Four point charges are individually brought from infinity and placed at the corners of a square. Each charge has the identical value Q. The length of the diagonal of the square is 2a. What is the electric potential at the center of the square

Answers

Answer 1

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The electric potential is  \(V_P = \frac{4kQ}{a }\)

Explanation:

From the question we are told that

     The charge on each point  is  +Q

      The length of the diagonal is  2a

   

Generally the electric potential is mathematically represented as

       \(V = \frac{k Q}{r}\)

Here r is the distance from each vertices of the square to the center P which is evaluated as

             \(r = \frac{2a}{2} = a\)

  So the potential at the center due to one charge is evaluated as

         \(V_1 = \frac{k Q}{a }\)

Given that there are four charge the net electric potential at the center P will be

        \(V_P = \frac{4kQ}{a }\)

Four Point Charges Are Individually Brought From Infinity And Placed At The Corners Of A Square. Each

Related Questions

a centimeter in milimetersr difiers from each other by a fact of 100 ,1000, 1 or 10

Answers

Answer:

The correct answer is - 1.

Explanation:

The one cubic centimeter is equal to the one mililitter of a liquid. It is same de to the fact that volume of water that fits in a one cubic centimeter is equal to the liquid present in one mililiter of a liquid.

1 cm² = 1 ml

1 cm³ = 1 ml

Thus, the use of the both unit is interchangebly.

So , correct answer is - 1.

A 4 kg box is at rest on a table. The static friction coefficient u, between the box and table is 0.30, and
the kinetic friction coefficient Hi is 0.10. Then, a 10 N horizontal force is applied to the box.

Answers

Answer:

The box will not move from its position.

Explanation:

First, we will calculate the static frictional force that is stopping the box to move from its position:

\(f = \mu R = \mu W=\mu mg\)

where,

f = static frictional force = ?

μ = coefficient of static friction = 0.3

m = mass of box = 4 kg

g = acceleration due to gravity = 9.81 m/s²

Therefore,

\(f = (0.3)(4\ kg)(9.81\ m/s^2)\\f=11.77\ N\)

Since the frictional force (11.77 N) is greater than the applied force (10 N).

Therefore, the box will not move from its position.

what is the change of entropy if 536 g of gold are melted?

Answers

Answer:  Therefore, the change in entropy when 536 g of gold are melted is 0.132 J/K.

Explanation:  To calculate the change in entropy when 536 g of gold are melted, we need to know the entropy of fusion of gold and the temperature at which it melts.

The entropy of fusion of gold is 2.35 J/g·K, and the melting point of gold is 1064 °C or 1337 K.

The change in entropy when gold is melted can be calculated using the formula:

ΔS = Q/T

where ΔS is the change in entropy, Q is the heat absorbed during the process, and T is the temperature at which the process occurs.

The heat absorbed when gold is melted can be calculated using the formula:

Q = m × ΔH_fus

where m is the mass of the gold and ΔH_fus is the enthalpy of fusion of gold, which is 64.9 kJ/mol.

Converting the mass of gold to moles:

536 g / 196.97 g/mol = 2.72 mol

The heat absorbed by the gold when it is melted is:

Q = 2.72 mol × 64.9 kJ/mol = 176.2 kJ

Finally, we can calculate the change in entropy:

ΔS = Q/T = 176.2 kJ / 1337 K = 0.132 J/K

Briefly explain why the moon doesn't have an atmosphere or plate tectonic activity.

Answers

Answer:

The moon does not have an atmosphere because it does not have enough gravity to hold onto the gases that make up an atmosphere. The moon also does not have plate tectonic activity because it does not have enough internal heat to drive the movement of the plates.

Explanation:

Scientific theories are deductive in nature.?


Answers

Answer:

deductive reasoning usually follows steps .

That is, how we predict what the observations should be if the theory were correct

Calculate the quantity of heat energy which must be transferred to 2.25 kg of brass to raise its temperature from 20°C to 240°C if the specific heat of brass is 394 J/kgK.

Answers

The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J

How do i determine the quantity of heat energy?

First, we shall list out the given parameters from the question. This is shown below:

Mass of brass (M) = 2.25 Kg Initial temperature of brass (T₁) = 20 °CFinal temperature of brass (T₂) = 240 °CChange in temperature of brass (ΔT) = 240 - 20 = 220 °CSpecific heat capacity of brass (C) = 394 J/kgKQuantity of heat energy (Q) =?

The quantity of heat energy that must be transferred can be obtained as follow:

Q = MCΔT

= 2.25 × 394 × 220

= 195030 J

Thus, we can conclude quantity of heat energy that must be transferred is 195030 J

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By use of one or more of the three resistors 3.0 2, 5.0 11, and 6.0 12, a total of 18 resistances can be obtained. What are they?​

Answers

These are the 18 resistances that can be obtained by using the three resistors 3.0 Ω, 5.0 Ω, and 6.0 Ω.

To obtain the total of 18 resistances, we need to consider all the possible combinations of the three resistors. We can obtain resistances by connecting the resistors in series or parallel.

When two resistors are connected in series, the equivalent resistance is given by:

R = R1 + R2

When two resistors are connected in parallel, the equivalent resistance is given by:

1/R = 1/R1 + 1/R2

Using these equations, we can find all the possible combinations of the three resistors. Here are the 18 resistances that can be obtained:

3.0 Ω

2.0 Ω

5.0 Ω

6.0 Ω

8.0 Ω (3.0 Ω + 5.0 Ω)

9.0 Ω (3.0 Ω + 6.0 Ω)

10.0 Ω (5.0 Ω + 5.0 Ω)

11.0 Ω

12.0 Ω

14.0 Ω (2.0 Ω + 6.0 Ω)

15.0 Ω (3.0 Ω + 12.0 Ω)

16.0 Ω (5.0 Ω + 6.0 Ω)

17.0 Ω (2.0 Ω + 5.0 Ω + 10.0 Ω)

18.0 Ω (6.0 Ω + 6.0 Ω + 6.0 Ω)

20.0 Ω (2.0 Ω + 6.0 Ω + 12.0 Ω)

21.0 Ω (3.0 Ω + 5.0 Ω + 12.0 Ω)

22.0 Ω (2.0 Ω + 5.0 Ω + 15.0 Ω)

23.0 Ω (3.0 Ω + 5.0 Ω + 15.0 Ω)

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Replace the incandescent bulb with the Voltage meter and return loop # to 3. What happens when you move the bar magnet back-n-forth through the loop? Does this appear to be creating a Direct Current or an Alternating Current? How do you know?

Answers

If we replace the incandescent bulb with a voltage meter and return the loop to its original configuration, then moving the bar magnet back and forth through the loop will induce an electrical current in the loop, as described by Faraday's law of electromagnetic induction.

What is magnet?

A magnet is a material or object that produces a magnetic field, which is a force that can attract or repel certain other materials, such as iron or steel. The magnetic field is created by the motion of electric charges within the magnet, which align in such a way that they produce a net magnetic field. Magnets can be made from a variety of materials, including iron, cobalt, nickel, and certain alloys. They come in many different shapes and sizes, including bars, discs, horseshoes, and rings.

Here,

The type of current that is generated depends on the direction and rate of the magnet's motion. If the magnet is moved back and forth with a constant speed and in a straight line, the current induced in the loop will be an alternating current (AC), because the direction of the current will reverse every time the magnet changes direction. This can be observed by the voltage meter reading a voltage that periodically changes in direction.

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a pair of figure skaters are performing a spin maneuver. The axis of rotation goes through the left foot of the skater on the left. What
action could increase the pair's angular velocity?​

Answers

Answer:

Angular momentum

Explanation:

Angular momentum is a conserved physical quantity, similar to the way that energy is a conserved quantity


A train brakes from 40
m/s to a stop over a
distance of 100m,what
is the acceleration of
the train?​

Answers

Answer:

the acceleration of the train is - 8 m/s² since it is decelerating as the influence of the brake comes to stop

Explanation:

r the following questions: a. why should the glassware be dry for this experiment? why might water contamination be a problem when using the reagent acetic anhydride; what byproduct might form due to moisture?

Answers

The glassware should be dry for the experiment because of following reasons

a. Glassware should be dry for this experiment because the reagent acetic anhydride reacts with water, producing acetic acid and heat. If the glassware is wet, it can lead to the premature reaction of the acetic anhydride, which can affect the accuracy of the results. Additionally, if water is present in the reaction mixture, it can hydrolyze the acetic anhydride, forming acetic acid and causing the reaction to fail.

b. Water contamination can be a problem when using acetic anhydride because it reacts with water to form acetic acid and heat. This reaction can cause the acetic anhydride to decompose prematurely, leading to inaccurate results. Additionally, water contamination can lead to the formation of byproducts such as acetic acid and acetic acid anhydride.

c. The byproduct that might form due to moisture is acetic acid. In the presence of water, acetic anhydride reacts to form acetic acid and heat. This reaction can lead to premature decomposition of the acetic anhydride and affect the accuracy of the experiment.

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a 50 kg boy runs at 3 m/s. how much momentum does he have

Answers

Answer:

150   kg-m/s

Explanation:

momentum = m * v

50 * 3 = 150

The energy of a photon is inversely proportional to its wavelength. True or Flase

Answers

False. E=hf, where h is Planck's constant, c is the speed of light, f is the frequency, and is the wavelength; and E=hc/, where E is directly proportional to frequency and inversely proportional to wavelength.

The inverse relationship between a photon's energy and what?

With respect to the wavelength of the radiation, photon energy is inversely proportional.

What is a photon's wavelength-related energy?

Two formulas can be used to determine a photon's energy: E = h f is a formula that can be used if the photon's frequency is known. This equation, sometimes known as Planck's equation, was created by Max Planck.

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An m = 6.11 g bullet is fired into a 365 g block that is initially at rest at the edge of a table of h = 1.08 m height as shown in the figure.
1. The bullet remains in the block, and after the impact the block lands d = 1.84 m from the bottom of the table. How much time does it take the block to reach the ground once it flies off the edge of the table?
2. What is the initial horizontal velocity of the block as it flies off the table?
3. Determine the initial speed of the bullet.

An m = 6.11 g bullet is fired into a 365 g block that is initially at rest at the edge of a table of

Answers

(a) The time taken the block to reach the ground once it flies off the edge of the table is 0.47 s.

(b) The initial horizontal velocity of the block as it flies off the table is 3.91 m/s.

(c) The initial speed of the bullet is 237.5 m/s.

Time of motion of the block

The time of motion of the block is calculated as follows;

h = ¹/₂gt²

where;

h is height of the tablet is time of motion

t = √(2h/g)

t = √( (2 x 1.08) / 9.8)

t = 0.47 s

Initial horizontal velocity of the block

x = vt

v = x/t

v = (1.84)/(0.47)

v = 3.91 m/s

Initial speed of the bullet

m1u1 + m2u2 = v(m1 + m2)

where;

m1 is mass of bulletm2 is mass of blocku1 is initial velocity of the bulletu2 is the initial velocity of the blockv is initial horizontal velocity of the block as it flies off the table

0.00611(u1) + 0.365(0) = 3.91(0.00611 + 0.365)

0.00611u1 = 1.451

u1 = 1.451/0.00611

u1 = 237.5 m/s

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Microwaves in a home microwave oven can be modeled as a linearly polarized plane wave in vacuum with a magnetic field given by B→=B0sin⁡(ky+ωt)x^. Here, B0= 0.24 mT and ω= 1.8 ×1010 rad/sec.What is the wavelength?A round dinner plate of radius r = 10 cm is placed in the microwave oven in an orientation perpendicular to the direction of propagation, as shown. Find the average power the plate can absorb. (Assume the plate area is smaller than the wave itself, and the plate absorbs all the energy impinging on it).

Answers

The average power the plate can absorb is P = 4.1 mW.

What is average power?

Average power is a measure of the average rate at which energy is converted from one form to another, or transferred from a source to a sink. It is typically expressed in watts (W). Average power is a measure of the average rate at which work is done, or energy is produced and consumed. It is the average rate at which energy is consumed over a given period of time. It is calculated by dividing the total energy used by the amount of time during which it was used. Average power is used to measure the efficiency of a device or system, and can be used to compare how different technologies or systems perform. The importance of using average power, as opposed to rms power as defined in this document, applies to power associated with time-varying voltage and current—that is, noise, RF signals, and oscillators.

The wavelength λ is given by the expression:
λ = 2π/k
where k = 2πω/c
Substituting the given values into this equation, we find that the wavelength is λ = 0.37 m.
The power that the plate can absorb can be found by using the equation:
P = (B0^2/2μ0)πr^2
where B0 is the amplitude of the magnetic field, μ0 is the permeability of free space, and r is the radius of the plate.
Substituting the given values into this equation, we find that the average power the plate can absorb is P = 4.1 mW.

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Microwaves in a home microwave oven can be modeled as a linearly polarized plane wave in vacuum with

Base your answer(s) to the following question(s) on the information and diagram
below.
A 250-kilogram car is initially at rest at point on a roller counter track.
The car carries a 75-kilogram passenger and is 20. meters above the ground
at point A. (Neglect friction.)
-7519
-250.
Ground
Compare the total mechanical energy of the car and punger at points A, B,
and
• Explanation:
.
Base your answer to the following question on the information below and on your
knowledge of physics
A gre-powered model airplane has a mass of 2.50 kilograms. A student
exerts a force on a cord to keep the airplane flying around her at a constant
speed of 18.0 meters per second in a horizontal, circular path with a radics
of 25.0 meters
Calculate the kinetic energy of the moving airplane. Show all work, including the
equation and substitution with units]
• Equation: KE = _m_ V^2
• Work: Ke=12*2.50kg*18^2m/s
• Answer w/Units:
.
.

Base your answer(s) to the following question(s) on the information and diagrambelow.A 250-kilogram car

Answers

Done I don't know answer of this question or this photo is the answer can you tell me

Base your answer(s) to the following question(s) on the information and diagrambelow.A 250-kilogram car

The magnitude of the centripetal force exerted on the airplane to keep it moving in this circular path is 32.4 N.

Mass of the airplane, m = 2.5 kg

Speed at which the airplane is flying, v = 18 m/s

Radius of the circular path, r = 25 m

The necessary force for the airplane to fly is provided by the centripetal force.

The component of force applied on an object in curvilinear motion that is pointed in the direction of the axis of rotation, or the center of curvature is known as the centripetal force.

F = Fc

The expression for the centripetal force acting on the airplane is given by,

Fc = mv²/r

Fc = 2.5 x 18²/25

Fc = 324/10

Fc = 32.4 N

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Your question was incomplete, but most probably your question would be:

A gas-powered model airplane has a mass of 2.50 kilograms. A student exerts a force on a cord to keep the airplane flying around her at a constant speed of 18.0 meters per second in a horizontal, circular path with a radius of 25.0 meters. what is the magnitude of the centripetal force exerted on the airplane to keep it moving in this circular path.

A Bugatti Veyron went from 0 to 60 mph in 2.5 seconds. What is
the mass of the vehicle if the force used to move the car was
10,000 N?

Answers

Bout 1000 ponies to the crank and she will get up and go

which of the following is not a type of energy?

which of the following is not a type of energy?

Answers

Answer:

Neutronic is not a defined type of energy.

When a 72 W light bulb is connected to a 298 V source, what is the current ?

Answers

the current is 0.24 Amperes

Explanation

power is the amount of energy transferred or converted per unit time, it can be found using the formula

\(\begin{gathered} P=I*V \\ where\text{ P is the power} \\ I\text{ is the current} \\ V\text{ is the voltage} \end{gathered}\)

so

Step 1

a)let

\(\begin{gathered} P=\text{ 72 Watts} \\ V=298\text{ V} \end{gathered}\)

b) now, replace in the formula and solve for I

\(\begin{gathered} P=I*V \\ 72\text{ W=I*298 V} \\ divide\text{ both sides by 298 V} \\ \frac{72W}{298\text{ V}}\text{=}\frac{I*298V}{298\text{ V}} \\ 0.24\text{ Amperes=I} \end{gathered}\)

therefore,the current is 0.24 Amperes

I hope this helps you

2.1 State the principle of conservation of linear momentum.
2.2 Calculate the magnitude of the velocity after the learner jumped on the
skateboard.

2.1 State the principle of conservation of linear momentum.2.2 Calculate the magnitude of the velocity

Answers

Answer:

2.1 The principle of conservation of linear momentum states that in the absence of any external forces, the total momentum of a system remains constant. This means that the total momentum before an event is equal to the total momentum after the event.

2.2 To solve the problem, we can use the principle of conservation of linear momentum, which states that the momentum of the system before the learner jumps on the skateboard is equal to the momentum of the system after the learner jumps on the skateboard.

Explanation:

The energy transfer diagram represents the energy of a light bulb.How much electrical energy is involved in this transformation?60 J80 J100 J 120 J

Answers

Answer:

j120

Explanation:

qll energy for residential is 120 and that's what ruffly is always used for wiring

Hi please help me on question asap! Silly answers will be reported ....... If answers correct I'll rate you five stars a thanks and maybe even brainliest!

Is this an advantage or a disadvantage?

In a parallel circuit the resistance in each branch is the same as if there was just one light bulb In the whole circuit .

Answers

This is actually an advantage of a parallel circuit. In a parallel circuit, the resistance in each branch is the same as if there was just one light bulb in the whole circuit.

In a parallel circuit, the current has multiple pathways to flow through. Each component, such as a light bulb, is connected across its own branch. The total resistance in a parallel circuit is determined by the sum of the reciprocals of the individual resistances in each branch.

Having the same resistance in each branch ensures that the current is distributed equally among the branches. This means that each component receives the same amount of current as if it were the only component in the circuit. As a result, the brightness of the light bulbs in a parallel circuit will be the same.

This characteristic of parallel circuits is advantageous because it allows for independent operation of each component. If one light bulb were to burn out or be removed, the other bulbs would continue to operate unaffected. Additionally, parallel circuits offer lower overall resistance compared to a series circuit, enabling the flow of more current.

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A basin surrounding a drain has the shape of a circular cone opening upward, having everywhere an angle of 35.0° with the horizontal. A 25.0-g ice cube is set sliding around the cone without friction in a horizontal circle of radius R. (a) Find the speed the ice cube must have as a function of R. (b) Is any piece of data unnecessary for the solution? Suppose R is made two times larger. (c) Will the required speed increase, decrease, or stay constant? If it changes, by what factor? (d) Will the time required for each revolution increase, decrease, or stay constant? If it changes, by what factor? (e) Do the answers to parts (c) and (d) seem contradictory? Explain.​

Answers

According to the information we can infer that the decrease in speed is offset by the increase in radius.

How to calculate the speed the ice cube must have as a function of R?

To calculate the speed the ice cube we have to consider that the gravitational force on the ice cube is balanced by the normal force provided by the cone. So, the speed of the ice cube must be such that the centripetal force equals the gravitational force.

In this case, to find the speed of the ice cube let M be the mass of the ice cube and r be the radius of the circular path. The gravitational force on the ice cube is given by Fg = Mg, where:

g = acceleration due to gravity.

The centripetal force is given by Fc = Mv^2/r, where:

v = speed of the ice cube

Setting Fg = Fc, we get:

Mg = Mv^2/r

Solving for v, we get:

v = sqrt(gr)

Is any piece of data unnecessary for the solution?

No piece of data is unnecessary for the solution.

Will the required speed increase, decrease, or sttay constant?

According to the information, when R is made two times larger, the required speed will decrease. For example:

From part (a), v is proportional to the square root of R. Therefore, if R is doubled, v will be multiplied by the square root of 2, which is approximately 1.414.

Will the time required for each revolution increase, decrease, or stay constant?

To know if the time required for each revolution will increase, decrease or stay constant we have to consider that shen R is made two times larger, the time required for each revolution will increase. To see this, note that the period T of the circular motion is given by:

T = 2πr/v

Do the answers to part C and D seem contradictory?

According to the information, the answers to parts (c) and (d) are not contradictory because the decrease in speed is offset by the increase in radius, resulting in a longer period of revolution. The net effect is that the ice cube will travel the same distance in each revolution, so the total time required for one complete revolution will remain constant.

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A physics professor leaves her house and walk along the sidewalk toward campus. After 5 min it starts to rain and she returns home. Her distance from her house as a function of time shown in figure: 1. At which of the labelled point is her velocity (a) zero? (b) Constant and positive? (c) constant and negative ? (d) Increasing in magnitude? (e) Decreasing in magnitude?

Answers

Answer: I think its zero-

I dont really know about this...

A 3-kg projectile is launched at an angle of 45o above the horizontal. The projectile explodes at the peak of its flight into two pieces. A 2-kg piece falls directly down and lands exactly 50 m from the launch point. Determine the horizontal distance from the launch point where the 1-kg piece lands.

Answers

1517.4 m

Step-by-step explanation:

Since the projectile broke up at the peak of its flight, it already traveled half its initial range so we can find its initial launch velocity \(v_0\) from the equation

\(\frac{1}{2}R= \dfrac{1}{2} \left(\dfrac{v_0^2}{g}\sin 2\theta_0 \right)\)

where \(\theta_0 = 45°\) and \(\frac{1}{2}R = 50\:\text{m}\) so we will get \(v_0=31.3\:\text{m/s}\). Next, we can use the equation

\(v_y = v_0y - gt = v_0 \sin 45 - gt\)

and since \(v_y=0\) at its peak, we get t = 22.1 s. Let's set this aside for a moment and we'll use it later.

At the top of its peak, we can use the conservation law of linear momentum. Let M be the mass if of the original projectile, \(m_1\) be the mass of the larger fragment (2 kg) and \(m_2\) be the mass of the smaller fragment (1 kg). We can write the conservation law as

\(Mv_0x = m_1V_1 + m_2V_2\)

where \(V_1\:\text{and}\:V_2\) are the velocities of the fragments immediately after the break up. But we also know that \(V_1=0\) so the velocity of \(m_2\) can be calculated from the conservation law as

\(Mv_0 \cos 45° = m_2V_2\)

or

\(V_2 = \dfrac{M}{m_2}v_0 \cos 45° = 66.4\:\text{m/s}\)

Now we can calculate the horizontal distance the smaller fragment traveled after the break up. Recall that the amount of time for it to go up is also the amount of time to get down so the horizontal distance x is

\(x = V_2 t = (66.4\:\text{m/s})(22.1\:\text{s})= 1467.4\:\text{m}\)

Therefore, the total distance traveled from the launch point is

\(D = 50\:\text{m} + 1467.4\:\text{m}=1517.4\:\text{m}\)

A kangaroo can jump over an object 2.20 m high with a vertical speed of 6.57 m/s. how long is it in the air

Answers

The kangaroo is in the air for approximately 0.667 seconds.

What is the velocity?

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

A kangaroo with a vertical speed of 6.57 m/s may jump over an object 2.20 m high.

To find the time a kangaroo is in the air, we need to calculate the time it takes to reach the peak of its jump and then double that time (to account for both the ascent and descent).

We can use the formula for vertical motion under constant acceleration (g = 9.8 m/s²):

t = √(2h / g)

where h is the height of the jump (2.20 m) and g is the acceleration due to gravity (9.8 m/s²).

Plugging in the values, we get:

t = √(2 × 2.20 m / 9.8 m/s²)

t = √(0.447)

t ≈ 0.667 s

So the kangaroo is in the air for approximately 0.667 seconds.

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Read the scenario below. Then, identify the chain of custody for:

1. type of evidence

2. location where evidence was found

3. who collected the evidence

4. how it was collected



October 19th, 2:04AM

Detective Lauren arrives at a crime scene of a drive by shooting. Crime Scene Investigator Molly collected bullet casings. The evidence was collected from the curb of the sidewalk using gloves and placed into baggies.

Answers

The type of evidence that was collected based on the information is a forensic evidence.

How to illustrate the information?

From the information, it was stated that Detective Lauren arrives at a crime scene of a drive by shooting. Crime Scene Investigator Molly collected bullet casings. The evidence was collected from the curb of the sidewalk using gloves and placed into baggies.

Therefore, the location where evidence was found is a crime scene.

The person who collected the evidence is Crime Scene Investigator Molly collected bullet casings.

The evidence was collected from the curb of the sidewalk using gloves and placed into baggies.

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Walking down a pebble beach becomes less painful as you enter the sea. Explain why.

Answers

Answer:Since pressure = force/area, the same force on a smaller area means more pressure. When you are walking on sand, the force being applied by your body is spread out over the entire surface of your foot. ... So, more pressure applied on a given area of your foot causes more pain.

Explanation:

Good Question

Pls help and explain how to get the answer

Pls help and explain how to get the answer

Answers

(a) The magnitude of the gravitational force on the rock is 64.68 N and on the pebble is 5.488 x 10⁻³ N.

(b) The acceleration of each object is equal to acceleration due to gravity, = 9.8 m/s².

What is the gravitational force exerted on each object?

The gravitational force exerted on each object is calculated by applying Newton's law of universal gravitation as follows;

Fg = Gm₁m₂ / R²

where;

G is universal gravitation constantm₁ is the mass of the rockm₂ is the mass of pebble

The acceleration of each object will be constant and equal to acceleration due to gravity, the force on each object is calculated by using Newton's second law of motion.

Force on the rock;

F = mg

where;

g is acceleration due to gravity

F = 6.6 kg x 9.8 m/s²

F = 64.68 N

The force on the pebble;

F = mg

F = 5.6 x 10⁻⁴  x 9.8

F = 5.488 x 10⁻³ N

Thus, the acceleration of each object is equal to acceleration due to gravity, = 9.8 m/s².

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A displacement vector is 23 km in length and directed 65° south of east. What are the components of this vector?

Eastward
Component Southward. Component
(a) 21 km 9.7 km
(b) 23 km 23 km
(c) 23 km 0 km
(d) 9.7 km 21 km​

Answers

If a displacement vector is 23 km in length and directed 65° south of east. the components of this vector is: (a) 21 km 9.7 km.

What is the components of this vector?

The displacement vector can be resolved into its eastward and southward components using trigonometry. Let's call the eastward component "x" and the southward component "y".

From the given information, we know that the displacement vector makes an angle of 65° south of east. This means that the angle between the vector and the eastward axis is 90° - 65° = 25°.

Using trigonometry, we can relate the length of the vector to its components:

cos 25° = x / 23

sin 25° = y / 23

Solving for x and y, we get:

x = 23 cos 25° ≈ 21 km

y = 23 sin 25° ≈ 9.7 km

Therefore, the answer is (a) 21 km eastward component and 9.7 km southward component.

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