1. Draw four illustrations of a globe and paper that are positioned to yield equatorial, transverse, oblique, and polar aspect projections. Label the equator in each. Use your textbook or lecture material if you need a reference.2. On any map, why is there distortion at areas that do not fall on lines of tangency or secancy?

Answer:

a = 6.67 m/s²

Explanation:

F = 10.0 N

m = 1.50 kg

a = ?

F = ma

10.0 = (1.50)a

6.67 = a

Answer:

W/7

Explanation:

By principle of moments,

Sum of clockwise moment = sum of anticlockwise moment

Weight × 7d = W × d

Weight = W/7

Since the two children are in rotational equilibrium, the weight of the second child is W/7.

The weight of the second child can be determined from the principle of moments.

The principle of moments states that for a body in equilibrium, the sum of the clockwise moments and anticlockwise moments about a point is zero.

Let the weight of the second child be X

From the principle of moments:

W × d = 7×d × X

X = W/7

Therefore, the weight of the second child is W/7.

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Explanation:

Let T is the period of a pendulum. The SI unit of time is seconds (s).

It depends on the acceleration of gravity, g, and the length of the pendulum, l.

The SI unit of acceleration of gravity, g and the length of the pendulum, l are m/s² and m respectively.

If we divide m and m/s², we left with s². If the square root of s² is taken, we get s only i.e. the SI unit of period of a pendulum.

So,

[tex]T\propto \sqrt{\dfrac{l}{g}}[/tex]

Hence, this is the required solution.

Explanation:

A circuit breaker is an electrical switch designed to protect an electrical circuit from damage caused by overcurrent/overload or short circuit. Its basic function is to interrupt current flow after protective relays detect a fault.

Circuit breakers have been designed to detect when there is a fault in the electricity, so it will “trip” and shut down electrical flow. ... This detection is key to preventing surges of electricity that travel to appliances or other outlets, which can cause them to break down

Answer:

stress = 98000 N/m^2

strain = 3.92 x 10^-6

change in height = 0.0196 mm

Explanation:

Height, h = 5 m

Area, A = 3 m²

mass, m = 30000 kg

Stress is defined as the force per  unit area.

[tex]stress = \frac{mg}{A}\\\\stress = \frac{30000\times 9.8}{3}\\\\stress = 98000 N/m^2[/tex]

Young's modulus of concrete is Y = 2.5 x 10^10 N/m^2

Young's modulus is defined as the ratio of stress to the strain.

[tex]Y = \frac{stress}{strain}\\\\2.5\times 10^{10}= \frac{98000}{strain}\\\\strain = 3.92\times 10^{-6}[/tex]

let the change in height is h'.

Strain is defined as the ratio of change in height to the original height.

[tex]3.92\times 10^{-6} = \frac{h'}{5}\\\\h' = 1.96\times 10^{-5}m = 0.0196 mm[/tex]

Answer:

false

Explanation:

took the test

Answer:

2.21 N

Explanation:

The force in this case is the total mass multiplied by the acceleration due to gravity. You are not asked for the solution to be in terms of the torque which is the usual way to solve these problems. That's why you are not given where the fulcrum is.

The fulcrum feels F1 + F2 + 34 * 980

F2 = 141.7 * 980 = 138866

F1 = 50.3 * 980  =  49294

Ruler = 34 * 980=  33320

Total Force = 221480 The units here are dynes

I just saw in the middle of the question that g = 9.80

So the answer becomes 221480 / 1000 = 221.48   because we needed kg

And that answer becomes 221.48/100 2.21 because the force of gravity should be 9.8 not 980

The total force exerted on the fulcrum is

Answer:

V = 5 Volts

Explanation:

Given the following data;

Work done = 20 Joules

Charge = 4 Coulombs

To find the potential difference;

Mathematically, the work done in moving a charge is given by the formula;

W = qv

Where;

W is the work done

q is the quantity of charge

v is the potential difference

Substituting we have;

20 = 4 * v

V = 20/4

V = 5 Volts

Answer:

[tex]K.E_{max}=0.8973J[/tex]

Explanation:

From the question we are told that:

Mass [tex]m=1.64kg[/tex]

Equation of Mass

[tex]X=0.33cos(3.17t)[/tex]...1

Generally equation for distance X is

[tex]X=Acos(\omega t)[/tex]...2

Therefore comparing equation

Angular Velocity [tex]\omega=3.17rad/s[/tex]

Amplitude A=0.33

Generally the equation for Max speed is mathematically given by

[tex]V_{max}=A\omega[/tex]

[tex]V_{max}=0.33*3.17[/tex]

[tex]V_{max}=1.0461m/s[/tex]

Therefore

[tex]K.E_{max}=0.5mv^2[/tex]

[tex]K.E_{max}=0.5*1.64*(1.0461)^2[/tex]

[tex]K.E_{max}=0.8973J[/tex]

Answer:

If efficiency is .22 then  W = .22 * Q   where Q is the heat input

Heat Input    Q = 2510 / .22 = 11,400 J

Heat rejected = 11.400 - 2510 = 8900  J of heat wasted

Also, 8900 J / (4.19 J / cal) = 2120 cal

An efficiency is the measure of productivity of an engine. The heat rejected by the engine is 8900 Joules.

An efficiency of a heat engine is the ratio of the work done and heat supplied.

Given is the automobile engine has the efficiency 22% and Work done is 2510 Joules.

The efficiency is written as,

η= W / Qs.

The work done is W= Qs - Qr, where Qr is the rejected heat.

The heat rejected can be represented as

Qr = W ( 1/η -1)

Substituting the value into the equation, we get the rejected heat.

Qr = 2510 (1/0.22 -1)

Qr = 8900 Joules.

Thus, the heat rejected by the engine is 8900 Joules.

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By Newton's second law, the net force on the object is

∑ F = T - mg = - ma

where

• T = 25 N, the tension in the string

• m is the mass of the object

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

• a = 2.0 m/s², the acceleration of the elevator-object system

Solve for m :

25 N - m (9.8 m/s²) = - m (2.0 m/s²)

==>   m = (25 N) / (9.8 m/s² - 2.0 m/s²) ≈ 3.2 kg

Answer:

T=273+25=298 K

n= m/M = 10/ 4 = 2.5

R=0.08206 L.atm /mol/k

760mmHg = 1 atm therefore

600mmHg = X atm

760 X = 600mmHg

X = 600/760 = 0.789 atm

P = 0.789 atm

V= ?

PV= nRT

0.789 V = 2.5 × 0.08206 × 298

V= 2.5 × 0.08206 ×298 / 0.789

V= 77.48 L

I hope I helped you ^_^

Answer:

What is (a) the x component and (b) the y component of the net electric field at the square's center

Explanation:

someone to check if the answer is correct

Answer:

The velocities of the skaters are [tex]v_{1} = 3.280\,\frac{m}{s}[/tex] and [tex]v_{2} = 0.024\,\frac{m}{s}[/tex], respectively.

Explanation:

Each skater is not under the influence of external forces during process, so that Principle of Momentum Conservation can be used on each skater:

First skater

[tex]m_{1} \cdot v_{1, o} = m_{1} \cdot v_{1} + m_{b}\cdot v_{b}[/tex] (1)

Second skater

[tex]m_{b}\cdot v_{b} = (m_{2}+m_{b})\cdot v_{2}[/tex] (2)

Where:

[tex]m_{1}[/tex] - Mass of the first skater, in kilograms.

[tex]m_{2}[/tex] - Mass of the second skater, in kilograms.

[tex]v_{1,o}[/tex] - Initial velocity of the first skater, in meters per second.

[tex]v_{1}[/tex] - Final velocity of the first skater, in meters per second.

[tex]v_{b}[/tex] - Launch velocity of the meter, in meters per second.

[tex]v_{2}[/tex] - Final velocity of the second skater, in meters per second.

If we know that [tex]m_{1} = 70\,kg[/tex], [tex]m_{b} = 0.043\,kg[/tex], [tex]v_{b} = 32\,\frac{m}{s}[/tex], [tex]m_{2} = 58.5\,kg[/tex] and [tex]v_{1,o} = 3.30\,\frac{m}{s}[/tex], then the velocities of the two people after the snowball is exchanged is:

By (1):

[tex]m_{1} \cdot v_{1, o} = m_{1} \cdot v_{1} + m_{b}\cdot v_{b}[/tex]

[tex]m_{1}\cdot v_{1,o} - m_{b}\cdot v_{b} = m_{1}\cdot v_{1}[/tex]

[tex]v_{1} = v_{1,o} - \left(\frac{m_{b}}{m_{1}} \right)\cdot v_{b}[/tex]

[tex]v_{1} = 3.30\,\frac{m}{s} - \left(\frac{0.043\,kg}{70\,kg}\right)\cdot \left(32\,\frac{m}{s} \right)[/tex]

[tex]v_{1} = 3.280\,\frac{m}{s}[/tex]

By (2):

[tex]m_{b}\cdot v_{b} = (m_{2}+m_{b})\cdot v_{2}[/tex]

[tex]v_{2} = \frac{m_{b}\cdot v_{b}}{m_{2}+m_{b}}[/tex]

[tex]v_{2} = \frac{(0.043\,kg)\cdot \left(32\,\frac{m}{s} \right)}{58.5\,kg + 0.043\,kg}[/tex]

[tex]v_{2} = 0.024\,\frac{m}{s}[/tex]

Answer:

Explanation:

The density of pure water is 1 gram per 1 milliliter or one cubic cm. By knowing the density of water we can use it in dilution equations or to calculate the specific gravity of other solutions.

It can also help us determine what other substances are made of using the water displacement experiment. This is done by observing how much water is displaced when an object is submerged in the water. As long as you know the density of the water, the mass of the object being submerged and the volume of increase you can calculate the density of the object.

This was done by the great Archimedes in discovering what composed the kings crown.

Answer:

810.94 m/s

Explanation:

Applying,

v = √(2gR)............. Equation 1

Where v = escape velocity of the spherical asteroid, g = acceleration due to gravity, R = radius of the earth

From the question,

Given: g = 0.636 m/s², R = 517 km = 517000 m

Substitute these values into equation 1

v = √(2×0.636×517000)

v = √(657624)

v = 810.94 m/s

Hence, the escape velocity is 810.94 m/s

Answer is 0.0024

Explanation

divide the length value by 1000.

Complete question:

A wire 2.80 m in length carries a current of 5.60 A in a region where a uniform magnetic field has a magnitude of 0.300 T. Calculate the magnitude of the magnetic force on the wire assuming the following angles between the magnetic field and the current.

a) 60 ⁰

b) 90 ⁰

c) 120 ⁰

Answer:

(a) When the angle, θ = 60 ⁰,  force = 4.07 N

(b) When the angle, θ = 90 ⁰,  force = 4.7 N

(c) When the angle, θ = 120 ⁰,  force = 4.07 N

Explanation:

Given;

length of the wire, L = 2.8 m

current carried by the wire, I = 5.6 A

magnitude of the magnetic force, F = 0.3 T

The magnitude of the magnetic force is calculated as follows;

[tex]F = BIl \ sin(\theta)[/tex]

(a) When the angle, θ = 60 ⁰

[tex]F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(60)\\\\F = 4.07 \ N[/tex]

(b) When the angle, θ = 90 ⁰

[tex]F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(90)\\\\F = 4.7 \ N[/tex]

(c) When the angle, θ = 120 ⁰

[tex]F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(120)\\\\F = 4.07 \ N[/tex]

Speed= distance/time

Or time = distance/speed

According to your question

Speed=15m/s

and. Distance=1.2km. ,we must change kilometer in meter because given speed is in m/s

D= 1.2km = 1.2×1000m =1200meter

Time = distance/ speed

1200/15 =80second

Or. 1min and 20 sec will be your answer.

Answer:

ΔE[tex]_{int[/tex],₁ = 977.7 J , Q₁ = 977.7 J and W₁ = 0 J

Explanation:

Given the data in the question;

T[tex]_i[/tex] = 300 K, T[tex]_f[/tex] = 412 K, n = 0.7 mol

since helium is monoatomic;

Cv = (3/2)R, Cp = (5/2)R

W₁ = 0 J [ at constant volume or ΔV = 0]

Now for the first cylinder; from the first law of thermodynamics;

Q₁ = ΔE[tex]_{int[/tex],₁ +  W₁

Q₁ = ΔE[tex]_{int[/tex],₁ = n × Cv × ΔT

we substitute  

Q₁ = ΔE[tex]_{int[/tex],₁ = 0.7 × ( 3/2 )8.314 × ( 412 - 300 )

Q₁ = ΔE[tex]_{int[/tex],₁ = 0.7 × 12.471 × 112

Q₁ = ΔE[tex]_{int[/tex],₁ = 977.7 J

Therefore, ΔE[tex]_{int[/tex],₁ = 977.7 J , Q₁ = 977.7 J and W₁ = 0 J

Answer:

Archimedes was born about 287 BCE in Syracuse on the island of Sicily. He died in that same city when the Romans captured it following a siege that ended in either 212 or 211 BCE. One story told about Archimedes' death is that he was killed by a Roman soldier after he refused to leave his mathematical work.

Answer:

the rock speed is increased

A rock is initially at rest concerning the earth, but the speed of the rock will increase when it hits the ground.

The resistance to something rolling or moving over another solid object is called friction. Even though frictional forces can be helpful, like the traction needed to walk without slipping, they also present a considerable amount of resistance to motion. About 20% of the engine power in a car is used to combat frictional forces in the moving parts.

The primary cause of friction between metals appears to be the forces of attraction, also known as adhesion, between the contact zones of the surfaces, which are always microscopically unequal. Because of friction caused by the imperfections of the tougher surface rubbing up against the softer surface, these "welded" connections are sheared.

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Answer:

wire 66.0 cm long carries a 0.750 A current in the positive direction of an x axis through a magnetic field $$\vec { B } = ( 3.00 m T ) \hat { j } ...

Top answer · 1 vote

Answer:

True. A permanent magnet like the earth produces its own B field due to movement of the iron core. The earths magnetic field is the reason why we have an atmosphere and it also is the only defense against solar flares. A coil of wire or solenoid that has current have so much moving charge that the motion of the electrical charge can create a significant G b-field

Answer:

 v = -v₀ / 2

Explanation:

For this exercise let's use kinematics relations.

Let's use the initial conditions to find the acceleration of the electron

            v² = v₀² - 2a y

when the initial velocity is vo it reaches just the negative plate so v = 0

           a = v₀² / 2y

now they tell us that the initial velocity is half

          v’² = v₀’² - 2 a y’

          v₀ ’= v₀ / 2

at the point where turn v = 0              

          0 = v₀² /4  - 2 a y '

          v₀² /4 = 2 (v₀² / 2y)  y’

          y = 4 y'

          y ’= y / 4

We can see that when the velocity is half, advance only ¼ of the distance between the plates, now let's calculate the velocity if it leaves this position with zero velocity.

         v² = v₀² -2a y’

         v² = 0 - 2 (v₀² / 2y) y / 4

         v² = -v₀² / 4

         v = -v₀ / 2

We can see that as the system has no friction, the arrival speed is the same as the exit speed, but with the opposite direction.

Explanation:

15.556 metres per second

Answer:

Explanation:

From the given information:

From the rotational axis, the distance of the force of gravity is:

d_g = 25+5.0 cm

d_g = 30.0 cm

d_g = 30.0 × 10⁻² m

However, the relative distance of FB  cos 75.9° from the axis is computed as:

d_B = 5.0 cm

d_B = 5.0 × 10⁻² m

The net torque rotational equilibrium = zero (0)

i.e.

[tex]\tau_g -\tau_B = 0 \\ \\ F_gd_g -F_gcos 75.9^0 d_B = 0 \\ \\ F_B = \dfrac{F_g d_g}{F_g cos 65.6} \\ \\ F_B = \dfrac{(3.2)(9.8)(30*10^{-2})}{(5.0*10^{-2} * cos 75.9)} \\ \\ \mathbf{F_B = 772.4 N}[/tex]

= 772.4 N

Thus, the force exerted = 1772.4 N

Answer: [tex]2.4705\ kg.m^2[/tex]

Explanation:

Given

length of the rod is L=0.9 m

Mass of the rod m=3.8 kg

Point masses has mass of m=2.3 kg

Moment of Inertia of the rod about the center is

[tex]\Rightarrow I_o=\dfrac{1}{12}ML^2[/tex]

Moment of inertia of combined system is the sum of rod and two point masses.

[tex]\Rightarrow I=I_o+2mr^2[/tex]

[tex]\Rightarrow I=\dfrac{1}{12}3.8\times 0.9^2+2\times 2.3\times \left(\dfrac{0.9}{2}\right)^2\\\\\Rightarrow I=1.539+0.9315\\\Rightarrow I=2.4705\ kg-m^2[/tex]