A man stands on a scale and holds a heavy object in his hands. What happens to the scale reading if the man quickly lifts the object upward and then stops lifting it?

Answer:

Explanation:

1. Impulse, I = F.t

  The statement impulse is the product of Force and distance is false.

2. F = m g

   Force necessary to lift the object depends on the mass of the object.

   statement 2 is false.

3. Joule is equal to Newton times meter.

    Statement 3 is false.

4. Work done to lift an object is correct statement.

   Statement 4 is true.

5. Kinetic energy of an object is due to motion.

  Statement 5 is false.

6. Stopping distance is directly proportional to the square of velocity.

     If velocity is doubled, stopping distance is quadrupled.

    Statement 6 is false.

The correct answer is 1.False; 2.False; 3.False; 4.True; 5.False; 6.False.

1. Impulse is the product of force and time, not force and distance. Therefore, the statement is false.

2. The force necessary to lift an object is not simply g, but weight, which is calculated as mass times the gravitational acceleration g. So, this statement is false.

3. A joule is the unit of work or energy, equivalent to one newton meter (N·m), not a newton times a second. Thus, the statement is false.

4. Work is indeed done to lift an object in the classroom since work is the force applied over a distance in the direction of the force. Therefore, this statement is true.

5. Kinetic energy is the energy of motion, not the energy of position. Thus, this statement is false.

6. If the stopping distance is doubled when speed is quadrupled, it overlooks the fact that stopping distance increases with the square of the speed, meaning a quadrupling of speed typically increases the stopping distance by a factor of sixteen, not two. So, this statement is false.

The annual electricity cost of the compressor is $15,386.25.

To calculate the annual electricity cost of the compressor, we first need to find the energy consumption of the motor. We can use the formula:

Energy Consumption = Power x Time

Given that the compressor operates at full load for 2500 hours a year and has a power of 75 hp, we need to convert the power to watts:

1 hp = 746 watt

So, the power of the motor is 75 x 746 = 55,950 watts.

Now, we can calculate the energy consumption:

Energy Consumption = 55,950 watts x 2500 hours

Next, we need to convert the energy consumption to kilowatt-hours (kWh):

1 kWh = 1000 watt-hours

So, the energy consumption in kWh is 55,950 watts x 2500 hours / 1000 = 139,875 kWh.

Finally, we can calculate the annual electricity cost by multiplying the energy consumption by the unit cost of electricity:

Annual Electricity Cost = 139,875 kWh x $0.11/kWh

Therefore, the annual electricity cost of this compressor is $15,386.25.

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Answer:

Both A and B

Explanation:

The interaction of magnetic fields and armature results into a rotational force of the armature hence turning motion. It's important to note that you will always need two magnetic fields in order to experience the force since one magnetic field is at the rotating armature and another at the casing. Considering the arguments of these two technicians, both of them are correct in their arguments.

Answer:

The charge on the particle = -0.00075 C = -0.75 mC = -750 μC

Explanation:

The solution to this question is presented in the attached image to this answer.

The Biot Savart's formula for calculating magnetic field due to moving point charge is used in this calculation.

Hope this Helps!!!

Answer:

Protein kinase A

Explanation:

Protein kinase A is also called Cyclic AMP- dependent protein kinase or A kinase. It is an enzyme that enhance protein covalently using the phosphate group. The function of this enzyme is that it helps to end the effect of different hormones working via the Cyclic AMP signalling pathway. Protein kinase A can be found in the cytoplasm which phosphorylate proteins.

Protein kinase A helps the cell in regulating sugar, glycogen and lipids metabolism level.

Answer:

The answer is Protein Kinase A.

Refer below for the explanation.

Explanation:

In cell science, protein kinase A is a group of compounds whose movement is reliant on cell levels of cyclic AMP. PKA is otherwise called cAMP-subordinate protein kinase. Protein kinase A has a few capacities in the cell, including guideline of glycogen, sugar, and lipid digestion.

Answer:

v' = 0.714 m/s

Explanation:

Solution:

- Assuming no external torque is acting on the system then the angular momentum is conserved for the system.

- The initial momentum angular Mi and final angular momentum Mf are as follows:

                                  Mi = Mf

                                  m*L*v = m*x*L*v'

Where,

             m : mass of the telescope

             L : Length of teether line

             v: Initial speed

             v' : Changed speed.

- Then we have:

                                  L*v = x*L*v'

                                  v' = v / x

                                  v' = 2 / 2.8

                                  v' = 0.714 m/s

Answer:

The answer to the question is

The linear speed of the telescope will be 5.6 m/s if the length of the line is changed to x*L where  x = 2.8; and initial velocity v = 2 m/s

Explanation:

Speed = v₁ = ωL = 2 m/s

When the line is changed to x*L where x = 2.8 the linear speed will be

v₂ = 2.8 × L× ω = 2.8× 2 = 5.6 m/s

The linear speed varies with the angular speed following the relation v/r =ω where

ω = angular speed

v = linear speed and

r = radius of the path of travel of the object at the vertex

Answer:

Explanation:

A law and theory are distinct levels in the scientific method. They do not lead to one another.

A law is a description of an observed phenomenon in the natural world. Laws are always true and do not provide explanations as to why they hold true.

A theory is an explanation of an observed phenomenon. It is usually based on experimental evidence and bounded most time in the limits of available data.

Answer:

[tex]2.33*10^{15}Hz[/tex]

Explanation:

The relationship between velocity v, frequency f and wavelength for electromagnetic waves is given by;

[tex]v=\lambda f..............(1)[/tex]

Given;

[tex]v=3*10^8m/s\\\lambda=129nm=129*10^{-9}m\\f=?[/tex]

We make substitutions into equation (1)  as follows;

[tex]f=\frac{v}{\lambda}\\f=\frac{3*10^8}{129*10^{-9}}[/tex]

Explanation:

Below is an attachment containing the solution.

Answer:

A. CHARLES' LAW

B. GAY-LUSSAC'S LAW

C. BOYLE'S LAW

Explanation:

THE QUESTION SEEKS ANSWER BY MATCHING THE PROPERTIES COMPARED BY A GAS LAW TO THE GAS LAW IN QUESTION.

A. CHARLES' LAW COMPARES TEMPERATURE AND VOLUME.

IT ESTABLISHED THE FACT THAT VOLUME AND TEMPERATURE ARE DIRECTLY PROPORTIONAL AT A FIXED PRESSURE

B. GAY-LUSSAC'S LAW COMPARE PRESSURE AND TEMPERATURE.

IT ESTABLISHED THE FACT THAT PRESSURE AND TEMPERATURE ARE DIRECTLY PROPORTIONAL FOR A GIVEN VOLUME OF GAS

C. BOYLE'S LAW COMPARES PRESSURE AND VOLUME

IT ESTABLISHED THAT BOTH ARE INVERSELY PROPORTIONAL AT A GIVEN TEMPERATURE

Answer:

1) D

2) B

3) E

Explanation: Edge 2020

Answer:

11.4 rad/s

Explanation:

The motion of the diver is a free-fall motion, so its center of mass falls down with constant acceleration of

[tex]g=9.8 m/s^2[/tex] towards the water

Therefore, we can use the following suvat equation:

[tex]s=ut-\frac{1}{2}gt^2[/tex]

where:

s = 9.3 m is the vertical displacement of the diver

u = 0 is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex]

And t is the total time of flight. Solving for t,

[tex]t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(9.3)}{9.8}}=1.38 s[/tex]

So, the diver takes 1.38 s to reach the water.

During this time, the diver makes 2.5 revolutions; since 1 revolution is equal to an angle of [tex]2\pi[/tex] radians, then the total angular displacement is

[tex]\theta=2.5\cdot 2\pi =15.7 rad[/tex]

Therefore, the average angular velocity of the diver is the ratio between the total angular displacement and the time taken:

[tex]\omega=\frac{\theta}{t}=\frac{15.7}{1.38}=11.4 rad/s[/tex]

Answer:

Intensity Of MRI signal is related as square of [tex]B_{0}[/tex]

or

Intensity is related as [tex]B_{0}^{2}[/tex].

Explanation:

MRI simply means Magnetic Resonance Imaging. In this process by the resonance of magnetic field the frequency is produced which is used to image the body parts (Mainly the brain).

The signal Strength is the rate of change of Magnetization (M) with respect to the time. For the calculation of Intensity we use Bloch equation which is given by

[tex]\frac{dH}{dt} = M \times \gamma B[/tex]

On further solving

[tex]\frac{dH}{dt} =\mu B \times \gamma B \\\frac{dH}{dt} = \mu \times \gamma B^{2}[/tex]

So, Intensity is related as [tex]B_{0}^{2}[/tex].

Answer:

The answer to the question is

The distance d, which locates the point where the light strikes the bottom is   29.345 m from the spotlight.

Explanation:

To solve the question we note that Snell's law states that

The product of the incident index and the sine of the angle of incident is equal to the product of the refractive index and the sine of the angle of refraction

n₁sinθ₁ = n₂sinθ₂

y = 2.2 m and strikes at x = 8.5 m, therefore tanθ₁ = 2.2/8.5 = 0.259 and

θ₁ =  14.511 °

n₁ = 1.0003 = refractive index of air

n₂ = 1.33 = refractive index of water

Therefore sinθ₂ =  [tex]\frac{n_1sin\theta_1}{n_2}[/tex]  = [tex]\frac{1.003*0.251}{1.33}[/tex] = 0.1885 and θ₂ = 10.86 °

Since the water depth is 4.0 m we have tanθ₂ = [tex]\frac{4}{x_2}[/tex] or x₂ = [tex]\frac{4}{tan\theta_2 }[/tex] =[tex]\frac{4}{tan(10.86)}[/tex] = 20.845 m

d = x₂ + 8.5 = 20.845 m + 8.5 m = 29.345 m.

Answer:

The answer is

The wavelength of the light is 557.2 x 10⁻⁻⁹nm

Explanation:

The wavelength of a wave is the distance between adjacent troughs and crests while the frequency of a wave is the number of completed cycles that pass a given per unit time

Electromagnetic radiation, such as light is usually described n terms of its frequency and wavelength

The equation relating the three quantities of speed of light, frequency and wavelength is as follows

Speed of light, c = Frequency of the light wave, ν × Wavelength of the light, λ

That is c = ν × λ

Where c =  299792458 m/s, v = 5.38 x 10¹⁴ Hz

Therefore the wavelength = [tex]\frac{c}{v}[/tex]  = 5.572 x 10⁻⁷ m 557.2 x 10⁻⁻⁹nm

Answer:

The acceleration of the centre of mass of spool A is equal to the magnitude of the acceleration of the centre of mass of spool B.

Explanation:

From the image attached, the description from the complete question shows that the two spools are of equal masses (same weight due to same acceleration due to gravity), have the same inextensible wire with negligible mass is attached to both of them over a frictionless pulley; meaning that the tension in the wire is the same on both ends.

And for the acceleration of both spools, we mention the net force.

The net force acting on a body accelerates the body in the same direction as that in which the resultant is applied.

For this system, the net force on either spool is exactly the same in magnitude because the net force is a difference between the only two forces acting on the spools; the tension in the wire and their similar respective weights.

With the net force and mass, for each spool equal, from

ΣF = ma, we get that a = ΣF/m

Meaning that the acceleration of the identical spools is equal also.

Hope this Helps!

Answer:

If the diameter is 54cm, then the radius is half that, the radius is:

r = 54cm/2 = 27cm

Then the perimeter of the wheel is p = 2*pi*27cm

this would mean that the pebble travels the distance:

d = 3*2*pi*27cm in one second.

Then the velocity of the pebble is:

speed = 3*2*3.1416*27cm/s = 509cm/s

Now, we know that the pebble does 3 cycles in a second, so does each cycle in 1/3 seconds, so the period would be the time that it needs to do one cycle, that we already find that is equal to 1/3 seconds.

Final answer:

The pebble stuck in the bicycle wheel tread has a speed of 5.091 m/s, and the period of its motion is 0.333 seconds.

Explanation:

To solve for the pebble's speed and the period of its motion, we will perform calculations based on the given wheel diameter and the frequency of the pebble's motion. The wheel's diameter is 54.0 cm, which gives us a radius (r) of 27.0 cm or 0.27 meters.

The speed (v) of the pebble on the tread of the wheel can be found using the formula for the circumference (C) of the wheel and multiplying by the frequency (f) of the pebble's motion:

C = 2πr

v = C × f

Plugging in the values we get:

C = 2 × π × 0.27 m = 1.697 m

f = 3 rev/s (since it goes by three times every second)

v = 1.697 m × 3 rev/s = 5.091 m/s

The period (T) is the inverse of frequency:

T = 1 / f

T = 1 / 3 rev/s = 0.333 s

Therefore, the pebble's speed is 5.091 meters per second, and the period of the pebble stone is 0.333 seconds.

Answer:

The answer for this is that they each have the same number of protons.

Explanation:

Plutonium is an element that is also used in nuclear power plants, because of the same amount of protons in it, plutonium is used in nuclear power plants.

The fact about all uranium atoms is that they have the same number of protons that make them very large and can be harmful if not carefully treated.

Answer:

same number of protons

Explanation:

Answer:

q₃=5.3nC

Explanation:

First, we have to calculate the force exerted by the charges q₁ and q₂. To do this, we use the Coulomb's Law:

[tex]F= k\frac{|q_aq_b|}{r^{2} } \\\\\\F_{13}=(9*10^{9} Nm^{2} /C^{2} )\frac{|(-4.00*10^{-9}C)q_3|}{(.250m)^{2} } =576q_3N/C\\\\F_{23}=(9*10^{9} Nm^{2} /C^{2} )\frac{|(2.40*10^{-9}C)q_3|}{(.300m)^{2} } =240q_3N/C\\[/tex]

Since we know the net force, we can use this to calculate q₃. As q₁ is at the right side of q₃ and q₁ and q₃ have opposite signs, the force F₁₃ points to the right. In a similar way, as q₂ is at the left side of q₃, and q₂ and q₃ have equal signs, the force F₂₃ points to the right. That means that the resultant net force is the sum of these two forces:

[tex]F_{Net}=F_{13}+F_{23}\\\\4.40*10^{-9} N=576q_3N/C+240q_3N/C\\\\4.40*10^{-6} N=816q_3N/C\\\\\implies q_3=5.3*10^{-9}C=5.3nC[/tex]

In words, the value of q₃ must be 5.3nC.

Explanation:

Porosity is the percentage of spaces,(hollow) within a rock or a material that can contain air or fluid. This can be used in geology( study of rocks), soil mechanics, engineering and pharmaceutics. Industrial CT scanning can be used to test for porosity of a substance. While permeability is the ability of water or other fluids to flow through a rock or material that has spaces ( that is, that are porous). This is also applicable in the fields of chemical engineering and geology.

Porosity refers to the amount of void space in a material that can hold water, while permeability measures how well those spaces are connected, affecting water movement. Materials with high permeability have larger, well-connected pores, allowing water to flow easily; materials with low permeability do not. The hydraulic conductivity is a measure of permeability that accounts for both material and fluid properties.

Difference Between Porosity and Permeability

The difference between porosity and permeability concerns the storage and movement of water in subsurface materials like rock or sediment. Porosity refers to the percentage of open space within a material that can potentially hold water, expressed as a ratio of the volume of voids to the total volume of the material. Permeability, on the other hand, is about how well those pores are interconnected, determining the ease with which water can move through the material. Higher permeability indicates the presence of larger, well-connected pores, enabling water to flow with less friction. Conversely, materials with low permeability have fewer, smaller, and poorly connected pores, which restricts water movement.

Understanding both porosity and permeability is crucial when discussing groundwater storage and extraction, as they define an aquifer's ability to store and transmit water. Soil texture plays a significant role in determining these properties. Coarse-grained soils with larger pores tend to have both higher porosity and permeability, whereas fine-grained soils like clay can have high porosity but low permeability due to poorly connected pores.

Answer: The IF clause.

Explanation: This is the IF clause; you can use it as:

IF (something = true) then "something happens"

else "other thing happens"

Some example of it can be, suppose that your program reads a number X that the user inputs, then you can do:

If ( X > 5) then

print: "the number X is bigger than five"

Else

print: "the number X is smaller than five"

Where, of course, the statements depend on the language used, but the "if" clause works almost the same in every language.

Answer:

width of slit(a)≅ 0.1mm

Explanation:

Wave length of laser pointer =λ = 685 nm

Distance between screen and slit = L = 5.5 m

Width of bright band = W=8.0cm=0.08m

width of slit=a

recall the formula;

W=(2λL)/a

a=2λL/W

a=(2 *685*10⁻⁹*5.5m)/0.08m

a=7535*10⁻⁹/0.08

a=94187.5 *10⁻⁹

a=0.0000941875m

a=0.0941875mm

a≅0.1mm

Answer:

The wide of silt is a=93.5×10⁻⁶m

Explanation:

Given data

Wavelength λ=680 nm

Length L=5.5 m

Width w=8.0 cm

To find

Width of slit a

Solution

A single slit of width a has a bright central maximum of width

ω=2λL/a

a=2λL/ω

Substitute the given values

[tex]a=\frac{2*(680*10^{-9}m)5.5m}{0.08m} \\a=93.5*10^{-6}m[/tex]

The wide of silt is a=93.5×10⁻⁶m

Answer:

Technician B

Explanation:

Answer:

30 C

Explanation:

Given:

Current flowing in the circuit (I) = 50 A

Start-up time (t) = 0.60 s

Now, we know that, charge drawn in through a cross sectional area of the circuit is given as:

[tex]q=It[/tex]

Where, 'q' is the amount of charge drawn, 'I' is the current and 't' is the start-up time.

Now, plug in 50 A for 'I', 0.60 s for 't' and solve for 'q'. This gives,

[tex]q=50\ A\times 0.60\ s\\\\q=30\ C[/tex]

Therefore, the amount of charge drawn in the circuit at the start-up of the compressor of an air conditioner is 30 C.

Final answer:

The work done by the spring force to ready the pen for writing is 0.404 J.

Explanation:

To find the work done by the spring force, we can use the formula for work: work = (1/2)k(x²), where k is the spring constant and x is the displacement of the spring from its unstressed length.

In this case, the spring is initially compressed 5.1 mm and then compressed an additional 6.1 mm. So the total displacement is 5.1 mm + 6.1 mm = 11.2 mm.

Substituting the values into the formula, we have work = (1/2)(257 N/m)((11.2 mm / 1000)²) = 0.404 J. The calculated work of 0.404 J represents the energy transferred to or from the spring as it undergoes the specified compressions, providing insight into the mechanical behavior of the system under the influence of the spring force.

Final answer:

The acceleration of the object from 3 seconds to 7 seconds is 2 m/s².

Explanation:

To calculate the acceleration of the object, you can use the formula:

acceleration = (final velocity - initial velocity) / time

Using the given information, the final velocity is 8 m/s, the initial velocity is 0 m/s, and the time is 7 seconds - 3 seconds = 4 seconds.

Substituting the values into the formula:

acceleration = (8 m/s - 0 m/s) / 4 s = 2 m/s²

Therefore, the acceleration of the object from 3 seconds to 7 seconds is 2 m/s².

The acceleration of the object from 3 seconds to 7 seconds is 2 m/s².

To calculate the acceleration of the object from 3 seconds to 7 seconds, we use the formula:

Acceleration = (Final Velocity - Initial Velocity) / Time Interval

Given:

So, the calculation is:

Acceleration = (8 m/s - 0 m/s) / 4 s = 2 m/s²

The acceleration of the object from 3 seconds to 7 seconds is 2 m/s².

Answer:

A. [tex]T_2=M_2g[/tex]

B. [tex]T_2=(M_1+M_2)g[/tex]

Explanation:

Since the only forces acting on the blocks are the tensions and the weights (both in the vertical direction), and the system has acceleration zero, we can write the equilibrium equations for M₁ and M₂ as:

[tex]T_1-T_2-M_1g=0\\ \\T_2-M_2g=0[/tex]

From the second equation, we get:

[tex]T_2=M_2g[/tex],

Which is the answer to the part A.

Next, we substitute this result in the first equation and obtain:

[tex]T_1-M_2g-M_1g=0\\ \\T_1=(M_1+M_2)g[/tex],

Which is the answer to the part B.

Final answer:

To find the tensions in ropes supporting hanging blocks, one must draw free-body diagrams for each mass, and apply Newton's Second Law. The tension in the lower rope equals the weight of the lower mass or this weight adjusted for acceleration. The tension in the upper rope is the sum of the weight of the upper mass and the tension in the lower rope.

Explanation:

The student's question revolves around the concept of tension in ropes in a physics context, where two blocks are hanging one under the other. The physics involved here includes Newton's second law and the interplay of gravitational and tensional forces in a system. To find the tensions T₁ and T₂, we need to draw free-body diagrams for each block and apply Newton's Second Law, F = ma, where F is the net force, m is the mass and a is the acceleration of the block.

For block M₂, which hangs at the bottom, the tension T₂ is the force counteracting the gravitational pull downward. Hence, assuming the system is at equilibrium or moving at constant speed (acceleration = 0), T₂ would equal the weight of M₂, given by the formula T₂ = M₂ × g.

For block M₁, which is above M₂, the tension T₁ is slightly more complicated to calculate as it must support its own weight as well as the tension from the lower rope T₂. Therefore, the tension T₁ in the upper rope would be T₁= (M₁ + M₂) × g again assuming no net acceleration.

If the entire system is accelerating, we must incorporate the net force necessary to accelerate both masses. This changes the calculations respectively:
For the lower block (M₂), T₂ = M₂ × (g + a) if accelerating upward, or T₂ = M₂ × (g - a) if accelerating downward.
For the upper block (M₁), T₁ = (M₁ × g) + T₂ because T₁ has to support both the weight of M₁ and the tension from the lower rope.

Answer:

So three lowest possible values of d ar 0.85m, 2.55m and 4.25m

Explanation:

The wavelength of wave:

λ=v/f

λ=340/200=1.7m

The destructive interference condition is:

Δd=(m+1/2)λ             where m=0,1,2,3........

For minimum destructive interference ,the value of m is equal to zero

Δd=(0+1/2)×1.7

Δd=0.85m

For m=1

Δd=(1+1/2)×1.7

Δd=2.55m

For m=2

Δd=(2+1/2)×1.7

Δd=4.25m

So three lowest possible values of d ar 0.85m, 2.55m and 4.25m

The interference of sound waves is causing silence at your location. The three lowest possible values for the distance between two speakers creating this effect, given the given frequency of 200Hz and sound speed of 340m/s, are 0.85m, 2.55m and 4.25m.

This is a problem related to sound interference; that is when two or more sound waves overlap, the resultant sound you hear is different than when you hear the sound waves individually.

You are not hearing anything because the sounds from the two speakers are arriving out of phase at your location, causing destructive interference.

At destructive interference, the path difference is (n + 1/2)λ. For the first three lowest values for d, n = 0, 1, 2. The speed of sound v = λf, so λ = v / f. Substituting these values in we get d = (n + 1/2) * v/f.

Now, let's plug in the given values: f=200Hz, v=340m/s.

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When the volume of gas is reduced at constant temperature, the average velocity of the molecules, the average force of an individual collision, and the average number of collisions with the wall all increase.

When the volume of a sample of gas is reduced at constant temperature, the average velocity of the molecules increases, the average force of an individual collision between molecules and the container walls increases, and the average number of collisions with the wall, per unit area, per second increases.

When the volume of a gas is reduced at constant temperature, the gas molecules’ average velocity remains unchanged, the force of each collision increases, and collisions with the wall per unit area per second become more frequent.

If the volume of a sample of gas is reduced at constant temperature, according to Boyle's law, the average velocity of the molecules remains the same, the average force of an individual collision increases, and the average number of collisions with the wall, per unit area, per second increases.

At a constant temperature, the kinetic energy of the gas molecules, as well as their average velocity, does not change. This is in accordance with the kinetic theory of gases. However, as the volume decreases, the gas molecules have less space to move around, which means they will encounter the container walls more frequently. Hence, the number of collisions with the wall per unit area per second increases. Since the same amount of molecules exert force over a smaller area of the container wall (because the volume is reduced), the average force per collision also increases.

It's important to clarify that while the average velocity does not change, the frequency of collisions leads to the increased pressure we observe in a confined volume of gas. Consequently, the gas exerts a greater pressure on the walls of the container.

Answer:

Explanation:

Check attachment for solution

The analytical method of the components allows to find the results for the questions about the sum vector are:

     a) In the attached we have a scheme of the vectors

     b) the modulus is C = 96.3 m

     c) The angle is θ = 27.0º

Given parameters

To find

    a) Draw the vectors and their sum.

    b) The module.

    c) the adirection.

The sum of vectors has several methods of resolution:

The analytical method consists:

In the attached we have a diagram of each vector and its sum. Let's use trigonometry to find the component of each vectors.

Vector A

            cos θ₁ = [tex]\frac{A_x}{A}[/tex]  

            sin θ₁ = [tex]\frac{A_y}{A}[/tex]  

            Aₓ = A cos θ₁

            [tex]A_y[/tex] = A sin θ₁

            Aₓ = 40 cos (-20) = 37.59 m

            [tex]A_y[/tex]= 40 sin (-20) = -13.68 m

Vector B

           cos θ₂ = [tex]\frac{B_x}{B}[/tex]  

           sin θ₂ = [tex]\frac{B_y}{B}[/tex]  

           Bₓ = B cos θ₂

           [tex]B_y[/tex] = B sin θ₂

           Bₓ = 75 cos 50 = 48.21 m

           [tex]B_y[/tex] = 75 sin 50 = 57.45 m

we add the components.

           Cₓ = Aₓ + Bₓ

           [tex]C_y = A_y + B_y[/tex]  

           Cₓ = 37.59 + 48.20 = 85.8 m

           Cy = -13.68 + 57.45 = 43.8 m

b) We use the Pythagorean theorem to find the modulus of the resultant vector.

          C² = Cₓ² + [tex]C_y^2[/tex]  

          C = [tex]\sqrt{85.8^2 + 43.8^2 }[/tex]  

         C = 96.3 m.

c) We use trigonometry to find the angle of the resultant vector.

         tan θ =[tex]\frac{C_y}{C_x}[/tex]  

         θ = tan⁻¹ [tex]\frac{C_y}{C_x}[/tex]  

         θ = tan⁻¹ [tex]\frac{43.8}{85.8}[/tex]  

         θ = 27.0º

In conclusion, using the analytical method of the components we can find the results for the questions about the sum vector are:

     a) In the attached we have a scheme of the vectors

     b) the modulus is C = 96.3 m

     c) The angle is θ = 27.0º

Learn more about vector addition here:  brainly.com/question/25681603

Answer:

123 J transfer into the gas

Explanation:

Here we know that 123 J work is done by the gas on its surrounding

So here gas is doing work against external forces

Now for cyclic process we know that

[tex]\Delta U = 0[/tex]

so from 1st law of thermodynamics we have

[tex]dQ = W + \Delta U[/tex]

[tex]dQ = W[/tex]

so work done is same as the heat supplied to the system

So correct answer is

123 J transfer into the gas

Answer: q=5.70 x 10^13 C

Explanation:

gravitational attraction = electrostatic repulsion GMm/d^2 = kQ^2/d^2 as you can see the d^2 cancel out. that is why lunar distance is irrelevant. G is the universal gravitational constant = 6.67 x 10^-11 m^3 / kgs^2 M is earth's mass = 5.972 × 10^24 kg m is moon's mass = 7.342×10^22 kg Q is charge on earth and moon. k is coulomb's constant = 9 x10^9 N m^2 /C^2 On solving equation for Q. Q = sqrt (GMm/k) = sqrt ( 6.67 x 10^-11 x 5.972 x 10^24 * 7.342×10^22 / 9 x10^9) = 5.70 x 10^13 C

To neutralize the gravitational attraction between the Moon and the Earth using equal charges, calculate the total gravitational force and equate it to the electrostatic force of the charges. q=5.70 x 10¹³ C

gravitational attraction = electrostatic repulsion

GMm/d² = kQ²/d² as you can see the d² cancel out. that is why lunar distance is irrelevant. G is the universal gravitational constant = 6.67 x 10⁻¹¹ m³ / kgs² M is earth's mass = 5.972 × 10²⁴ kg m is moon's mass = 7.342×10²² kg Q is charge on earth and moon. k is coulomb's constant = 9 x10⁹ N m² /C² On solving equation for Q. Q = √ (GMm/k) = √ ( 6.67 x 10⁻¹¹x 5.972 x 10²⁴ × 7.342×10²²  / 9 x10⁹) = 5.70 x 10¹³ C