A woman stands on a scale in a moving elevator. Her massis
60.0 kg and the combined mass of the elevator and scale is
anadditional 815 kg. Starting from rest, the elevatoraccelerates
upward. During the acceleration, there is tensionof 9410 N in the
hoisting cable. What does the scale readduring the
acceleration?

Answer:

Q must be placed at 0.53 L

Explanation:

Given  data:

q_1 = 4.0 μC , q_2 = 3.0μC

Distance between charge is L

third charge q be placed at  distance x cm from q1

The force by charge q_1 due to q is

[tex]F1 = \frac{k q q_1}{x^2}[/tex]

[tex]F1 = \frac{k q ( 4.0 μC )}{ x^2}[/tex]                  ----1

The force by charge q_2 due to q is

[tex]F2 =  \frac{k q q_2}{(L-x)^2}[/tex]

[tex]F2 = \frac{kq (3.0 μC)}{(L-x)^2}[/tex]                   --2

we know that net electric force is equal to zero

F_1 = F_2

[tex]\frac{k q ( 4.0 μC )}{x^2}   =\frac{k q ( 3.0 μC )}{(l-x)^2}[/tex]

[tex]\frac{4}{3}*(L-x)^2 = x^2[/tex]

[tex]x = \sqrt{\frac{4}{3}*(L - x)[/tex]

[tex]L-x = \frac{x}{1.15}[/tex]

[tex]L = x + \frac{x}{1.15} = 1.86 x[/tex]

x = 0.53 L

Q must be placed at 0.53 L

The third charge should be placed either between the two charges or on the extended line of the two charges to make the electric force on that charge zero. The exact position depends on the charges involved and can be calculated using the principle of superposition and Coulomb's Law.

The problem deals with the principle of superposition in electrostatics and the force on a charge due to other charges nearby. The force on any charge due to a number of other charges is simply the vector sum of the forces due to individual charges. Starting from this principle, we can try to figure out where the third charge must be placed so that the net force on it is zero.

The two possible positions along the line of the charges are on either side of the two given charges, let's call them 4.0 µC (charge_1) and 3.0 µC (charge_2). These positions can be calculated using the formula of force between two point charges (Coulomb's Law): F = k(q1 x q2)/r² where F is force, k is Coulomb's constant, q1 and q2 are charges and r is distance between charges.

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The false statement among the provided ones about conservative forces is 'None of these statements are true'. Conservative forces rely on the starting and ending points, not the path taken, and the work done on any closed path is always zero. These forces also have a close relationship with potential energy.

The statements provided about conservative forces generally hold true however the false statement is 'None of these statements are true', as all other statements presented are indeed accurate. A conservative force is a type of force where the work done is independent of the path. That is, the work it does only depends on the starting and ending points, not the route taken. This implies that during any closed path or loop, the total work done by a conservative force is zero.

Consider a simple example, such as the gravitational force. If you lift an object to a certain height and then back to its original position, the total work done by the gravitational force is zero as the starting and ending points are the same.

An important concept related to the conservative force is potential energy. When work is done against a conservative force, potential energy is accumulated. Conversely, the component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.

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Answer:

[tex]\lambda=8.006\times 10^{-11}\ m[/tex]

Explanation:

Given that,

The speed of an electron, [tex]v=9.1\times 10^6\ m/s[/tex]

We need to find the wavelength of this electron. It can be calculated using De -broglie wavelength concept as :

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

h is the Planck's constant

[tex]\lambda=\dfrac{6.63\times 10^{-34}}{9.1\times 10^{-31}\times 9.1\times 10^6}[/tex]

[tex]\lambda=8.006\times 10^{-11}\ m[/tex]

So, the wavelength of the electron is [tex]8.006\times 10^{-11}\ m[/tex]. Hence, this is the required solution.

Final answer:

To find the speed and direction of the wind as observed by a stationary observer when a cyclist is traveling southeast along a road and there is a wind blowing from the southwest, we can use vector addition. By breaking down the velocities of the cyclist and the wind into their components and adding them together, we can determine that the speed of the wind is 15 km/h in the direction of 135°.

Explanation:

The question is asking for the speed and direction of the wind as observed by a stationary observer when a cyclist is traveling southeast along a road at 15 km/h and there is a wind blowing from the southwest at 25 km/h. To calculate the speed and direction of the wind, we can use vector addition. The velocity of the cyclist is given as 15 km/h in the southeast direction. The velocity of the wind is given as 25 km/h in the southwest direction. To find the speed and direction of the wind, we need to add the velocities of the cyclist and the wind.

We can represent the velocity vectors as follows:

Velocity of cyclist = 15 km/h (southeast)

Velocity of wind = 25 km/h (southwest)

To add these vectors, we can break them down into their components:

Velocity of cyclist = 15 km/h * sin(45°) (south) + 15 km/h * cos(45°) (east)

Velocity of wind = 25 km/h * sin(225°) (south) + 25 km/h * cos(225°) (west)

Adding the components of the velocities:

Velocity of cyclist + Velocity of wind = (15 km/h * sin(45°) + 25 km/h * sin(225°)) (south) + (15 km/h * cos(45°) + 25 km/h * cos(225°)) (east)

Calculating the components:

Velocity of cyclist + Velocity of wind = (-10.61 km/h) (south) + (-10.61 km/h) (east)

To find the speed and direction of the wind, we can use the Pythagorean theorem and trigonometry:

Speed of wind = sqrt((-10.61 km/h)^2 + (-10.61 km/h)^2) = 15 km/h

Direction of wind = atan2((-10.61 km/h), (-10.61 km/h)) = 135°

Therefore, the speed of the wind as observed by the stationary observer is 15 km/h in the direction of 135°.

Answer:

Explained

Explanation:

Equipotential lines cannot cross each other because. The equipotential at a given point in space is has single value of potential throughout. If two equipotential lines intersect with each other, that would mean two values of potential, that would not mean equipotential line. Hence two equipotential lines cannot cross each other.

Equipotential lines are imaginary lines that connect points with the same electric potential. Two equipotential lines cannot cross each other because that would mean two different points on the same line have the same electric potential, which is not possible.

Equipotential lines are imaginary lines that connect points with the same electric potential. Two equipotential lines cannot cross each other because that would mean two different points on the same line have the same electric potential, which is not possible.

For example, imagine a hill with contour lines representing lines of equal height. If two contour lines were to cross each other, it would mean that two different points on the hill have the same height, which is not possible.

In electricity, the electric potential difference between two points on an equipotential line is zero. If two equipotential lines were to cross, it would create a contradiction, as the potential difference between the two points of intersection would be both zero and non-zero.

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Final answer:

The volume of the larger sphere is eight times greater than that of the smaller sphere, and since their masses are proportional to their volumes for objects of uniform density, we can find the radius of the larger sphere to be twice that of the smaller sphere with a radius of 4.10 cm, resulting in a radius of 8.20 cm for the larger sphere.

Explanation:

The question concerns a comparison of the volumes of two spheres made from the same uniform rock. Since the mass of one sphere is eight times greater than the other, and since mass is proportional to volume for objects with uniform density, we can deduce that the volume of the larger sphere is also eight times greater than the smaller sphere. Given that the volume of a sphere (V) is calculated as V = (4/3)πR³, where R is the radius, we understand that because the volumes are proportional to the cube of the radii, we can calculate the radius of the larger sphere if we know the radius of the smaller one. Specifically, if the radius of the smaller sphere is 4.10 cm and its volume is V, then the volume of the larger sphere is 8V, and its radius is 2 times that of the smaller sphere since 2³ equals 8. Therefore, the radius of the larger sphere is 2 × 4.10 cm = 8.20 cm.

Answer:

Frequency is 0.5 Hz and the wave speed is 10 m/s.

Explanation:

As we know that frequency is defined as the how many times the no of cycles repeat in one second so if the wave is vibrating up and down  twice during 1 second then the frequency in 1 second is

[tex]f=\frac{1}{2} hz\\F=0.5hz[/tex]

Therefore frequency is 0.5 Hz.

Now the distance of wawe in each second is,

[tex]d=20m[/tex]

Now the wave velocity is,

[tex]v=fd[/tex]

Here, f is frequency, d is the distance, v is the wave velocity.

Substitute all the variables

[tex]v=0.5\times 20\\v=10m/s[/tex]

Therefore the wave speed is 10 m/s.

In the given question, the wave's frequency is 2 Hertz (Hz), which means it oscillates twice per second. The wave speed, or distance covered by the wave per second, is identified as 20 m/s. These are fundamental concepts in the Physics of wave mechanics.

In this question, we're dealing with the topics of wave frequency and wave speed. The frequency of a wave relates to how many cycles of the wave occur per unit of time - in this case, the wave is oscillating twice per every second, meaning that its frequency is 2 Hertz (Hz).

The wave speed is the speed at which the wave is travelling. Given that the wave travels a distance of 20 m each second, the speed of the wave is 20 m/s (meters per second).

It's important to note that these two properties are interconnected. In general, the speed of a wave (v) is calculated by multiplying its wavelength (λ) by its frequency (f). So, using the relationship v = λf, the properties of a wave can be determined if the other two are known.

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Answer:

The linear expansion coefficient of the material is [tex]4.952\times10^{-5}\ K^{-1}[/tex]

Explanation:

Given that,

Volume = 1.5 l

Temperature = 20°C

Increased temperature = 55°C

Volume = 7.8 mL

We need to calculate the linear expansion coefficient of the material

Using formula of  linear expansion

[tex]\Delta V=V_{0}\beta \Delta T[/tex]

[tex]\Delta V=V_{0}(3\alpha \Delta T)[/tex]

[tex]\alpha =\dfrac{\Delta V}{3V_{0}\Delta T}[/tex]

Put the value into the formula

[tex]\alpha=\dfrac{7.8\times10^{-3}}{3\times1.5\times(55-20)}[/tex]

[tex]\alpha=0.00004952[/tex]

[tex]\alpha=4.952\times10^{-5}\ K^{-1}[/tex]

Hence, The linear expansion coefficient of the material is [tex]4.952\times10^{-5}\ K^{-1}[/tex]

Answer:

The smallest distance the student that the student could be possibly be from the starting point is 6.5 meters.

Explanation:

For 2 quantities A and B represented as

[tex]A\pm \Delta A[/tex] and [tex]B\pm \Delta B[/tex]

The sum is represented as

[tex]Sum=(A+B)\pm (\Delta A+\Delta B)[/tex]

For the the values given to us the sum is calculated as

[tex]Sum=(2.9+3.9)\pm (0.1+0.2)[/tex]

[tex]Sum=6.8\pm 0.3[/tex]

Now the since the uncertainity inthe sum is [tex]\pm 0.3[/tex]

The closest possible distance at which the student can be is obtained by taking the negative sign in the uncertainity

Thus closest distance equals [tex]6.8-0.3=6.5[/tex]meters

Answer:

6.45 a

Explanation:

Charge on O, q1 = 4q

Charge on A, q2 = - 3 q

OA = a

Let the net force is zero at point P, where AP = x , let a charge Q is placed at P.

The force on point P due to the charge q1 = The force on point P due to the  

                                                                          charge q2

By using Coulomb's law

[tex]\frac{Kq_{1}Q}{OP^{2}}=\frac{Kq_{2}Q}{AP^{2}}[/tex]

[tex]\frac {K4qQ}{(a+x)^{2}}= \frac {K3qQ}{x^{2}}[/tex]

[tex]\frac{a+x}{x}=\sqrt{\frac{4}{3}}[/tex]

[tex]\frac{a+x}{x}=1.155[/tex]

a + x = 1.155 x

0.155 x = a

x = 6.45 a

Thus, the force is zero at x = 6.45 a.

Answer:0.114 C

Explanation:

Given

Total 4.7 C is distributed in two spheres

Let [tex]q_1[/tex] and [tex]q_2[/tex] be the charges such that

[tex]q_1+q_2=4.7[/tex]

and Force between charge particles is given by

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

[tex]4.7\times 10^11=\frac{9\times 10^9\times q_1\cdot q_2}{0.1^2}[/tex]

[tex]q_1\cdot q_2=0.522[/tex]

put the value of [tex]q_1[/tex]

[tex]q_2\left ( 4.7-q_2\right )=0.522[/tex]

[tex]q_2^2-4.7q_2+0.522=0[/tex]

[tex]q_2=\frac{4.7\pm \sqrt{4.7^2-4\times 1\times 0.522}}{2}[/tex]

[tex]q_2=0.114 C[/tex]

thus [tex]q_1=4.586 C[/tex]

Answer:

vo = 0.175m/s

a = -0.040625 m/s^2

Explanation:

To solve this problem, you will need to use the equations for constant acceleration motion:

[tex]x = \frac{1}{2}at^2 +v_ot+x_o \\v_f^2 - v_o^2 = 2(x-x_o)a[/tex]

In the first equation you relate final position with the time elapsed, in the second one, you relate final velocity at any given position. In both equations, you will have both the acceleration a and the initial velocity vo as variables. We can simplify with the information we have:

1. [tex]x = \frac{1}{2}at^2 +v_ot+x_o\\0.1m = \frac{1}{2}a(8s)^2 +v_o(8s)+0m \\0.1 = 32a + 8v_o[/tex]

2. [tex]v_f^2 - v_o^2 = 2(x-x_o)a\\(-0.15m/s)^2 - v_o^2 = 2(0.1m-0m)a\\0.0225 - v_o^2 = 0.2a\\a = \frac{0.0225 - v_o^2}{0.2} = 0.1125 - 5v_o^2[/tex]

Replacing in the first equation:

[tex]0.1 = 32(0.1125 - 5v_o^2) + 8v_o\\0.1 = 3.6 - 160v_o^2 + 8v_o\\160v_o^2 - 8v_o - 3.5 = 0[/tex]

[tex]v_0 = \frac{-(-8) +- \sqrt{(-8)^2 - 4(160)(-3.5)}}{2(160)} \\ v_o = 0.175 m/s | -0.125 m/s[/tex]

But as you are told that the ball was projected om the air track, it only makes sense for the velocity to be positive, otherwise it would have started moving outside the air track, so the real solution is 0.175m/s. Then, the acceleration would be:

[tex]a = 0.1125 - 5v_o^2\\a = -0.040625  m/s^2[/tex]

Answer:

pressure of water will be 49.7 atm

Explanation:

given data

pressure = 30 psi = 2.04 atm

water = 2 pound = 907.18

mole of water vapor = 907.19 /2 = 50.4 mole

volume = 4 ft³ = 113.2 L

temperature = 40 F = 277.59 K

to find out

pressure of water

solution

we will apply here ideal gas condition

that is

PV = nRT  .......................1

put here all value and here R = 0.0821 , T temperature and V volume and P pressure and n is no of mole

and we get here temperature

PV = nRT  

2.04 × 113.2 = 50.4×0.0821×T

solve it and we get

T = 55.8 K

so we have given right chamber has twice the volume of the left chamber i.e

volume = twice of volume + volume

volume = 2(113.2) + 113.2

volume = 339.6 L

so from equation 1 pressure will be

PV = nRT

P(339.6) = 50.4 × ( 0.0821) × (277.59)

P = 3.3822 atm = 49.7 atm

so pressure of water will be 49.7 atm

Answer:

density of liquid 0.848 g/ml

Explanation:

from the information given in the question

mass of water = 34.914 - 25.296 = 9.618 g

volume of pycnometer = volume of water

which will be equal to [tex]= \frac{ mass}{density}[/tex]

[tex]= \frac{9.618}{0.9970} = 9.646 ml[/tex]

mass of liquid =33.485-25.296 = 8.189 ml

density of liquid[tex]= \frac{mass}{volum\ of\ liquid}[/tex]

                           = [tex]\frac{8.189}{9.646} =0.848 g/ml[/tex]

Answer:

[tex]q=9.83\times 10^{-8}\ C[/tex]

Explanation:

Given that,

Mass of the two spheres, m₁ = m₂ = 1 g = 0.001 kg

Distance between spheres, d = 2.2 cm = 0.022 m

Acceleration of the spheres when they are released, [tex]a=180\ m/s^2[/tex]

Let q is the charge on each spheres. The force due to motion is balanced by the electrostatic force between the spheres as :

[tex]ma=k\dfrac{q^2}{d^2}[/tex]

[tex]q=\sqrt{\dfrac{mad^2}{k}}[/tex]

[tex]q=\sqrt{\dfrac{0.001\times 180\times (0.022)^2}{9\times 10^9}}[/tex]

[tex]q=9.83\times 10^{-8}\ C[/tex]

So, the magnitude of charge on each sphere is [tex]9.83\times 10^{-8}\ C[/tex]. Hence, this is the required solution.

To find the magnitude of the charge on the spheres, we utilize Coulomb's Law and Newton's Second Law, set up an equation, and solve for the charge q. Ensure consistency in the units while solving.

To find the magnitude of the charge on the spheres, we start by using Coulomb's Law, which is expressed as F = k*q1*q2/r^2. Here, F is the force, k is Coulomb's constant (8.99 * 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the separation. Given that the spheres are charged equally (q1 = q2), we can refer to them just as q.

The spheres start accelerating once released, and the only force in operation is the electrostatic force. Thus, according to Newton's second law (F = ma), the force can also be expressed as F = 2*(mass*acceleration) because two spheres are involved.

By equating both expressions for F, we have 2*(mass*acceleration) = k*q^2/r^2. From this equation, we can solve for q = sqrt((2*mass*acceleration*r^2)/k). Substituting given values, we have q = sqrt((2 * 1.0 g * 180 m/s^2 * (2.2 cm)^2)/(8.99 * 10^9 N m^2/C^2)).

Remember to convert grams to kilograms and centimeters to meters to maintain consistency in the units while solving.

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Answer:

a) The acceleration is 2.14 m/s^{2}

b) The distance traveled by the car is 65.61 m

c) The average velocity is 18.75 m/s

Explanation:

Using the equations that describe an uniformly accelerated motion:

a) [tex]a=\frac{v_f - v_o}{t} =\frac{22.5m/s - 15.0 m/s}{3.50s}[/tex]

b) [tex]d= d_0 + v_0 t + \frac{1}{2} a t^{2} = 0 +15.0 x 3.5 + \frac{2.14x3.50^{2} }{2} = 65.61 m[/tex]

c) [tex]v_m =\frac{d}{t}=\frac{65.61}{3.5}  =18.75 m/s[/tex]

Answer:

Average speed, v = 11.37 m/s

Explanation:

Given that,

The distance covered by the traveler, d = 217 miles = 349228 meters

Time taken, [tex]t = 8\ hours \ 32\ minutes =8\ h+\dfrac{32}{60}\ h=8.53\ h[/tex]

or t = 30708 s

We need to find the average speed for this trip. The average speed is given by :

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{349228\ m}{30708\ s}[/tex]  

v = 11.37 m/s

So, the average speed for this trip is 11.37 m/s. Hence, this is the required solution.

Final answer:

The absolute pressure at the bottom of the Mariana Trench is calculated by adding the atmospheric pressure to the hydrostatic pressure due to the water column, resulting in approximately 509,367.85 lbf/in.².

Explanation:

To calculate the absolute pressure at the bottom of the Mariana Trench, we start by understanding that pressure in a static fluid increases linearly with depth. The increase in pressure, ΔP, due to the water column can be calculated using the formula ΔP = ρgh, where ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth. Given the constants, ρ = 64.2 lb/ft³, g = 32.1 ft/s², and h = 6.8 miles (35,856 ft), we first convert the depth into feet as pressure calculations require consistent units. The calculation is as follows: ΔP = 64.2 lb/ft³ * 32.1 ft/s² * 35,856 ft = 73,346,473.6 lb/ft². Converting this to lbf/in.², we divide by 144 (since 1 ft² = 144 in.²), resulting in ΔP approximately 509,353.15 lbf/in.². Adding the atmospheric pressure of 14.7 lbf/in.² at the surface, the absolute pressure at the bottom of the Mariana Trench in lbf/in.² is approximately 509,367.85 lbf/in.².

The absolute pressure at the depth of the Mariana Trench is approximately [tex]\(7.42 \times 10^9 \, \text{lbf/in}^2\),[/tex]calculated using the hydrostatic pressure formula.

To find the absolute pressure at the depth of the Mariana Trench, we can use the hydrostatic pressure formula:

[tex]\[ P = P_0 + \rho \cdot g \cdot h \][/tex]

Where:

-  P is the absolute pressure at the depth,

-  P0  is the atmospheric pressure at the surface (given as 14.7 lbf/in²),

-  rho  is the density of seawater (given as 64.2 lb/ft³),

-  g  is the acceleration due to gravity (given as 32.1 ft/s²), and

-  h  is the depth of the trench (given as 6.8 miles).

First, let's convert the depth from miles to feet:

[tex]\[ 6.8 \text{ miles} \times 5280 \text{ ft/mile} = 35904 \text{ ft} \][/tex]

Now, we can plug in the values into the formula:

[tex]\[ P = 14.7 \text{ lbf/in}^2 + (64.2 \text{ lb/ft}^3) \times (32.1 \text{ ft/s}^2) \times (35904 \text{ ft}) \][/tex]

Let's calculate this value.

To find the absolute pressure at the depth of the Mariana Trench, we'll first calculate the pressure due to the water column using the hydrostatic pressure formula:

[tex]\[ P = P_0 + \rho \cdot g \cdot h \][/tex]

Where:

- [tex]\( P_0 = 14.7 \, \text{lbf/in}^2 \)[/tex] is the atmospheric pressure at the surface,

-[tex]\( \rho = 64.2 \, \text{lb/ft}^3 \)[/tex] is the density of seawater,

- [tex]\( g = 32.1 \, \text{ft/s}^2 \)[/tex] is the acceleration due to gravity, and

- [tex]\( h = 6.8 \, \text{miles} \times 5280 \, \text{ft/mile} = 35904 \, \text{ft} \)[/tex]is the depth of the trench in feet.

Plugging in the values:

[tex]\[ P = 14.7 + (64.2 \times 32.1 \times 35904) \][/tex]

Let's calculate this.

[tex]\[ P = 14.7 + (64.2 \times 32.1 \times 35904) \][/tex]

[tex]\[ P = 14.7 + (64.2 \times 32.1 \times 35904) \][/tex]

[tex]\[ P = 14.7 + (206368.8 \times 35904) \][/tex]

[tex]\[ P = 14.7 + 7417798272 \][/tex]

[tex]\[ P ≈ 7417798286.7 \, \text{lbf/in}^2 \][/tex]

Therefore, the absolute pressure at the depth of the Mariana Trench is approximately [tex]\( 7.42 \times 10^9 \, \text{lbf/in}^2 \).[/tex]

The final temperature can be calculated using the principle of conservation of energy. Using the formulas Q = mcΔT and Q = mcΔT, we can find the heat lost by the iron and the heat gained by the ethyl alcohol. The final temperature of all 3 substances are, T_f = 12.08 °C.

To calculate the final temperature of the substances, we can use the principle of conservation of energy. The heat gained by one substance is equal to the heat lost by another substance. First, we calculate the heat lost by the iron using the formula Q = mcΔT, where Q is the heat lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Then, we calculate the heat gained by the ethyl alcohol using the same formula. Finally, we use the principle of conservation of energy to find the final temperature.

We have:

Using the formula Q = mcΔT, we can calculate:

Since the heat lost by the iron is equal to the heat gained by the ethyl alcohol, we can set up the equation:

(200 g)(452 J/g °C)(120 °C - T_f) = (300 g)(2.30 J/g °C)(T_f - 20 °C)

To solve for T_f, we can simplify and rearrange the equation:

(90400 - 452T_f) J = (T_f- 13800) J

Combining like terms:

13800 J = 1142T_f J

Dividing both sides by 1142:

T_f = 12.08 °C

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Answer:

W = 0 :The work done on the wall is zero,because the wall is not moving

Explanation:

Work theory

Work is the product of a force applied to a body and the displacement of the body in the direction of this force.

W= F*d Formula (1)

W: Work (Joules) (J)

F: force applied (N)

d=displacement of the body (m)

The work is positive (W+) if the force goes in the same direction of movement.

The work is negative (W-)if the force goes in the opposite direction to the movement

Data

F= 400-N

d= 0

Problem development

We apply formula (1) to calculate the work done on the wall:

W= 400*0

W=0

Answer:

Option A decreases with increase in altitude

Explanation:

This can be explained as the value of gravitational acceleration, 'g' is not same everywhere.

It has its maximum value at poles of the Earth and minimum on its equator.

Thus a person will weigh more at poles than equator.

This variation is in accordance to:

[tex]g = \frac{GM_{E}}{radius^{2}}[/tex]

Thus the gravitational acceleration changes as inverse square of the Radius of the Earth.

Thus as we move away from the Earth's center, gravitational acceleration, g decreases.

Answer:

Acceleration, [tex]a=14970.05\ km/h^2[/tex]

Explanation:

Given that,

Initially, the jetliner is at rest, u = 0

Final speed of the jetliner, v = 250 km/h

Time taken, t = 1 min = 0.0167 h

We need to find the acceleration of the jetliner. The mathematical expression for the acceleration is given by :

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

[tex]a=\dfrac{250}{0.0167}[/tex]

[tex]a=14970.05\ km/h^2[/tex]

So, the acceleration of the jetliner is [tex]14970.05\ km/h^2[/tex]. Hence, this is the required solution.

Answer:

circuit sketched in first attached image.

Second attached image is for calculating the equivalent output resistance

Explanation:

For calculating the output voltage with regarding the first image.

[tex]Vout = Vin \frac{R_{2}}{R_{2}+R_{1}}[/tex]

[tex]Vout = 5 \frac{2000}{5000}[/[tex]

[tex]Vout = 5 \frac{2000}{5000}\\Vout = 5 \frac{2}{5} = 2 V[/tex]

For the calculus of the equivalent output resistance we apply thevenin, the voltage source is short and current sources are open circuit, resulting in the second image.

so.

[tex]R_{out} = R_{2} || R_{1}\\R_{out} = 2000||3000 = \frac{2000*3000}{2000+3000} = 1200[/tex]

Taking into account the %5 tolerance, with the minimal bound for Voltage and resistance.  

if the -5% is applied to both resistors the Voltage is still 5V because the quotient  has 5% / 5% so it cancels. to be more logic it applies the 5% just to one resistor, the resistor in this case we choose 2k but the essential is to show that the resistors usually don't have the same value. applying to the 2k resistor we have:

[tex]Vout = 5 \frac{1900}{4900}\\Vout = 5 \frac{19}{49} = 1.93 V[/tex]

[tex]Vout = 5 \frac{2100}{5100}\\Vout = 5 \frac{21}{51} = 2.05 V[/tex]

[tex]R_{out} = R_{2} || R_{1}\\R_{out} = 1900||2850= \frac{1900*2850}{1900+2850} = 1140[/tex]

[tex]R_{out} = R_{2} || R_{1}\\R_{out} = 2100||3150 = \frac{2100*3150 }{2100+3150 } = 1260[/tex]

so.

[tex]V_{out} = {1.93,2.05}V\\R_{1} = {1900,2100}\\R_{2} = {2850,3150}\\R_{out} = {1140,1260}[/tex]

Answer:

0.063

Explanation:

velocity of the car, v = 40 km/h = 11.11 m/s

radius, r = 200 m

Let the coefficient of friction is μ.

The coefficient of friction relates to the velocity on banked road is given by

[tex]\mu =\frac{v^{2}}{rg}[/tex]

where, v is the velocity, r be the radius of the curve road and μ is coefficient of friction.

By substituting the values, we get

[tex]\mu =\frac{11.11^{2}}{200\times 9.8}[/tex]

μ = 0.063

Answer:

Force exerted on the right cube by the middle cube:

F= 12.02N : in the positive direction of the x axis( +x)

Explanation:

We apply Newton's second law for forces in the direction of the x-axis.

∑Fx= m*a

∑Fx:  algebraic sum of forces ( + to the right, - to the left)

m: mass

a: acceleration

We apply Newton's first law for forces in the direction of the y-axis.

∑Fx= mt*a   , mt: total mass = 6*3= 18 kg

36-6= 18*a

[tex]a=\frac{36-6}{18} = 1.67 \frac{m}{s}[/tex]

∑Fy= 0

Nt-Wt=0   , Nt=Wt

Nt: total normal   ,  Wt= total Weight: mt*g  , g: acceleration due to gravity

Wt=18*9,8=176.4 N

Nt=176.4 N

μk=Ff/Nt Ff: friction force = 6 N

μk=6/176.4 = 0.034

∑Fx= m₁*a

F-Ff₁= 6*1.67 , Equation  (1)

F:Force exerted on the right cube by the middle cube

Ff₁= μk*N₁ , N₁=W₁ = 9.8*6= 58.8 N

Ff₁= 0.034*58.8 = 2 N

In the  Equation  (1):

F-2= 10.02

F= 2+10.02= 12.02N

F= 12.02N

Answer:

shadow length 7.67 cm

Explanation:

given data:

refractive index of water is 1.33

by snell's law we have

[tex]n_{air} sin30 =n_{water} sin\theta[/tex]

[tex]1*0.5 = 1.33*sin\theta[/tex]

solving for[tex] \theta[/tex]

[tex]sin\theta = \frac{3}{8}[/tex]

[tex]\theta = sin^{-1}\frac{3}{8}[/tex]

[tex]\theta =  22 degree[/tex]

from shadow- stick traingle

[tex]tan(90-\theta) = cot\theta = \frac{h}{s}[/tex]

[tex]s = \frac{h}{cot\theta} = h tan\theta[/tex]

s = 19tan22 = 7.67 cm

s = shadow length

The calculated shadow length is approximately 10.97 cm.

To determine the length of the shadow cast by the stick, we can use basic trigonometry.

Specifically, we'll use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.

Given:

The formula for tangent is:

tan(θ) = opposite / adjacent

Here, the opposite side is the height of the stick, and the adjacent side is the length of the shadow. Thus, we can rearrange this formula to solve for the length of the shadow (adjacent side):

adjacent = opposite / tan(θ)

Substituting the given values:

adjacent = 19 cm / tan(60°)

We know that tan(60°) is √3 or approximately 1.732.

So:

adjacent = 19 cm / 1.732 ≈ 10.97 cm

Therefore, the length of the shadow cast by the stick is approximately 10.97 cm.

Answer:

The thrown rock strike 2.42 seconds earlier.

Explanation:

This is an uniformly accelerated motion problem, so in order to find the arrival time we will use the following formula:

[tex]x=vo*t+\frac{1}{2} a*t^2\\where\\x=distance\\vo=initial velocity\\a=acceleration[/tex]

So now we have an equation and unkown value.

for the thrown rock

[tex]\frac{1}{2}(9.8)*t^2+29*t-300=0[/tex]

for the dropped rock

[tex]\frac{1}{2}(9.8)*t^2+0*t-300=0[/tex]

solving both equation with the quadratic formula:

[tex]\frac{-b\±\sqrt{b^2-4*a*c} }{2*a}[/tex]

we have:

the thrown rock arrives on t=5.4 sec

the dropped rock arrives on t=7.82 sec

so the thrown rock arrives 2.42 seconds earlier (7.82-5.4=2.42)

The thrown rock hits the ground approximately 1.89 seconds earlier than the dropped rock when released simultaneously from a height of 300 meters.

To determine how much earlier the thrown rock strikes the ground compared to the dropped rock, we need to use the kinematic equation Projectile motion that relates displacement (Δx), initial velocity (vi), acceleration (a), and time (t): Δx = vi * t + 0.5 * a * t₂.

Since we're dealing with gravity, acceleration due to gravity (a) is 9.8 m/s². For the rock that is dropped, the initial velocity (vi) is 0 m/s, while the rock thrown downward has an initial velocity of 29 m/s.

First, we'll find the time it takes for the dropped rock to hit the ground:

Next, we use the same equation to find the time for the thrown rock:

This forms a quadratic equation in the form of at₂ + bt + c = 0. To solve for t, we use the quadratic formula. We only need the positive root since time cannot be negative:

Finally, the difference in time between when the two rocks hit the ground is:

Therefore, the thrown rock hits the ground approximately 1.89 seconds earlier than the dropped rock.

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Answer:

x = -29.032m

Explanation:

Since the third charge is positive, it cannot be between the other two charges, because it would be repelled by the positive one and attracted by the negative one, so the electric force would never be zero.

This leaves only two options: To the left of the positive one or to the right of the negative one.

If it was located on the right of the negative charge, the force of the positive charge would be weaker because of both the distance is larger and its charge is smaller than the negative charge. So, there is no point the would make the result force equal zero.

This means that the third charge has to be at the left of the positive charge. With this in mind, we make the calculations:

[tex]F_{13}=K*\frac{Q_{1}*Q_{3}}{d^{2}} =F_{23}=K*\frac{Q_{2}*Q_{3}}{(x_{2}+d)^{2}}[/tex]

Replacing the values of Q1=1.77, Q2=4.09, X2=15.1, we solve for d and get two possible results:

d1 = 29.032m   and d2 = -5.99m

Since we assumed in our formula that the third charge was on the left of the positive charge, the distance d has to be positive so that our final result can be a negative position. This is X = -d

This way, we get:

X = -29.032m

Answer:

Explanation:

Given

sprinter achieve maximum speed in 3.8 sec

Let v be the maximum speed and a be the acceleration in first 3.8 s

[tex]a=\frac{v-0}{3.8}[/tex]

distance traveled in this time span

[tex]x=ut+\frac{1}{2}at^2[/tex]

here u=0

[tex]x=\frac{1}{2}\times \frac{v-0}{3.8}\times 3.8^2[/tex]

[tex]x=\frac{3.8}{2}v[/tex]

remaining distance traveled in 9.3-3.8 =5.5 s

[tex]100-x=v\times 5.5[/tex]

put value of x

[tex]100-\frac{3.8}{2}v=5.5v[/tex]

100=1.9v+5.5v

100=7.4v

[tex]v=\frac{100}{7.4}=13.51 m/s[/tex]

Thus average acceleration in first 3.8 sec

[tex]a_{avg}=\frac{0+a}{2}[/tex]

and [tex]a=\frac{13.51}{3.8}=3.55 m/s^2[/tex]

[tex]a_{avg}=\frac{3.55}{2}=1.77 m/s^2[/tex]

Average acceleration during last 5.5 sec will be zero as there is no change in velocity.

Average acceleration for the entire race[tex]=\frac{13.51}{9.3}=1.45 m/s^2[/tex]

The average acceleration in the first 3.8 seconds would be the final speed divided by 3.8 s. During the next 5.5 seconds, the average acceleration is zero because there is no change in velocity. The average acceleration for the entire race can be calculated as the final velocity divided by total time.

The average acceleration is calculated by the change in velocity divided by the change in time. In this case, for the first 3.8 seconds, the sprinter was accelerating, so the average acceleration was the final speed (which we do not know yet) divided by 3.8 s. However, in the remaining 5.5 seconds, the sprinter did not accelerate or decelerate, so the average acceleration is zero.

For the first part, we first need to calculate the steady speed. This is given by the distance covered (100 m minus the distance covered in first 3.8 seconds) divided by the time for this (5.5 seconds). We will assume a uniform acceleration in the first 3.8 seconds. His average speed in this period will then be half his maximum speed. So, maximum speed = (2 * distance in first 3.8 secs) / 3.8. Finally, the average acceleration for entire race can be calculated by the total change in velocity (which is the final velocity) divided by the total time (which is 9.3 s).

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Answer:

The answer is 8 N

Explanation:

The Lorentz force for a current carrying wire is

f = I * L x B

So, for magnetic forces to manifest the current must not be parallel to the magnetic field. So the cases where the wire is parallel to the field would result in a force of zero applied on the wires  by the magnetic field because the cross product becomes zero.

For the perpendicular cases:

f = I * L * B

f = 80 * 0.1 * 1 = 8 N