Determine the linear velocity of an object with an angular velocity of 5.9 radians per second at a distance of 12 centimeters from the center. use . round the answer to the nearest tenth.

Answers

Answer 1
The linear velocity of a rotating object is the product of the angular velocity and the radius of the circular motion. Angular velocity is the rate of the change of angular displacement of a body that is in a circular motion. It is a vector quantity so it consists of a magnitude and direction. From the problem, the angular velocity is 5.9 rad per second and the radius is given as 12 centimeters. We calculate as follows:

Linear velocity = angular velocity (radius)
Linear velocity = 5.9 (12 ) = 70.8 cm / s

The linear velocity of the body in motion is 70.8 centimeters per second or 0.708 meters per second.

Related Questions

Which part of a stream's sediment load moves the slowest?

Answers

The bed load moves the slowest from all the parts of the stream's sediment. It consists of particles suspended that are suspended and float around the bed. This part is the slowest in motion, as it rolls, and moves with the flow. The particles near the bed are not dissolved so they settle at the bottom and move with the stream.

A rocket is headed away from earth at a speed of 0.8c. the rocket fires a missile at a speed of 0.7c (the missile is aimed away from earth and leaves the rocket at 0.7c relative to the rocket). how fast is the missile moving relative to earth? select one:

a. 1.5c

b. a little less than 1.5c

c. a little over c

d. a little under c

e. 0.75c

Answers

To solve this problem, let us consider that the Earth is the origin, the initial reference point. Therefore the speed of rocket plus the missile would be 0.8 C

Now after the rocket had moved away from Earth, it fired a missile at a speed of 0.7 C. Now the reference made to this is relative to the rocket. We have established that our initial reference point is the Earth, therefore the real speed of the missile with reference to Earth is:

Speed of missile relative to Earth = 0.8 C + 0.7 C

Speed of missile relative to Earth = 1.5 C

 

Answer is:

A

Imagine that you're standing in a large room when a loud noise is made. You begin hearing a series of echoes. Which characteristic of sound best explains what just happened?

Answers

The characteristic of sound that would best explain the series of echoes you are hearing would be reverberation. It is created when a sound wave is being reflected to the surfaces causing it to have a many reflection building up and decaying as these waves are being absorbed bu the surfaces in the area which could be tables, chairs, people or the air. Reverberation is the group of the reflected sounds in an enclosed area. 

Imagine that you're standing in a large room when a loud noise is made. You begin hearing a series of echoes. The characteristic of sound that best explains what just happened is: Reverberation.

When you measure the current and voltage in a ac circuit with a multimeter, is your result the peak value or the rms value?

Answers

Ac voltmeters and ammeters usually give rms readings.

A helicopter’s speed increases from 30 m/s to 40 m/s in 5 seconds.
What is the acceleration of this helicopter?

Answers

So, acceleration is the change of velocity in time. If no vectors are used, one can use speed:

a = (final speed - start peed)/ time = 10/5= 1 m/s^2,

Notice that the units are m/s^2, or (m/s)/s. That is speed (m/s) per unit time (s)

its 2 meters per sec

What hall voltage is produced by a 0.200-t field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm/s?

Answers

The hall voltage will be calculated using the formula:

E = Blv

where: 

>Hall voltage: E = ?
>Magnetic field:
               B = 0.200 Tesla or Wb/m^2
>Width of conductor or Diameter of Aorta:
               l = 2.60 cm, converting to meter = .0260 m
>Velocity of charge flowing:
              v = 60 cm/s, converting to meter = 0.6 m/s

Substituting the given :

E = (0.200 Wb/m^2) * (0.260 m) * (0.6 m/s)
E = (0.200 Wb/m^2) * (0.156 m^2/s)
E = 0.0312 Wb/s

Since 1 volt = 1 Wb/s then,

E = 0.0312 V or 31.2 mV

Question Part Points Submissions Used A bare helium nucleus has two positive charges and a mass of 6.64 ✕ 10−27 kg. What is kinetic energy in joules at 1.80% of the speed of light?

Answers

The Kinetic Energy (KE) is calculated using the formula:

KE = 0.5 m v^2

Where,

m = mass of bare helium nucleus = 6.64 ✕ 10^−27 kg

v = velocity = 0.018 c = 0.018 * 3 ✕ 10^8 m / s^2 = 5.4 ✕ 10^6 m / s^2

Calculating:

KE = 0.5 (6.64 ✕ 10^−27 kg) (5.4 ✕ 10^6 m / s^2)^2

KE = 9.68✕ 10^−14 J

how does bare soil surface type affect the amount of runoff?

Answers

The bare soil surface affects runoff because it has no nutrients or real resistants. Run-off rate increases because there is nothing there to absorb the rain water. A porous surface type will absorb a little runoff. A non-porous surface will not absorb much at all. It increases it since there is less plant material to slow down the water.
 Run-off rate increases because there is nothing there to absorb the rain water. If the bare soil is comprised of porous-type, then it can absorb a little runoff. But if the soil is non-porous surface, then it will not absorb much at all. 

A piano has a mass of 185 kg, and the coefficient of friction between it and the floor is 0.39. What is the maximum force of friction between the piano and the floor?

707 N
523 N
1813 N
1208 N

Answers

coefficient of friction x mass x g

707 N

185×0.39×9.8

I just did it and found the answer

What conditions are required for a solar eclipse?

Answers

The phase of the Moon must be new, and the nodes of the Moon's orbit must be nearly aligned with Earth and the Sun.
Final answer:

A solar eclipse occurs when the Moon blocks the Sun from the Earth's viewpoint during a New Moon phase. The Moon also needs to be crossing the line of nodes, the intersection of the Earth's and Moon's orbit plain.

Explanation:

A solar eclipse occurs when the Moon moves between the Sun and the Earth, casting a shadow on the Earth. This event happens only during a New Moonphase, which is one of the conditions needed. Not all New Moon phases result in a solar eclipse because the Moon's orbit is tilted relative to the Earth's orbit around the Sun. Therefore, for a solar eclipse to take place, the Moon must be in the New Moon phase, and it must also be at a position in its orbit where it crosses the plane of the Earth's orbit around the Sun. This place is known as the line of nodes.

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How much horizontal force f must a sprinter of mass 47 kg exert on the starting blocks to produce this acceleration? express your answer in newtons using two significant figures?

Answers

This statement is missing the first sentence which states the horizontal acceleration.

I found that the desired horizontal acceleration is 15.0 m/s^2.

Now, you must use second law of Newton to calculate the force.

Second Law of Newton: F = m * a

=> F = 47 kg * 15 m/s^2 = 705 N

Answer: 705 N

Final answer:

To find the horizontal force a 47 kg sprinter must exert on the starting blocks to achieve a given acceleration, Newton's Second Law is used. Assuming the acceleration is 4.20 m/s², the required force is calculated to be approximately 197 N.

Explanation:

To determine how much horizontal force (f) a sprinter must exert on the starting blocks to produce a certain acceleration, we can use Newton's Second Law of Motion, which states that force equals mass times acceleration (F = ma). Since the student asked for the amount of force for a sprinter with a mass of 47 kg but did not provide the acceleration, we'll assume the acceleration is the same as provided in the reference problems: 4.20 m/s² (as from a 63.0-kg sprinter).

Using the formula F = ma:

Force (F) = mass (m) × acceleration (a)

F = 47 kg × 4.20 m/s²

F = 197.4 N

Therefore, the sprinter must exert a force of approximately 197 N on the starting blocks to achieve the given acceleration.

A point charge q1 = +2.90 µc is held stationary at the origin. a second point charge q2 = -5.30 µc moves from the point x = 0.110 m, y = 0 to the point x = 0.280 m, y = 0.280 m. how much work is done by the electric force on q2?

Answers

A point charge with a charge q1 = + 2.90 uC is held stationary at the origin hence coordinates are (0, 0).

 

A second point charge with a charge q2= - 5.40 uC moves from the point x = 0.110 m, y = 0 to the point x = 0.280 m, y = 0.280 m  [(0.110, 0) to (0.28, 0.28)]

 

The initial distance between the two charges is:

Initial distance = r1 = 0.110 m

 

The final distance between the two charges is calculated using hypotenuse formula:

Final distance = r2 = sqrt [0.28^2 + 0.28^2]

r2 = sqrt [2 * 0.0784]

r2 = sqrt [0.1568]

r2 = 0.396 m

 

Δr = r1 - r2 = 0.110 - 0.396 = - 0.286 m

 

r1r2 = 0.04356 m^2

 

Work is done by the electric force on q2= W. The formula to use with change in location is:

 

W =k q1 q2 [1/r2 - 1/r1]

W = 9*10^9 * 2.9*10^-6 * -5.3*10^-6 [(1/0.396) – (1/0.110)]

W = 0.908 J = 9.08*10^-1 J            (ANSWER)

What is the speed of a proton that has been accelerated from rest through a potential difference of -1300 v ?

Answers

The speed of a proton is about 5.0 × 10⁵ m/s

[tex]\texttt{ }[/tex]

Further explanation

Let's recall the Kinetic Energy formula:

[tex]\boxed {E_k = \frac{1}{2}mv^2 }[/tex]

Ek = kinetic energy ( J )

m = mass of object ( kg )

v = speed of object ( m/s )

[tex]\texttt{ }[/tex]

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

potential difference = ΔV = -1300 V

mass of proton = m = 1.67 × 10⁻²⁷ kilograms

charge of proton = q = 1.60 x 10⁻¹⁹ coulombs

initial speed of proton = v₁ = 0 m/s

Asked:

final speed of proton = v = ?

Solution:

[tex]Ep_1 + Ek_1 = Ep_2 + Ek_2[/tex]

[tex]qV_1 + \frac{1}{2}mv_1^2 = qV_2 + \frac{1}{2}mv_2^2[/tex]

[tex]q(V_1 - V_2 ) = \frac{1}{2}m( v_2^2 - v_1^2 )[/tex]

[tex]q( 0 - V ) = \frac{1}{2}m ( v^2 - 0^2 )[/tex]

[tex]-q \Delta V = \frac{1}{2} m v^2[/tex]

[tex]v^2 = -2mq \Delta V[/tex]

[tex]v = \sqrt { (-2q \Delta V) \div m }[/tex]

[tex]v = \sqrt { -2 \times 1.60 \times 10^{-19} \times (-1300) \div (1.67 \times 10^{-27})}[/tex]

[tex]v \approx 5.0 \times 10^5 \texttt{ m/s}[/tex]

[tex]\texttt{ }[/tex]

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[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Mathematics

Chapter: Energy

The speed of a proton that has been accelerated from rest through a potential difference of - 1300 v  would be 4.99 × 10⁵ meters/ second.

What is an electric charge?

Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge.

As given in the problem we have to find out the speed  of a proton that has been accelerated from rest through a potential difference of -1300 volts,

The speed of the proton can be calculated with the expression given as follows,

1/2 × mass ×velocity ² = electric charge × potential difference  

v² = 2qV /m

v = √(2qV/m)

  = √ ( 2×1.6×10⁻¹⁹ ×1300 / 1.67×10⁻²⁷)

  =4.99 × 10⁵ meters/seconds

Thus, the speed of the proton would be 4.99 × 10 ⁵  meters/seconds.

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How many ohms of resistance are in a 120–volt hair dryer that draws 7.6 amps of current?

A. 16 ohms
B. 910 ohms
C. 0.063 ohms
D. 6,900 ohms

Answers

Resistance = Volt/Amps

R = 120/7.6=15.789 Ohm ~ 16 ohm.

So, (A) is the answer

The concept Ohm's law is used here to determine the resistance. The resistance is found to be 16 ohm .The correct option is A.

What is Ohm's law?

The relationship between the electric current and the potential difference is given by the Ohm's law. The current which flows through the conductors is directly proportional to the voltage applied. Mathematically the relationship is given as:

V = IR

V - Potential difference

R - Resistance

I - Current

R = V / I

R = 120 / 7.6

R = 15.7 ohm ≈ 16 ohm

The ohm's law holds true if the provided temperature and the other physical factors remain constant. In certain components, increasing the current raises the temperature. In this case Ohm's law is violated.

It is the Ohm's law which maintains the desired voltage drop across the electronic components. It helps to determine the voltage, resistance or current of an electric circuit.

Thus the correct option is A.

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"the mass of mars, 6.40 × 1023 kg, is about one-tenth that of the earth, and its radius, 3395 km, is about half that of earth. what is the mean density of mars in kg/m3? "

Answers

. Density is a value for mass, such as kg, divided by a value for volume, such as m3. Density is a physical property of a substance that represents the mass of that substance per unit volume. To calculate the density of mars, we need its mass and its volume. We calculate as follows:

mass of Mars =   6.40 × 10^23 kg
volume of Mars = 4πr³ / 3  (assuming the planet is a sphere)
                               r = 3395 km = 3395000 m
                          =  4π(3395000 m)³ / 3 
                          = 1.64 x 10^20 m^3

Density = mass / volume 
Density =  6.40 × 10^23 kg / 1.64 x 10^20 m^3
Density = 3904.56 kg/m^3

Therefore, the density of the planet Mars is 3904.56 kg/m^3.

When introduced into a region where an electric field is present, an electron with initial velocity will eventually move?

Answers

A magnetic field is made by electric currents that is induced from opposite terminals of charges. When a current-carrying conductor is placed in a magnetic field, the electrons move to a certain direction. The guide used for this is Fleming's Left-Hand Rule as shown in the picture. It shows that the motion of the electron is in right angles or perpendicular to the force of the magnetic field. The resulting path of the direction of the electron will be in circular motion.This is the concept used in transformers where a voltage is induced from coils of currents. The electrons move in a helical or circular motion.

An electron moves in an electric field towards regions of lower potential due to the decrease in its electric potential energy.

An electron moves in an electric field towards regions of lower potential. This is because the electron will move in the direction that tends to decrease its electric potential energy.

An electron moves toward lower electrical potential in an electric field, and will exhibit motion based on the Lorentz force when in a magnetic field. If both electric and magnetic fields are present, perpendicular velocity filtering can occur.

When an electron with initial velocity is introduced into a region where an electric field is present, it will be accelerated by the electric field. An electron moves toward regions of lower potential because it has a negative charge and is repelled by areas of higher negative potential and attracted to areas of higher positive potential. For example, if the electric field is uniform and points in the direction opposite to the electron's initial velocity, the electron will decelerate until it comes to rest, then accelerate in the direction of the field.

In a uniform magnetic field, the electron will start to move in a circular path due to the magnetic force acting perpendicular to its velocity. The radius of this path and the direction of the magnetic force can be determined using the Lorentz force law. If there is both an electric field and a magnetic field present, perpendicular to each other and the velocity of the charged particle, there exists a particular velocity at which the particle will experience no net force, leading to the concept of a velocity filter.

A solenoid having an inductance of 6.95 μh is connected in series with a 1.24 kω resistor. (a) if a 12.0 v battery is connected across the pair, how long will it take in seconds for the current through the resistor to reach 73.6% of its final value? (b) what is the current through the resistor at a time t = 1.00τl?

Answers

In electrical circuit, this arrangement is called a R-L series circuit. It is a circuit containing elements of an inductor (L) and a resistor (R). Inductance is expressed in units of Henry while resistance is expressed in units of ohms. The relationship between these values is called the impedance, denoted as Z. Its equation is

Z = √(R^2 + L^2)
Z =  √((1.24×10^3 ohms)^2 + (6.95×10^-6 H)^2)
Z = 1,240 ohms

The unit for impedance is also ohms. Since the circuit is in series, the voltage across the inductor and the resistor are additive which is equal to 12 V. Knowing the impedance and the voltage, we can determine the maximum current.
I = V/Z=12/1,240 = 9.68 mA
But since we only want to reach 73.6% of its value, I = 9.68*0.736 = 7.12 mA. Then, the equation for R-L circuits is
[tex]I= \frac{V( 1- e^{-t/τ} )}{R} [/tex], where τ = L/R = 6.95×10^-6/1.24×10^3 = 5.6 x 10^-9
Then,
[tex]7.12x 10^{-3} = \frac{12( 1- e^{-t/5.6x 10^{-9} } )}{1240} [/tex]

t = 7.45 nanoseconds
Part B.) If t = 1.00τ, then t/τ = 1. Therefore,
[tex]I= \frac{12( 1- e^{-1 } )}{1240}[/tex]
 
I = 6.12 mA 

The _________ specifies the station that sent the frame.

Answers

Ans: The source Address field specifies the station that sends the frame. 

The format of an Ethernet frame includes a destination address at the beginning which contains the address of the device which is sending the frame. And, the source address tells us which station the information is received from. 

What number does a bit that is turned on represent? what number does a bit that is turned off represent?

Answers

In digital electronics, only two numbers are used to represent the state of the bit. These two numbers are "0" and "1" where:

- The bit that is turned on is represented by the number "1" 
- The bit that is turned off is represented by the number "0" 

There is a 250-m-high cliff at half dome in yosemite national park in california. suppose a boulder breaks loose from the top of this cliff. (a) how fast will it be going when it strikes the ground? (b) assuming a reaction time of 0.300 s, how long will a tourist at the bottom have to get out of the way after hearing the sound of the rock breaking loose (neglecting the height of the tourist, which would become negligible anyway if hit)? the speed of sound is 335 m/s on this day.

Answers

(a) It will strike the ground in 7.14 seconds

(b) The tourist at the bottom must get out in 6.10 seconds

Further explanation

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem !

Given:

h = 250 m

Unknown:

t₁ = ?

t₂ = ?

Solution:

Question (a) :

We can use the following formula to calculate time taken for the rock to reach the ground,

[tex]h = v ~ t + \frac{1}{2} ~ g ~ t^2[/tex]

[tex]250 = 0 \times t + \frac{1}{2} \times 9.8 ~ t^2[/tex]

[tex]250 = \frac{1}{2} \times 9.8 ~ t^2[/tex]

[tex]250 = 4.9 ~ t^2[/tex]

[tex]t^2 = 250 \div 4.9[/tex]

[tex]t = \sqrt{250 \div 4.9}[/tex]

[tex]t = \frac{50}{7} ~ seconds[/tex]

[tex]\large {\boxed {t \approx 7.14 ~ seconds} }[/tex]

Question (b) :

Firstly, we will find the time taken by sound to reach the tourist.

[tex]t_{sound} = \frac{250 ~ m}{335 ~ m/s}[/tex]

[tex]\boxed{ t_{sound} = \frac{50}{67} ~ s }[/tex]

Next, we will find how long will a tourist have to get out of the way.

[tex]t_2 = t_1 - ( t_{sound} + t_{reaction})[/tex]

[tex]t_2 = \frac{50}{7} - ( \frac{50}{67} + 0.300})[/tex]

[tex]\large {\boxed {t_2 \approx 6.10 ~ seconds} }[/tex]

The tourist only has about 6 seconds before getting hit by the stone.

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Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate

Final answer:

The boulder will be going approximately 70.0 m/s when it strikes the ground, and a tourist will have approximately 1.046 seconds to react and move out of the way after hearing the sound of the rock breaking loose.

Explanation:

Calculating the Speed of a Falling Boulder and Reaction Time for Safety

For part (a) of the question, we want to calculate how fast a boulder will be going when it strikes the ground after falling from a height of 250 meters. We can use the equation of motion under the influence of gravity, which is v = sqrt(2gh), where g is the acceleration due to gravity (9.81 m/s²) and h is the height (250 m). Plugging in these values, we get the final velocity v as the square root of (2 * 9.81 m/s² * 250 m), which is approximately 70.0 m/s.

For part (b), we need to determine how long a tourist has to react and move out of the way after hearing the sound of the rock breaking loose. The sound travels at 335 m/s, so it will take the sound approximately 250 m / 335 m/s to reach the tourist, which is roughly 0.746 s. We must also add the tourist's reaction time of 0.300 s to this. Therefore, the total time the tourist has to react is the sum, which would be approximately 0.746 s + 0.300 s = 1.046 s.

Roughly what percent of the earth can see a lunar eclipse at one time?

Answers

During a lunar eclipse, the half of the planet that is in night mode can see it, because during that type of an eclipse, the earth gets in between the sun and the moon and the reason the moon turns red is because earth's atmosphere bends some light and that light hits the moon.

 

So roughly, 50% percent of the earth can see a lunar eclipse at one time.

 

To add, the lunar eclipse is an astronomical phenomenon and happens about two times per year, and a large portion of the Earth can see this type of eclipse, compared to solar eclipses.

Around 75% of the Earth can see a lunar eclipse at any given time due to the duration of the event and the rotation of the Earth.

Roughly 75% of the Earth can see a lunar eclipse at one time. During a lunar eclipse, Earth's shadow covers the entire Moon, and because the event lasts several hours, more people can observe the eclipse as the Earth rotates. In comparison to a solar eclipse, which is visible in a very narrow path on Earth, a lunar eclipse is observable from anywhere on the night side of the Earth. Since the eclipse takes about 5-6 hours from start to finish, different regions come into view of the eclipse over time, allowing for broad visibility.

What happens during one half-life of a radioactive isotope?

Answers

What happens during on half-life of a radioactive isotope is the following: Not only does it decay by giving off energy and matter, but it also decays at a rate that is characteristic to itself. The rate at which a radioactive isotope decays is measured in half-life. The term half-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate.

If you have anymore questions feel free to pm me

Answer:

In the field of radioactivity, the half-life is usually defined as the time required by an unstable radioactive isotope to disintegrate half of its initial composition. For different radioactive isotope elements, this value of half-life is different.

For example, the half-life of uranium-238 is approximately 4.5 billion years and the half-life of Carbon-14 is nearly 5700 years.

During the time of one half-life of a radioactive isotope, half of the parent atoms are disintegrated and forms a comparatively stable daughter isotope. This means that half of the initial concentration of the unstable isotope is reduced.

A student walks 5.00 m at an angle of 53.0° then walks another 8.00 m at angle of 130°. what is the magnitude of the student's final displacement?

Answers

This question can easily be answered using a scientific calculator via complex mode using the form r∠α wherein r is the magnitude and α is the angle. So, incorporating vector addition through scientific calculator:

5∠53° + 8∠130 = 10.34∠101.9°

Therefore, the student's displacement is 10.34 m, 101.9°. In other words, the student is heading 78.1° (180 - 101.9 = 78.1)  south of east.

Answer:

10.35 m

Explanation:

d1 = 5 m at angle 53 degree

d1 = 5 (Cos 53 i + Sin 53 j) = 3 i + 4 j

d2 = 8 m at an angle 130 degree

d2 = 8 (Cos 130 i + Sin 130 j) = - 5.14 i + 6.13 j

Total displacement = d = (3 - 5.14) i + (4 + 6.13) j = - 2.14 i + 10.13 j

magnitude of displacement = [tex]\sqrt{(-2.14)^{2}+(10.13)^{2}}[/tex] = 10.35 m

A pendulum of 50 cm long consists of small ball of 2kg starts swinging down from height of 45cm at rest. the ball swings down and strikes a bigger ball. what is the maximum kinetic energy of the 2kg bob

Answers

Assuming that all energy of the small ball is transferred to the bigger ball upon impact, then we can say that:

Potential Energy of the small ball = Kinetic Energy of the bigger ball

Potential Energy = mass * gravity * height

Since the small ball start at 45 cm, then the height covered during the swinging movement is only:

height = 50 cm – 45 cm = 5 cm = 0.05 m

Calculating for Potential Energy, PE:

PE = 2 kg * 9.8 m / s^2 * 0.05 m = 0.98 J

Therefore, maximum kinetic energy of the bigger ball is:

Max KE = PE = 0.98 J

A 0.520 kg mass suspended from a spring oscillates with a period of 1.50 s. how much mass must be added to the object to change the period to 2.05 s?

Answers

[tex]Given:\\m_1=0.520kg\\T_1=1.50s\\T_2=2.05s\\\\Find:\\\Delta m=?\\\\Solution:\\\\\Delta m=m_2-m_1\\\\T=2 \pi \sqrt{ \frac{m}{k} } \Rightarrow 2 \pi = \frac{T}{\sqrt{ \frac{m}{k} }} \\\\\frac{T_1}{\sqrt{ \frac{m_1}{k} }} =\frac{T_2}{\sqrt{ \frac{m_2}{k} }} \\\\T_1\sqrt{ \frac{m_2}{k} }} =T_2\sqrt{ \frac{m_1}{k} }} \\\\\frac{T_1^2m_2}{k} =\frac{T_2^2m_1}{k} \\\\T_1^2m_2=T_2^2m_1\Rightarrow m_2= \frac{T_2^2m_1}{T_1^2} \\\\\Delta m=\frac{T_2^2m_1}{T_1^2} -m_1=m_1(\frac{T_2^2}{T_1^2} -1)[/tex]

[tex]\\\\\Delta m=0.520kg( \frac{(2.05s)^2}{(1.50s)^2} -1)\approx 0.4512kg[/tex]

A portion of the atmosphere that becomes warmer than surrounding air will ____.

Answers

A portion of the atmosphere that becomes warmer than surrounding air will expand and rise. The warmer atmosphere the more space between the molecules. Therefore, warmer atmosphere expands to allow more space for the molecules. Cool air on the other hand, contracts because the molecules in cool air need less space.

True or false: for a low-pressure system to strengthen, the surface air pressure must decrease. select one:
a. True
b. False

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im not positive about this answer but ill go with a.true

Where in the ocean does oceanic lithosphere sink into the mantle? answer?

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The ocean lithosphere sinks into the mantle at deep ocean ridges.

What is the correct water depth for an echo travel time of 6 seconds? (for the purposes of this exercise, assume pressure and temperature effects on sound wave velocity are negligible.)?

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In physics, there are empirical values for common important parameters. For example, the speed of sound is equal to 340 meters per second. Unlike the speed of light, the speed of sound is dependent on temperature and pressure. But in standard room conditions, the speed is 340 m/s. Using this value of speed, we can find the depth given the time. You should also note that the distance the echo travels is exactly the same distance that object travelled. Therefore,

Distance = 340 m/s * 6 seconds
Distance = 2,040 meters deep

A sample of argon gas (molar mass 40 g) is at four times the absolute temperature of a sample of hydrogen gas (molar mass 2 g). the ratio of the rms speed of the argon molecules to that of the hydrogen is

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To solve this problem, let us recall that the formula for gases assuming ideal behaviour is given as:

rms = sqrt (3 R T / M)

where

R = gas constant = 8.314 Pa m^3 / mol K

T = temperature

M = molar mass

Now we get the ratios of rms of Argon (1) to hydrogen (2):

rms1 / rms2 = sqrt (3 R T1 / M1) / sqrt (3 R T2 / M2)

or

rms1 / rms2 = sqrt ((T1 / M1) / (T2 / M2))

rms1 / rms2 = sqrt (T1 M2 / T2 M1)

Since T1 = 4 T2

rms1 / rms2 = sqrt (4 T2 M2 / T2 M1)

rms1 / rms2 = sqrt (4 M2 / M1)

and M2 = 2 while M1 = 40

rms1 / rms2 = sqrt (4 * 2 / 40)

rms1 / rms2 = 0.447

 

Therefore the ratio of rms is:

rms_Argon / rms_Hydrogen = 0.45

Answer:

I would like to add to the above answer that .447 is equal to [tex]\frac{1}{\sqrt{5} }[/tex].

Explanation:

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