Ancient gold coins have been found in Greece and Italy. What property allows for gold to be stamped into coins?

Answers

Answer 1

Answer: malleability

Explanation:


Related Questions

Why does the time for 20 complete oscillations need to be taken in the pendulum oscillation experiment?​

Answers

Answer:

In order to minimize the uncertainty in the period, we measured the time for the pendulum to make 20 oscillations, and divided that time by 20

Explanation:

Class 10 cbse

Question: Draw the ray diagram in each case to show the position and nature of the image formed when the object is placed:
(i) at the centre of curvature of a concave mirror
(ii) between the pole P and focus F of a concave mirror
(iii) in front of a convex mirror

Answers

Explanation:

I hope it will help you. But I am in Grade nine .And sry too cuz I told the answer of Grade nine .

Class 10 cbse Question: Draw the ray diagram in each case to show the position and nature of the image
Class 10 cbse Question: Draw the ray diagram in each case to show the position and nature of the image
Class 10 cbse Question: Draw the ray diagram in each case to show the position and nature of the image
Class 10 cbse Question: Draw the ray diagram in each case to show the position and nature of the image

Study the current winds aloft chart for the Great Lakes (Michigan is fine) region. Estimate the average wind speed for 3000’ 12,000’ and FL350.
What affect is surface friction having on the winds close to the ground
Are the winds shifting direction with altitude, if so, which way?
What is the approximate location of the Jetstream currently? (Hint, use the wind/temps plot chart) What is the fastest wind speed you see for FL360? Which direction flight would it benefit?
How does this change seasonally?
Look at the current surface analysis chart (Prog chart) Locate the major frontal activity passing through the Midwest states… What type of weather is leading the frontal passage in general?
Temperatures
Wind speed/direction
Precipitation

Answers

The winds aloft chart for the Great Lakes (Michigan is fine) region displays the wind direction and speed at several altitudes. At 3000 feet, the wind speed is approximately 17 knots.

At 12,000 feet, the wind speed is about 44 knots. The wind speed at FL350 is approximately 67 knots.Surface friction has an effect on the winds close to the ground, slowing them down due to the frictional force exerted on the ground by air molecules. The winds shift direction with altitude, veering to the right of the direction of travel in the northern hemisphere. The approximate location of the Jetstream can be obtained by examining the wind/temperature plot chart. The fastest wind speed at FL360 appears to be approximately 145 knots, traveling towards the northeast. Flight to the east or southeast would benefit from this wind speed.Seasonally, winds aloft change depending on the position of the jet stream, which moves towards the poles during the summer months and towards the equator during the winter months.

The current surface analysis chart (Prog chart) shows the major frontal activity passing through the Midwest states. Precipitation is what leads the frontal passage in general, with both temperature and wind speed/direction changing from behind to ahead of the front.

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A 2kg mass moving at 1 m/s has a kinetic energy equal to...?

Answers

Answer:

kinetic energy = 1/2mv2

= 1/2 x 2 x 3^2

= 9J

Explanation:

If A is the set of even integers less than 10, and B is the set of multiples of 3 less than 20, what is the union of sets A and B? (A) {2, 4, 6, 8} (B) {3, 6, 9, 12, 15, 18} (C){6} D) {2, 3, 4, 6, 8, 9, 12, 15, 18} (E) {2, 4, 6, 8, 10, 12, 14, 16, 18}

Answers

Answer:

(D)

Explanation:

A(2,3,4,6,8)

B(6,9,12,15,18)

(AuB)=(2,3,4,6,8,9,12,15,18)

What are 5 examples of potential energy?

Answers

Potential energy is the energy an object possesses because of its position or state. It is the energy that an object has the capacity to do work, but has not yet done so. Here are five examples of potential energy:

Gravitational potential energy: This is the energy an object possesses due to its position in a gravitational field. For example, a ball held above the ground has gravitational potential energy because it has the potential to fall and do work. The formula for gravitational potential energy is mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.Elastic potential energy: This is the energy stored in an object when it is stretched or compressed. For example, a stretched rubber band has elastic potential energy. The more it is stretched, the more potential energy it has. The formula for elastic potential energy is 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position.Chemical potential energy: This is the energy stored in the bonds between atoms and molecules. For example, the chemical potential energy in a stick of dynamite is released when the chemical bonds are broken, creating an explosion.Nuclear potential energy: This is the energy stored in the nucleus of an atom. For example, the nuclear potential energy in a uranium atom is released when the nucleus is split, creating a nuclear reaction.Thermal potential energy: This is the energy stored in the motion of the atoms and molecules in a substance. For example, the thermal potential energy in a cup of hot coffee is released when it cools down to room temperature.

It's important to note that potential energy can be converted into kinetic energy, which is the energy of motion. This can happen spontaneously if an object is able to move due to a force acting on it, such as gravity.

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when the sledder slides to the top of the left hill (shown in the figure below), her speed is 6.5 m/s. the total mass of the girl and the sled is 55 kg. she continues sliding down, passes the valley and moves up on the right hill. what is the speed of the sledder at the top of the right hill assuming a thermal energy of 160 j is generated due to friction during the sliding process?

Answers

The speed of the sledder at the top of the right hill assuming a thermal energy of 160 j is generated due to friction during the sliding process is 1.8 m / s

According to law of conservation of energy,

m1 g h1 + 1 / 2 m1 v1² = m2 g h2 + 1 / 2 m2 v2²

m1 = m2 = m

m g h1 + 1 / 2 m v1² = m g h2 + 1 / 2 m v2² - W

W is included because there is some energy lost as heat.

g = 9.8 m / s²

h1 = 4.2 m

v1 = 6.5 m / s

h2 = 5.9 m

H = 160 J

m = 55 kg

g h1 + 1 / 2 v1² = g h2 + 1 / 2 v2² + W / m

( 9.8 * 4.2 ) + ( 1 / 2 * 6.5² ) = ( 9.8 * 5.9 ) + ( 1 / 2 * v2² ) + ( 160 / 55 )

41.16 + 21.13 = 57.82 + v2² / 2 + 2.91

v2² = 1.56 * 2

v2 = 1.8 m / s

Therefore, the speed of the sledder is 1.8 m / s

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I am having a bit of difficulty with this lab question:
_________________________________________
The passage of an occluded front may be accompanied by widespread precipitation and little temperature change at ground level. This is because occluded fronts are a combination of (1). [one / two / three] cold/cool air mass(es), which shifts a (2). [cold / warm / hot] air mass (3). [aloft / sideways / downwards].
_________________________________________
Currently, I have my answers as follows:
1. two cool/cold air masses
2. warm
3. downwards
Could someone help me out and let me know if I am correct? Thanks!

Answers

This is due to the fact that occluded fronts combine two cold air masses, which causes one of the cold air masses to go downward.

When a warm air mass is sandwiched between two cold air masses, an occluded front occurs. In an occlusion, the warm front passes over the cold front, which dives beneath it.

In a front is obscured, the warm front is fully supplanted by the cold front, in which the warm air masses have completely disappeared. Furthermore, there are frequent shifts in the various weather producing circumstances because of the cold front's relatively low temperature.

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Why should diameter of double walled tube must be big for a ice box​

Answers

The diameter should of the double-walled tube be big for an ice box​ is increase the thermal temperature.

Double wall pipes are an important safety tool when storing liquids such as those used in the chemical wastewater food and beverage industries. The majority of jacketed piping applications are for chemical wastewater-contaminated groundwater and chemical process safety.

Tube wall thickness in excess of that required for internal stresses and known loads not only provides a margin of safety against unexpected loads but also increases survival time when corrosion or fatigue mechanisms are in action. increase. Single-layer tubing is lightweight, flexible, and can be installed quickly with less personnel and equipment. The double wall is a smooth inner double wall with a corrugated outer tube.

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A potato gun fires a potato straight up with an initial velocity of 16 m/s. How high will it rise?

Answers

The maximum height to which the potato will rise is 13.06 m

Data obtained from the question

From the question given above, the folloing data were obtained:

Initial velocity (u) = 16 m/sFinal velocity (v) = 0 m/s (at maximum height) Acceleration due to gravity (g) = 9.8 m/s²Maximum height (h) =?

How to determine the maximum height

The maximum height can be obtaibed as illustarted below

v² = u² – 2gh (since the ball is going against gravity)

0² = 16² – (2 × 9.8 × h)

0 = 256 – 19.6h

Collect like terms

0 – 256 = –19.6h

–256 = –19.6h

Divide both side by –19.6

h = –256 / –19.6

h = 13.06 m

Thus, the potato will rise to a height of 13.06 m

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The seismic wave of an earthquake is represented by the equation r = 12.8 sin(θ), where r is measured in miles. the seismic wave is represented by curve having a center on the . the earthquake can be felt miles from its center.

Answers

Based on seismic wave of an earthquake represented by the equation r = 12.8 sin(θ), the seismic wave is represented by circular curve having a center on the positive y axis. The earthquake can be felt 6.4 miles from its center.

A seismic wave is defined as a wave of acoustic energy which travels through the Earth surface and plates. These waves are generally caused by movements of tectonic plates in the Earth (earthquakes). It may also be triggered by volcanoes, explosions, and landslides. As earthquake happen, it causes rocks located at a fault line to break or slip, and as a result Earth’s crust sections physically move in relation to one another. The movement of plates causes energy to be released. Two types of seismic waves spread outward from the earthquake center through Earth’s interior and along its surface. Based on the given equation, the seismic wave will be represented by a circular curve with a center on the positive y axis. An earthquake can be felt 6.4 miles from its center if θ = 8.

Note: The question is incomplete. The complete question probably is: The seismic wave of an earthquake is represented by the equation r = 12.8 sin(θ), where r is measured in miles. The seismic wave is represented by ______ (Circular, Rose, Limacon) curve having a center on the ______ (Positive x Axis, Negative x Axis, Positive Y axis, Negative Y axis). If θ = 8, the earthquake can be felt ________ (6.4, 12.8, 25.6) miles from its center.

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(b) By adding another component to the circuit, the student is able to obtain a range of
ammeter and voltmeter readings.
Ammeter
(amps)
0.10
0.15
0.20
0.25
0.30
Voltmeter
(volts)
1.0
2.0
4.0
7.0
11.0
Question:Which component did the student add to the circuit?

Answers

The students add a variable resistor to the circuit

What is a variable resistor?

variable resistor is a resistor of which the electric resistance value can be adjusted. A variable resistor is in essence an electro-mechanical transducer and normally works by sliding a contact (wiper) over a resistive element.

A variable resistor gives resistance. Resistance is the opposition to electric current and it is measured in ohms.

From ohm's in law, the potential difference between the ends of a conductor is proportional to current, provided temperature and other physical conditions are kept constant.

This means that by varying the resistor, different values of current and voltages will be acquired.

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Transcribed image text: The position of a ball rolling in a straight line is given by x = 2.0 - 3.6t + 1.7t2 where x is in meters and t in seconds, (a) What do the numbers 2.0, 3.6, and 1.7 refer to? (b) What are the units of each of these numbers? (c) Determine the position of the ball at t = 1.0 s, 2.0 s, and 3.0 s. (d) What is the average velocity over the interval t = 1.0 s to t = 3.0 s? Essay answers are limited to about 500 words (3800 characters maximum, including spaces). 3800 Character(s) remaining

Answers

a) 2.0 represents the initial position of the ball,  -3.6 represents the initial velocity of the ball  and 1.7 represents the acceleration of the ball.

b)The unit of 2.0 is meters, the unit of -3.6 is meters per second, and the unit of 1.7 is meters per second squared.

c) Position of of ball at t=1, 2, 3 are -1.9, 5.4 and 9.1 meters respectively

d) Average velocity is 5.5 meter per second

Part a

In the equation x = 2.0 - 3.6t + 1.7t2, the number 2.0 represents the initial position of the ball (i.e., the position of the ball at t = 0 seconds), -3.6 represents the initial velocity of the ball (i.e., the velocity of the ball at t = 0 seconds), and 1.7 represents the acceleration of the ball.

Part b

The unit of 2.0 is meters, the unit of -3.6 is meters per second, and the unit of 1.7 is meters per second squared.

Part c

To determine the position of the ball at t = 1.0 s, 2.0 s, and 3.0 s, we simply substitute these values into the equation:

When t = 1.0 s: x = 2.0 - 3.6(1.0) + 1.7(1.0)^2 = -1.9 meters

When t = 2.0 s: x = 2.0 - 3.6(2.0) + 1.7(2.0)^2 = 5.4 meters

When t = 3.0 s: x = 2.0 - 3.6(3.0) + 1.7(3.0)^2 = 9.1 meters

Part d

The average velocity over the interval t = 1.0 s to t = 3.0 s can be calculated by taking the displacement of the ball during this time interval and dividing it by the time interval:

Displacement = x(3.0) - x(1.0) = 9.1 - (-1.9) = 11.0 meters

Time interval = 3.0 s - 1.0 s = 2.0 s

Average velocity = Displacement / Time interval = 11.0 meters / 2.0 seconds = 5.5 meters per second.

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How to find velocity from acceleration time graph.

Answers

Answer:

We can only find the change in velocity by the area under the acceleration time graph by calculating the area under the curve to the given time. Then by the formula of the difference in the final and initial velocity you can find the final velocity of the object in the given time period.

Convert 350.0mL at 740 K to its new volume at standard temperature

Convert 350.0mL at 740 K to its new volume at standard temperature

Answers

Answer:

129.12 ml

Explanation:

If answer is correct feel free to replay me for explanation.

how does electricity work?​

Answers

Answer:Electricity works by getting a bunch of conductor elements together and creating a flow of electron-stealing patterns through them. This flow is called a current. ... Once you can control the direction the electrons are going, you can use them to power or charge anything from a light bulb to your TV to your electric car.

Explanation:trust

Molecules can be made up of two atoms of the same element;
cxygen gas is made up only of oxygen atoms.
A. for example
B. most importantly
C. on the other hand
D. therefore

Answers

Molecules can be made up of two atoms of the same element for example oxygen gas is made up only of oxygen atoms.

Molecules of an element :

Two or more atoms of the same or different element that are joined together to form a molecule are referred to as molecules. A molecule can be heteronuclear, which is a chemical compound made up of more than one element, like water, or homonuclear, which means it is made up of atoms of one chemical element, like oxygen (O2) (H2O).

Difference between molecule and compound :

When two or more atoms from the same element chemically combine, a molecule is created. A compound is created if the types of atoms differ from one another. Not all molecules are compounds because some molecules, like ozone (O3) and oxygen gas (pictured above), only contain one type of atom or element.

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what thing is that if you broke it only it work???

Answers

An egg
You have to crack it
A glow stick you have to crack it for it to glow

What is the density of wood

Answers

Wood density varies depending on species, growth condition, and tree developmental stage. For example, eastern cottonwood wood has a density of about ∼320 kg/m3 while oak species often exceed ∼550 kg/m3 (Isenberg, 1980)

i hope it will help you

Explanation:

density to the amount of wood in a unit , per volume of wood. the ratio of dry weight and green volume of the given wood is basic wood density.

Suppose you are testing a new amusement park roller coaster with an empty car with a mass of 100 kg. One part of the track is a vertical loop with a radius of 12.0 m. At the bottom of the loop (point A), the car has a speed of 25.0 m/s and at the top of the loop (point B), it has a speed of 8.00 m/s. As the car rolls from point A to point B, how much work is done by friction? Use 9.81 m/s2 for the acceleration due to gravity.

Answers

Answer:

Explanation:

Gain  of kinetic energy + work done by friction = loss of potential energy

= 1 / 2 m ( 25² - 8² ) + work done by friction = m x 9.8 x ( 12 + 12 )

= .5 x 100 x ( 625 - 64 ) + work done by friction = 100 x 9.8 x 24

28050 + work done by friction = 23520

work done by friction = -4530 J

a student placed 700g of water at 28C in a freezer. After 6 minutes and 15 seconds the water was transformed into ice. Calculate the latent heat of fusion given that 235200J of heat energy was transferred during the change of state

Answers

The latent heat of fusion is 335714.29 J/kg.

To calculate the latent heat of fusion, we can use the equation:

Q = m * L

Where:

Q = heat energy transferred

m = mass of the substance

L = latent heat of fusion

Given:

Mass of water (m) = 700 g = 0.7 kg

Heat energy transferred (Q) = 235200 J

To find the latent heat of fusion (L).

Since the water is being transformed into ice, we know that the heat energy transferred during this phase change is equal to the latent heat of fusion.

Rearrange the equation to solve for L:

L = Q / m

L = 235200 J / 0.7 kg

L ≈ 335714.29 J/kg

Therefore, the latent heat of fusion is approximately 335714.29 J/kg.

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5). A body of mass 75kg lying on a surface of
μ = 0.4 move in the direction of a horizontal force
of 300N applied to it.
a). Calculate the
i). friction force
ii). acceleration of the body
b). Explain the result in aii).

Answers

Explanation:

a) i) Calculation of the friction force:

The friction force can be determined using the equation:

friction force = coefficient of friction * normal force

The normal force is equal to the weight of the object, which can be calculated as:

normal force = mass * gravitational acceleration

where the gravitational acceleration is approximately 9.8 m/s².

normal force = 75 kg * 9.8 m/s² = 735 N

friction force = 0.4 * 735 N = 294 N

ii) Calculation of the acceleration of the body:

Now, we can calculate the acceleration using Newton's second law:

net force = mass * acceleration

Since the applied force and the friction force act in opposite directions, the net force can be calculated as:

net force = applied force - friction force

net force = 300 N - 294 N = 6 N

mass = 75 kg

6 N = 75 kg * acceleration

acceleration = 6 N / 75 kg = 0.08 m/s²

b) Explanation:

In part (a), we calculated the friction force to be 294 N and the acceleration of the body to be 0.08 m/s². The positive acceleration indicates that the body is moving in the direction of the applied force.

The friction force opposes the motion of the body and acts in the opposite direction to the applied force. In this case, the applied force of 300 N is greater than the friction force of 294 N. As a result, the net force acting on the body is 6 N in the direction of the applied force.

The small net force of 6 N, compared to the body's mass of 75 kg, results in a relatively low acceleration of 0.08 m/s². This indicates that the body will accelerate slowly in the direction of the applied force due to the presence of friction.

Overall, the friction force and the resulting acceleration of the body are determined by the coefficient of friction (μ) and the mass of the object. In this case, the body experiences a relatively high friction force, leading to a small acceleration.

the duration of a 20-year zero-coupon bond is group of answer choices equal to that of a 20-year 10oupon bond. larger than 20. smaller than 20. equal to 20.

Answers

The duration of a 20-year zero-coupon bond is equal to that of a 20-year coupon bond.

Duration is a measure of a bond's sensitivity to changes in interest rates. It takes into account the bond's maturity, coupon rate, and yield. In the case of a zero-coupon bond, there are no periodic interest payments, but the bond is sold at a discount to its face value, which is paid at maturity.

On the other hand, a coupon bond pays periodic interest payments and is sold at its face value. Despite these differences, the duration of a 20-year zero-coupon bond is equal to that of a 20-year coupon bond because they both have the same maturity of 20 years. However, the volatility of a zero-coupon bond may be higher than that of a coupon bond due to the absence of periodic cash flows, making it more sensitive to changes in interest rates.

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As an atom's nucleus gets larger the electric charges repelling the protons get larger. to compensate for this greater electric charge the atom

Answers

As an atom's nucleus gets larger, the electric charges repelling the protons also increase. This is because each proton carries a positive charge, and like charges repel each other. To compensate for this greater electric charge, the atom relies on the strong nuclear force, which acts to hold the protons and neutrons together in the nucleus.

The strong nuclear force is much stronger than the electric force, but its range is very short. As the size of the nucleus increases, the strong nuclear force needs to be stronger to keep the protons and neutrons bound together, overcoming the repulsive electric force between the protons.

In larger nuclei, neutrons also play a crucial role in stabilizing the nucleus. Neutrons do not carry any charge, so they do not contribute to the electric repulsion. However, they do contribute to the strong nuclear force, helping to bind the nucleus together more tightly. This is why heavier elements often have a higher ratio of neutrons to protons in their nuclei.

In summary, as an atom's nucleus gets larger, the electric charges repelling the protons get larger. To compensate for this greater electric charge, the atom relies on the strong nuclear force, with the help of neutrons, to hold the nucleus together.

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The cooling system of an automobile motor contains 20. 0 kg of water. What is the t of the water if the engine operates until 836,000 J of heat have been added to the water?

Answers

the temperature of the water in the cooling system will increase by 9.99°C if the engine operates until 836,000 J of heat have been added to the water.

To solve this problem, we need to use the specific heat capacity equation:
Q = mcΔT
where Q is the amount of heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
We know that the engine has added 836,000 J of heat to the water, and that the mass of the water is 20.0 kg. The specific heat capacity of water is 4.18 J/g°C.
First, we need to convert the mass of water from kg to g:
20.0 kg = 20,000 g
Now we can plug in the values:
836,000 J = (20,000 g)(4.18 J/g°C)(ΔT)
Solving for ΔT:
ΔT = 836,000 J / (20,000 g x 4.18 J/g°C)
ΔT = 9.99°C

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If 9.467 A current is passing through a straight wire, what would be the magnetic field induced at a point 3.9 centimeter away from the wire

Answers

For a current is passing through a straight wire, the Magnetic field is mathematically given as,

B=5.535*10^5T.

What would be the magnetic field induced at a point 3.9 centimeter away from the wire?

Generally, the equation for the Magnetic field  is mathematically given as

\(B=\frac{\mu i}{ 2 \pi r}\)

Therefore

\(B=\frac{4 \pi *10^{-7}*4.2.28}{2 \pi (1.6*10^-2)}\)

B=5.535*10^5T

In conclusion, the magnetic field

B=5.535*10^5T

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5) A toxic chemical accidentally released into the environment from a metal processing plant degrades according to the law dQ = -0. 04Q dt where t is measured in years. If the initial leak is of 60kg,

Answers

The given differential equation is:

dQ/dt = -0.04Q

where Q is the quantity of the toxic chemical and t is time in years.

To solve this differential equation, we can use separation of variables:

dQ/Q = -0.04 dt

Integrating both sides, we get:

ln|Q| = -0.04t + C

where C is the constant of integration. To find the value of C, we can use the initial condition that the initial leak is 60 kg:

ln|60| = -0.04(0) + C

C = ln|60|

Substituting this value of C back into the general solution, we get:

ln|Q| = -0.04t + ln|60|

Simplifying, we get:

ln|Q/60| = -0.04t

Exponentiating both sides, we get:

Q/60 = e^(-0.04t)

Multiplying both sides by 60, we get the final solution:

Q = 60e^(-0.04t)

Therefore, the quantity of the toxic chemical present at any time t (measured in years) after the initial leak is:

Q(t) = 60e^(-0.04t)

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what type of braking is used to smoothly and gradually reduce brake pedal pressure at the end of a braking maneuver

Answers

Trail braking is used to smoothly and gradually reduce brake pedal pressure at the end of a braking maneuver.

What is Pressure ?

Nothing would probably happen if you tried to pound a bowling pin into the wall, unless people decided to stop lending you their bowling pins. However, if you use the same amount of force to hammer a nail, the nail has a much higher chance of penetrating the wall. This demonstrates that sometimes understanding the force's magnitude alone is insufficient; you also need to understand how the force is distributed over the surface of impact. The relatively small area on the sharp nail tip was where the whole force between the wall and the nail was centred for the nail. The area of the bowling pin touching the wall was much larger, though, and as a result, the force was dispersed much more evenly.

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The type of braking is used to smoothly and gradually reduce the brake pedal pressure is called the trail braking.

What is pressure?

Pressure is defined as the force applied perpendicularly to an object's surface per unit area across which that force is dispersed. The pressure relative to the surrounding air is known as gauge pressure, also written gage pressure[a].

Gradual reduction of brake pedal pressure at the end of a braking maneuver is typically achieved through a process called "trail braking." Trail braking refers to the technique of continuing to apply the brakes after turning into a corner in order to maintain a greater level of control and stability of the vehicle.

This is done by gradually reducing the brake pressure as the vehicle enters the corner, allowing for a smoother and more controlled transition between braking and accelerating.

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Should the resistance of an ammeter low or high ?give reason

Answers

Answer:

The resistance of an ammeter should be low. This is because an ammeter is connected in series with the circuit for the measurement of electric current. In case, its resistance is high, then some amount of current may lost in heating it leading to the inaccurate reading. An ideal ammeter is one which has zero resistance.

A ball is thrown straight up. If the launch velocity is 15 m/s, at what SPEED will the ball return to the thrower’s hand?


a) -15 m/s
b) -9.8 m/s
c) 15 m/s
d) 0 m/s

Answers

Answer:

Vf = 15 m/s

Explanation:

First we consider the upward motion of ball to find the height reached by the ball. Using 3rd equation of motion:

2gh = Vf² - Vi²

where,

g = acceleration due to gravity = -9.8 m/s² (negative sign for upward motion)

h = height =?

Vf = Final Velocity = 0 m/s (Since, ball momentarily stops at highest point)

Vi = Initial Velocity = 15 m/s

Therefore,

2(-9.8 m/s²)h = (0 m/s)² - (15 m/s)²

h = (-225 m²/s²)/(-19.6 m/s²)

h = 11.47 m

Now, we consider downward motion:

2gh = Vf² - Vi²

where,

g = acceleration due to gravity = 9.8 m/s²

h = height = 11.47 m

Vf = Final Velocity = ?

Vi = Initial Velocity = 0 m/s

Therefore,

2(9.8 m/s²)(11.47 m) = Vf² - (0 m/s)²

Vf = √(224.812 m²/s²)

Vf = 15 m/s

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