 \times \alpha \times 288.88[/tex]

α = - 273.77 rad/s^2

Answer:

q=heat flux=216.83W/m^2

Ts=36.45C

Explanation:

What you should do is raise the heat transfer equation from the inside of the granite wall to the air.

You should keep in mind that in the numerator you place the temperature differences, while the denominator places the sum of the thermal resistances by conduction and convection.

When you have the heat value, all you have to do is use the convection equation q = h (ts-t) and solve for the surface temperature.

I attached procedure

Answer:

[tex]r_{al}=2.598cm[/tex]

Explanation:

Density =mass/volume

[tex]D_{al}=2.70103kg/m^{3}[/tex]

[tex]D_{iron}=7.86103/m^{3}[/tex]

condition for balance:

[tex]M_{iron}=M_{al}[/tex]

M=D*Volum

then:

[tex]D_{iron}*4/3*pi*r_{ir}^{3}=D_{al}*4/3*pi*r_{al}^{3}[/tex]

[tex]r_{al}=r_{ir}*\sqrt[3]{\frac{D_{iron}}{D_{al}}}[/tex]

[tex]r_{al}=2.598cm[/tex]

Answer:

1.28 cm

Explanation:

Density (ρ) is an intensive property resulting from the quotient of mass (m) and volume (V).

The density of Al is ρAl = 2.70 × 10³ kg/m³

The density of Fe is ρFe = 7.86 × 10³ kg/m³

A Fe sphere of radius 1.82 cm has the following volume.

V = 4/3 × π × r³

V = 4/3 × π × (0.0182 cm)³

V = 2.53 × 10⁻⁵ m³

The mass corresponding to this sphere is:

2.53 × 10⁻⁵ m³ × 2.70 × 10³ kg/m³ = 0.0683 kg

The Al sphere has the same mass, so its volume is:

0.0683 kg × (1 m³/7.86 × 10³ kg) = 8.69 × 10⁻⁶ m³

The radius corresponding to an Al sphere of 8.69 × 10⁻⁶ m³ is:

V = 4/3 × π × r³

8.69 × 10⁻⁶ m³ = 4/3 × π × r³

r = 0.0128 m = 1.28 cm

Answer:

7.1 m

Explanation:

Given:

Distance traveled by the student in the first attempt = [tex](2.9 \pm 0.1)\ m[/tex]

Distance traveled by the student in the second attempt = [tex](3.9 \pm 0.2)\ m[/tex]

So, the maximum distance that the student could travel in this attempt = [tex](2.9+0.1)\ m = 3.0\ m[/tex]

So, the maximum distance that the student could travel in this attempt = [tex](3.9+0.2)\ m = 4.1\ m[/tex]

Since the student first moves straight in a particular direction, rests for a while and then moves some distance in the same direction.

So, the largest distance that the student could possibly be from the starting point would be the largest distance of the final position of the student from the starting point.

And this distance is equal to the sum of the maximum distance possible in the first attempt and the second attempt of walking which is 7.1 m.

Hence, the largest distance that the student could possibly be from the starting point is 7.1 m.

Answer:

The average velocity of the car is 32 m/s.

Explanation:

Given that,

Initial position = 50 m

Final position = 210 m

Time = 5 sec

(a). We need to calculate the average velocity of the car

Using formula of average velocity

[tex]v_{avg}=\dfrac{v_{f}-v_{i}}{t}[/tex]

Put the value into the formula

[tex]v_{avg}=\dfrac{210-50}{5}[/tex]

[tex]v_{avg}=32\ m/s[/tex]

(b). We need to draw the position vs. time graph

We need to calculate the slope of the line of best fit.

Using formula of slop

[tex]slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Put the value into the formula

[tex]slope =\dfrac{210-50}{5-0}[/tex]

[tex]slope =32[/tex]

Hence, The average velocity of the car is 32 m/s.

Answer:

The wavelength of the particle is [tex]\lambda=\frac{h}{\sqrt{2V\cdot e\cdot m}}[/tex]

Explanation:

We know that after accelerating across a potential 'V' the potential energy of the charge is converted into kinetic energy as

[tex]\frac{1}{2}mv^{2}=V\cdot e\\\\\therefore v=\sqrt{\frac{2V\cdot e}{m}}[/tex]

now according to De-Broglie theory the wavelength associated with a particle of mass 'm' moving with a speed of 'v' is given by

[tex]\lambda =\frac{h}{mv}[/tex]

where

'h' is planck's constant

'm' is the mass of particle

'v' is the velocity of the particle

Applying the values in the above equation we get

[tex]\lambda =\frac{h}{m\cdot \sqrt{\frac{2V\cdot e}{m}}}[/tex]

Thus

[tex]\lambda=\frac{h}{\sqrt{2V\cdot e\cdot m}}[/tex]

Answer:

Wavelength of the particle is [tex]\frac{h}{\sqrt{2meV}}[/tex]

Solution:

As per the question:

The particle with mass, m and charge, e accelerates through V (potential difference).

The momentum of the particle, [tex]p_{p}[/tex] if it travels with velocity, [tex]v_{p}[/tex]:

[tex]p_{p} = mv_{p}[/tex]

Now, squaring both sides and dividing by 2.

[tex]\frac{1}{2}p_{p}^{2} = \frac{1}{2}m^{2}v_{p}^{2}[/tex]

[tex]K.E =\frac{1}{2m}p_{p}^{2} = \frac{1}{2}mv_{p}^{2}[/tex]

[tex]K.E = \frac{1}{2}mv_{p}^{2}[/tex]

Also,

[tex]p_{p} = \sqrt{2mK.E}[/tex]          (1)

Now, we know that Kinetic energy of particle accelerated through V:

K.E = eV       (2)

where

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

From eqn (1) and (2):

[tex]p_{p} = \sqrt{2mK.E}[/tex]              (3)

From eqn (2) and (3):

[tex]p_{p} = \sqrt{2meV}[/tex]

From the de-Broglie relation:

[tex]\lambda_{p} = \frac{h}{p_{p}}[/tex]      (4)

where

[tex]\lambda_{p}[/tex] = wavelength of particle

h = Planck's constant

From eqn (3) and (4):

[tex]\lambda_{p} = \frac{h}{\sqrt{2meV}}[/tex]

Answer:

Explanation:

The standard equation of the sinusoidal wave in one dimension is given by

[tex]y = A Sin\left ( \frac{2\pi }{\lambda }\left ( vt-x \right )+\phi  \right )[/tex]

Here, A be the amplitude of the wave

λ be the wavelength of the wave

v be the velocity of the wave

Φ be the phase angle

x be the position of the wave

t be the time

this wave is travelling along positive direction of X axis

The frequency of wave is f which relates with velocity and wavelength as given below

v = f x λ

The relation between the time period and the frequency is

f = 1 / T.