Which will hit the ground first if a golf ball and a soft ball are dropped from the same height simultaneously?

Answers

Answer 1

Answer:

they both would hit at the same time

Explanation:

Answer 2

Answer: Whichever one is heavier will hit first

Explanation:


Related Questions

Calculate the total displacement of a mouse walking along a ruler, if it begins at the location x = 5 m, and then does the following:

- It walks to x = 12 m
- It then walks a displacement of -8 m (NOT the same as x = -8 m)
- Lastly, it walks to the location x = 7 m​

Answers

Answer:

18

Explanation:

12 - 5 + 8 = 15

12 - 8 = 4

7 - 4 = 3

15 + 3 = 18

At what point of a projectile motion, acceleration and velocity are perpendicular to each other?

Answers

Answer:

At the topmost point where the velocity has only horizontal component whereas the acceleration is vertical.

Explanation:

There is only a horizontal component of velocity at the ap3x of the projectile, and acceleration is vertically downwards owing to gravitation, therefore velocity and acceleration are perpendicular to one another.

a) How does the equilibrant relate to the resultant?
b) If I had 4m pointing east and I subtracted 2m pointing west, what would my resultsnt be?

Answers

a) Resultant is a single force that can replace the effect of a number of forces. "Equilibrant" is a force that is exactly opposite to the resultant. Equillibrant and resultant have equal magnitudes but opposite directions.

b) let's say you have vector A as 4 m in the east and vector B as 2 m in the West.

Now we have to subtract B from A as per the question,

R = A - B

where (- B) corresponds to the same vector as B but has the opposite direction.

then we can say (- B) = 2 m East.

now,

R = 4 + 2 = 6 m east

An equilibrant is a force that exactly balances another force, resulting in a state of equilibrium or balance. When two forces act on an object in opposite directions, they create a net force that can cause the object to move. The equilibrant force is equal in magnitude to the net force but acts in the opposite direction, canceling out the net force and keeping the object stationary.

The equilibrant is important in physics because it helps us understand how objects remain in equilibrium despite the presence of multiple forces acting upon them. It also plays a key role in the analysis of statics, which is the branch of mechanics that deals with the study of objects at rest.

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Suppose that a piston-cylinder device is initially compressed isothermally and then expanded isobarically back to its initial volume. Find the total boundary work in kJ assuming that the device has 9.63 kg of air initially at 100 kPa and 23 C, which is isothermally compressed to 1 MPa.

Answers

To find the total boundary work, we need to calculate the work done during the isothermal compression and the work done during the isobaric expansion.

Given:

Initial pressure, P1 = 100 kPa

Final pressure, P2 = 1 MPa

= 1000 kPa

Initial temperature, T1 = 23°C

= 23 + 273

= 296 K

Mass of air, m = 9.63 kg

First, let's calculate the work done during the isothermal compression. The work done during an isothermal process can be calculated using the formula:

W1 = nRT ln(V2/V1)

Where:

n = number of moles of gas

R = gas constant

T = temperature in Kelvin

V1 = initial volume

V2 = final volume

To find the number of moles of air, we can use the ideal gas equation:

PV = nRT

Rearranging the equation, we get:

n = PV / RT

Substituting the given values:

n = (P1 * V1) / (R * T1)

Now, let's calculate the initial volume V1. We know that the volume of an ideal gas can be calculated using the formula:

V = (m/M) * R * T

Where:

m = mass of the gas

M = molar mass of the gas

The molar mass of air is approximately 28.97 g/mol.

V1 = (m/M) * R * T1

Substituting the given values:

V1 = (9.63 kg / 28.97 g/mol) * 8.314 J/(mol·K) * 296 K

Now we can calculate the work done during the isothermal compression:

W1 = nRT ln(V2/V1)

Substituting the values calculated above:

W1 = [(P1 * V1) / (R * T1)] * R * T1 * ln(V2/V1)

Next, let's calculate the work done during the isobaric expansion. The work done during an isobaric process is given by:

W2 = P2 * (V2 - V1)

Substituting the given values:

W2 = P2 * (V2 - V1)

Finally, we can calculate the total boundary work by adding the work done during the compression and expansion:

Total boundary work = W1 + W2

Now we can perform the calculations to find the numerical value of the total boundary work.

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can somebody helppp me pls thank you:)))))​

can somebody helppp me pls thank you:)))))

Answers

The picture is very blurry I wish I could help

HEY HEY HEY HEY

Explanation:

HEY HEY HEY HEY HEY

(ANSWER PLEASE)
Which of the following answer options are your employer's responsibility?

A) Develop a written hazard communication program


B) Implement a hazard communication program


C) Maintain a written hazard communication program

Answers

Realistically it would be all of them, but technically it would be A. Since they would have to at least give the employees a hazard communication program..

The option that represents your employer's responsibility is to develop a  written hazard communication program. Thus, the correct option for this question is A.

What are the advantages of a communication program?

The advantages of a communication program are as follows:

It helps in the clarification of the goals and objectives of an individual. It significantly articulates the relationship between the speaker and the listener.  It promotes the loyalty, engagement, and productivity of the team.

The responsibility of the employer is to develop and articulate the concept of a hazard communication program in detailed written form in order to satisfy the need and requirements of the team, person, society, etc. This becomes more important when it comes to synthesizing the thinking of large members in a single format.

Therefore, developing a written hazard communication program is an option that represents your employer's responsibility. Thus, the correct option for this question is A.

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1. Determinar cuanta fuerza es necesaria para empujar un móvil que se encuentra en reposo para que alcance una velocidad de 15 m/s en un tiempo de 20 segundos, considerando que dicho móvil tiene una masa de 1000Kg. No considere que existe fricción.

Answers

Responder:

Explicación:

Fuerza = Masa × aceleración

Dado que aceleración = velocidad final - velocidad inicial / tiempo

Fuerza = m (v-u) / t

Dado

Masa = 1000 kg

v = 15 m / s

u = 0 m / s

t = 20 segundos

Sustituye los valores dados en la fórmula para calcular la fuerza.

F = 1000 (15-0) / 20

F = 1000 (15) / 20

F = 15000/20

F = 750N

The 200-mm test tube also contained some water (besides the metal) that was subsequently added to the calorimeter (in Part A.4.). Considering a higher specific heat for water, will the temperature change in the calorimeter be higher, lower, or unaffected by this technique error?

Answers

Answer:

The temperature  change in the calorimeter will be lower

Explanation:

Water is an example of a molecular substance. They have relatively low melting points and boiling points usually below 300° C . Water reacts with metals to a degree varying with their position in the electrochemical series.

The specific heat of water is 4179.6 Joules which is relatively high . This typically implies that water absorbs a larger amount of heat but the increase in temperature of its boiling points is relatively low. Thus; in the 200-mm test tube that contains water and was subsequently added to the calorimeter , the heat present was initially absorbed by the water and that does not result to an increase in the temperature change in the calorimeter. Thus the temperature change in the calorimeter will be lower.

onsider a tall, skinny pine tree, initially upright, that falls over in a forest. as it is falling, its base remains in contact with the ground and does not move from side to side. what sort of path does the tree's center of mass follow as it falls?

Answers

The tree's center of mass follows circular path of radius of half of its length as it falls.

What is center of mass?

A place at which the entire mass of the body or all the masses of a system of particles appears to be concentrated is known as the centre of mass of a body or system of particles. According to physics, the center of mass is a location where the total of the weighted relative positions of the distributed mass has zero and is also referred to as the balancing point.

So, center of mass remains same in all position. The center of mass of the tall, skinny pine tree is at its half of length. As it falls, the tree's center of mass follows circular path of radius of half of its length as its base remains in contact with the ground and does not move from side to side.

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if two firecrackers produce a sound level of 86 db when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [hint: add intensities, not db 's.] express your answer to two significant figures and include the appropriate units.

Answers

The sound level of 86dB when fired simultaneously will have sound level of 82.9898dB.

Theory-

According to the Beta factor model, the common cause will have an equal impact on every member of a component group that shares a common cause.

The beta factor model is simple to use, models common cause failures, and only requires one parameter to be determined.

A drawback of the beta factor model is that it is impossible to quantify the failure of k–m components within a common cause component group.

As a result of multiplying the partial beta factors, the beta factor is calculated.

Mathematics-

\(\beta =10log\frac{2I}{i} \\\\\beta 1=10log\frac{I}{i} \\\\\beta =10log2 +\beta 1\\\\\beta 1=\beta -10log2\)

Calculation-

\(\beta 1=86-10log2\\\\\beta 1=86-3.0102\\\\\beta 1= 82.9898dB\)

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The
magnitude of the resultant vector of the vectors of magnitudes 8N
and 6N is
14 N
2 N
10 N
8 N

Answers

The magnitude of the resultant vector of the vectors with magnitudes 8N and 6N is 10N.

The magnitude of the resultant vector of two vectors can be found using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In the context of vectors, the magnitude of the resultant vector is equivalent to the length of the hypotenuse of a right triangle formed by the vectors.

In this case, we have two vectors with magnitudes of 8N and 6N.

Let's assume these vectors are represented by A and B, respectively. We can calculate the magnitude of the resultant vector, R, using the formula:

\(R = \sqrt{A^{2} + B^{2} }\)

\(R = \sqrt{8^{2}+6^{2}\)

R = 10N

Therefore, the magnitude of the resultant vector of the vectors with magnitudes 8N and 6N is 10N.

In conclusion, the correct answer is 10N. The magnitude of the resultant vector can be calculated using the Pythagorean theorem, where the magnitudes of the individual vectors are squared and summed, and then the square root is taken to find the magnitude of the resultant vector.

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35.On a cold winter day the sections of a bridge will...Select one:a. expand.b. contract.c. remain the same.d. none of the above.

Answers

We know that substances expand with high temperatures and contract with low temperatures, therefore, the bridge will contract and the answer is b.

What is the speed of light (f = 5.09 E14 Hz) in glycerol?

Answers

Answer:

The speed of light in glycerol is 2.04×108 m/s .

Explanation:

The speed of light in glycerol will be 2.03 ×10⁷ m/sec. The speed of light is found as the ratio of the speed of light in air and the refractive index.

What exactly is the Refractive Index?

The level of bending of a light beam as it goes from one medium to another is known as the refractive index of the medium.

The frequency of the wave is given as;

\(\rm f = 5.09 \times 10^{14} Hz\)

The refractive index of ethyl alcohol is n=1.4722

The substance's index of refraction yields the ratio of light speed in a vacuum to light speed in that medium, the speed of light is sound as;

\(\rm n = \frac{C}{v} \\\\ \rm v = \frac{C}{n} \\\\ \rm v = \frac{3 \times 10^8}{1.4722} \\\\ v= 20377660.00\ m/sec \\\\ v= 2.03 \times 10^7 m/sec\)

Hence, the speed of light in glycerol will be 2.03 ×10⁷ m/sec.

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What is the Opportunity Cost in textbooks from going from point A to B?

Answers

Answer:

60.00

Explanation:

you welcome

A butterfly is flying around and its velocity(v) as a function of time(t) is given in the graph below where rightwards is the positive velocity direction. What is the butterfly's displacement x from t=2 to 4s? Answer with two significant digits.

A butterfly is flying around and its velocity(v) as a function of time(t) is given in the graph below

Answers

Answer: 19 meters.

Explanation:

We want to find the total displacement between t = 2s and t = 4s.

To do it, we can integrate our function, first write our velocity equation.

for t ≤ 3s, we have a linear equation, let's write it:

A linear relationship can be written as:

y = a*t + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now we can see that our line passes through the points (1, 0) and (0, -2)

then the slope is:

a = (0 -(-2)/(1 - 0) = 2/1 = 2

and knowing that when t = 0s, v(0s) = -2m/s, then our equation is:

v(t) = (2m/s^2)*t - 2m/s for t ≤ 3s

now, for t ≥3s the equation is constant, v(t) = 4m/s.

then we have

v(t) = (2m/s^2)*t - 2m/s -------if t ≤ 3s

v(t) = 4m/s ----- if t ≥ 3s

Now we integrate over time to get the position:

for t ≤ 3s we have:

p(t) = (1/2)*(2m/s^2)*t^2 - 2m/s*t + C

where C is a constant of integration, as we are calculating the displacement  this constant actually does not matter, so we can use C = 0m

p(t) = (1m/s^2)*t^2 - 2m/s*t  for t ≤ 3s

and p(3s) =  (1m/s^2)*3s^2 - 2m/s*3s = 9m - 6m = 3m is the initial position of the other part of the function.

for t ≥ 3s we have:

p(t) = 4m/s*t + p(3s) = 4m/s*t + 3m

then the position equation is:

p(t) = (1m/s^2)*t^2 - 2m/s*t  ---- t ≤ 3s

p(t) = 4m/s*t + 3m --- if t ≥ 3s

Now the displacement will be:

p(4s) - p(2s) where for each time, you need to use the correct function:

p(4s) = 4m/s*4s + 3m = 16m + 3m = 19m

p(2s) =  (1m/s^2)*2s^2 - 2m/s*2s = 4m - 4m = 0m

p(4s) - p(2s) = 19m - 0m = 19m

The butterfly displacement x from t=2 to 4s is 19 meters.

What is displacement?

The spacing between two specified points is represented by the one-dimensional quantity of displacement (symbolised as d or s), commonly known as length or distance.

The total displacement between t = 2s and t = 4s.

Integrate our function, the velocity equation.

for t ≤ 3s, we have a linear equation, let's write it:

A linear relationship can be written as:

y = a x t + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

The line passes through the points (1, 0) and (0, -2)

The slope is:

a = (0 -(-2)/(1 - 0) = 2/1 = 2

When t = 0s, v(0s) = -2m/s, then our equation is:

v(t) = (2m/s²) x t - 2m/s for t ≤ 3s

now, for t ≥3s the equation is constant, v(t) = 4m/s.

v(t) = (2m/s²) x t - 2m/s -------if t ≤ 3s

v(t) = 4m/s ----- if t ≥ 3s

Now we integrate over time to get the position:

for t ≤ 3s we have:

p(t) = (1/2) x (2m/s²) x t^2 - 2m/s x t + C

where C is a constant of integration, to calculate the displacement  this constant actually does not matter,

p(t) = (1m/s²)*t^2 - 2m/s x t  for t ≤ 3s

and p(3s) =  (1m/s^2) x 3s² - 2m/s x 3s = 9m - 6m = 3m is the initial position of the other part of the function.

for t ≥ 3s we have:

p(t) = 4m/s x t + p(3s) = 4m/s x t + 3m

then the position equation is:

p(t) = (1m/s^2) x t² - 2m/s x t  ---- t ≤ 3s

p(t) = 4m/s x t + 3m --- if t ≥ 3s

Now the displacement will be:

p(4s) - p(2s) where for each time, you need to use the correct function:

p(4s) = 4m/s x 4s + 3m = 16m + 3m = 19m

p(2s) =  (1m/s²) x 2s²- 2m/s x 2s = 4m - 4m = 0m

p(4s) - p(2s) = 19m - 0m = 19m

Thus, the displacement is 19 m.

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box
Complete the concept map on ATP production. Choose your answer from the
Key Words
Electron Transport Chain
Krebs Cycle
Pyruvate
Glycolysis
Glucose
ADP
C
ATP
Acetyl COA
ADP
IC
ATP
CO2
High energy electrons and H*
ADP
IC
ATP
02
H2O​

Answers

Answer:

Glycolysis

Pyruvate

Krebs Cycle

Electron Transport Chain

Explanation:

The concept map on ATP production shows the process of cellular respiration in living organisms.

Cellular respiration begins with glucose which is broken down in the process of glycolysis that occur in cytoplasm and gives 2 ATP. Glycolysis gives pyruvate as end product that enter in the process of Krebs Cycle or citric acid cycle as a aerobic process, that occur in mitochondria and produces 2 ATP. This energy is then used in Electron Transport Chain to pump high energy electrons and H+ that produces 36 ATP.

boxComplete the concept map on ATP production. Choose your answer from theKey WordsElectron Transport

Who invented scuba?

1. Benjamin Franklin
2. Mathew Maury
3. Robert Falcon Scot
4. Cousteau and Gagnon

Answers

Answer:

2. Mathew Maury

Explanation:

2. Mathew Maury

4. Cousteau and Gagnon

Explanation:

they made the first successful scuba in 1942

Picture is below! Thank you​

Picture is below! Thank you

Answers

Answer:

The answer is can speed an object direction!!!!

what should you do before aiming and firing on a target?

Answers

Answer:

Below

Explanation:

Be sure of your target and what is in front of AND beyond it. Do not point your weapon at anything you do not want to shoot. Make sure your armament is properly  maintained/loaded  and functioning.  Hearing and eye protection for you and those around you is in place.  

I WILL GIVE BRAINLIEST TO THE FIRST PERSON WHO ANSWERS MY QUESTION!

Explain what we know about the center of the universe.

Answers

“There is no centre of the universe! According to the standard theories of cosmology, the universe started with a "Big Bang" about 14 thousand million years ago and has been expanding ever since. Yet there is no centre to the expansion; it is the same everywhere”.

Answer:

There is no center of the universe.

Explanation:

According to scientists, the universe started with a "Big Bang" millions of years ago and has been expanding ever since.

The disk component of a spiral galaxy includes which of the following parts?
A) halo
B) bulge
C) spiral arms
D) globular clusters
E) all of the above

Answers

The disk component of a spiral galaxy includes all of the above options: A) halo, B) bulge, C) spiral arms, and D) globular clusters.

The disk component is one of the main structural features of a spiral galaxy. It consists of a flattened, rotating disk of stars, gas, and dust.

The halo is a spherical region surrounding the central disk, containing older stars, globular clusters, and dark matter. It extends above and below the disk.

The bulge is a central, bulging region of the galaxy that contains a high concentration of stars. It is often shaped like a spheroid or an elliptical structure.

The spiral arms are the prominent spiral patterns that extend from the central disk. They contain younger stars, gas, dust, and star-forming regions.

Globular clusters are dense clusters of stars that orbit around the galaxy's center. They are found in the halo and sometimes within the bulge.

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why is fundamental unit called derived unit ?​

Answers

Since fundamental units are elementary in nature and cannot be reduced further, so it can not be reduced further, so it cannot be expressed in other units

The photo shows a sea urchin embryo. A sea urchin is a multicellular organism. جام Which two processes occur as the sea urchin embryo grows? A. The embryo's cells grow larger in size. B. The amount of DNA in the embryo's body cells decreases. C. The total number of cells in the embryo's body decreases. D. The embryo's cells take in water and nutrients. SUBMIT

The photo shows a sea urchin embryo. A sea urchin is a multicellular organism. Which two processes occur

Answers

Answer:

d and a

Explanation:

The embryo's cells grow larger in size, and the embryo's cells take in water and nutrients. The correct options are A and D.

The two processes that occur when the sea urchin embryo matures, according to the information presented, are:

The embryo's cells grow in size: During the embryo's growth and development, individual cells divide and grow in size, contributing to the organism's total growth.

The embryo's cells actively take in water and nutrients from the surrounding environment: As the embryo grows, its cells actively take in water and nutrients from the surrounding environment to support metabolic processes and offer the essential resources for growth and development.

Thus, choices A and D represent the proper processes that occur while the sea urchin embryo develops.

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If a transverse wave has a velocity of 27.9 meters per
second and a wavelength of 200 meters, what is the waves
frequency?

Answers

Answer:

0.14Hz

Explanation:

Given parameters:

Velocity  = 27.9m/s

Wavelength  = 200m

Unknown:

Frequency of the waves = ?

Solution:

To solve this problem, we use the wave - velocity equation:

          V  = F ∧  

V is the velocity

F is the frequency

∧ is the wavelength

 Now, let us insert the parameters and solve;

So;

              27. 9  = F x 200

                  F  = 0.14Hz

An electron with a charge of -1.6 × 10-19 coulombs experiences a field of 1.4 × 105 newtons/coulomb. What is the magnitude of the electric force on this electron due to this field? A. 1.6 × 10-3 newtons B. 1.4 × 1024 newtons C. 2.2 × 10-14 newtons D. 7.4 × 10-13 newtons E. 4.5 × 1014 newtons
***update, its not D lol

Answers

Answer:

Electric force, \(F=2.24\times 10^{-14}\ N\)

Explanation:

It is given that,

Charge on an electron is \(-1.6\times 10^{-19}\ C\)

Electric field, \(E=1.4\times 10^5\ N/m\)

We need to find the magnitude of the electric force on this electron due to this field. The electric force is given by :

\(F=qE\\\\F=1.6\times 10^{-19}\times 1.4\times 10^5\\\\F=2.24\times 10^{-14}\ N\)

So, the electric force is \(2.24\times 10^{-14}\ N\).

if matter cannot be created nor destroyed the how was matter created

Answers

It can’t be created nor destroyed although it can be changed from one form to the other

I hope this helps

Have a happy holidays:)

Some chlorine atoms have an atomic mass of 37, while others have an atomic mass of 35. What is the difference between the two types of chlorine atom?

A. The number of ions

B. The number of neutrons

C. The number of protons

D. The number of electrons​

Answers

Answer:

B. the number of neutrons

Answer:

B. The number of neutrons

Which definition describes mass

Answers

Answer:

Mass is a measure of the amount of matter in an object. Mass is usually measured in grams (g) or kilograms (kg). Mass measures the quantity of matter regardless of both its location in the universe and the gravitational force applied to it. Your mass on the earth and the moon are identical.

Explanation:

In the answer.

How to integrate 1/ 1 + x2

Answers

The integral of 1/(1 + x²) is (1/2)ln|1 + x²| + C where C is the constant of integration.

Integration is a mathematical process of finding the antiderivative of a function. To integrate the given expression 1/(1 + x²), we will use the substitution method.

Let u = 1 + x², du/dx = 2x dx, then dx = du/2x and the integral becomes:

∫1/(1 + x²) dx = ∫1/u * (1/2x) du= (1/2)∫1/u du

The antiderivative of 1/u is ln|u| + C, where C is the constant of integration.

Therefore, the final solution of the integral is (1/2)ln|1 + x²| + C.

Let us work through the steps:

Step 1:Let u = 1 + x² and then differentiate both sides with respect to x to obtain du/dx. du/dx = 2x

Substitute 2x dx = du into the integral ∫1/(1 + x²) dx to get the integral in terms of u:∫1/u * (1/2x) du = (1/2) ∫1/u du

Step 2:Calculate the antiderivative of 1/u, which is ln|u|. Thus, the final solution is (1/2)ln|1 + x²| + C, where C is the constant of integration. The constant C will vary depending on the initial conditions of the problem.

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Answer the following angular speed questions. (Enter your answers using exact values.) (a) A wheel of radius 22 ft. is rotating 13 RPM counterclockwise. Considering a point on the rim of the rotating wheel, what is the angular speed in rad/sec and the linear speed w in ft/sec? w = ___ rad/sec v = ___ ft/sec (b) A wheel of radius 6 in, is rotating 30°/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec? v = ___ in/sec w = ___ rpm
w = ___ rad/sec
(c) You are standing on the equator of the earth (radius 3960 miles). What is your linear and angular speed? v = ___ mph w = ___rad/hr (d) An auto tire has radius 12 inches. If you are driving 75 mph, what is the angular speed in rad/sec and the angular speed in RPM? w = ___ rad/sec w = ___ rpm

Answers

(a) The radius of the wheel = 22 ft

The wheel is rotating 13 RPM counterclockwise

Angular speed = angular velocity = ω = 2πf = 2 × π × 13 = 26π rad/min (since 1 rev = 2π radians)

Since 1 min = 60 sec, ω = (26π)/60 rad/sec = 13π/30 rad/sec

The linear speed v of a point on the rim of the wheel is given by v = r × ω = 22 × 13π/30 = 22.82 ft/s

Therefore, w = 13π/30 rad/sec and v = 22.82 ft/sec

(b) The radius of the wheel = 6 inThe wheel is rotating at 30°/sec

The angular speed = ω = 30°/sec × (π/180°) = π/6 rad/sec

The linear speed v of a point on the rim of the wheel is given by v = r × ω = 6 × π/6 = π in/sec

The angular speed in RPM can be calculated as follows:

In 1 min, the angle rotated = 360°No. of seconds in 1 min = 60∴

The angle rotated in 1 sec = 360°/60 = 6° or (π/30) radThe angular speed in rad/sec and the angular speed in RPM is given by w = π/6 rad/sec and w = (30/π) × π/6 = 5 RPM

(c) The radius of the Earth = 3960 milesThe circumference of the Earth = 2 × π × radius = 2 × π × 3960 ≈ 24,902 miles (approx.)

One rotation of the Earth is completed in 24 hours or 24 × 60 × 60 = 86,400 secLinear speed v of a point on the equator of the Earth is given byv = circumference of the Earth/time taken for 1 rotation= 24,902/86,400 ≈ 0.2887 miles/sec

Therefore, v = 0.2887 × 60 × 60 = 1040 miles/hourAngular speed = ω = 2πf = 2π/Twhere T = time taken for 1 rotation of the Earth= 24 hours = 24 × 60 × 60 = 86,400 sec∴ ω = 2π/86,400 rad/sec

Angular speed in RPM can be calculated as follows:In 1 min, the angle rotated = 360°No. of seconds in 1 min = 60∴

The angle rotated in 1 sec = 360°/60 = 6° or (π/30) radThe angle rotated in 24 hours = 360°No. of seconds in 24 hours = 24 × 60 × 60 = 86,400∴

The angle rotated in 1 sec = 360°/86,400 = 1/240° or π/43,200 radThe angular speed in RPM is given by w = (360°/43,200) × 60 = 0.1666 RPM (approx.)

(d) The radius of the tire = 12 inchesThe speed of the car = 75 mphLet the car travel for 1 hour in which the tire makes x revolutions∴

The distance travelled by the car in 1 hour = 75 miles = circumference of the tire × x= 2π × 12 × x inches= 24πx inchesTherefore, 24πx = 75 × 5280 × 12 inches or x = 19600 revolutions∴

The tire makes 19600 revolutions in 1 hour= 19600 × 2π radians= 39200π radians∴ Angular speed = ω = 39200π/3600 = 109.11 rad/sec= (109.11/2π) RPM= 17.36 RPM (approx.)

Therefore, the angular speed in rad/sec is 109.11 rad/sec and the angular speed in RPM is 17.36 RPM.

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