using the methos of dimensions derive an expression for the centripetal force f acting on a particle of mass m mivingv with velocity v in a circle of radius r? ​

Answers

Answer 1
Answer:

According to the Question:

[tex]\footnotesize\implies F \propto [m]^x [v]^y [r]^z[/tex]

[tex]\footnotesize\implies F =k [m]^x [v]^y [r]^z \:...(i)[/tex]

K = Dimensionless Constant

Now, substituting Dimensions of each physical quantity in equation (I):

[tex]\footnotesize\implies [M^1L^1T^{-2}] =[M^1L^0T^0]^x [M^0L^1T^{-1}]^y [M^0L^1T^0]^z[/tex]

[tex]\footnotesize\implies [M^1L^1T^{-2}] =[M]^x [L]^{y + z} [T]^{ - y}[/tex]

On comparing the powers of LHS and RHS:

[tex]\implies \bf x = 1[/tex]

[tex]\implies - y = - 2[/tex]

[tex] \implies \bf y = 2[/tex]

[tex]\implies y + z = 1[/tex]

[tex]\implies z = 1 - 2[/tex]

[tex]\implies \bf z = - 1[/tex]

[tex]\footnotesize\implies F = [m]^x [v]^y [r]^z[/tex]

[tex]\footnotesize\implies F = [m]^1 [v]^2 [r]^{ - 1}[/tex]

[tex]\implies\footnotesize \underline{ \boxed{ \bf \red{ F = \frac{m {v}^{2} }{r} }}}[/tex]


Related Questions

Give an example of when a conscientious objector might exercise their right:

Answers

Am sorry what can you be more specific

Which of the following is NOT an indicator of a chemical reaction?

OPTIONS

A. A phase change



B. A temperature change



C. A color change



D. A gas being created

Answers

Answer:

c

Explanation:

The changing of color of a substance is not necessarily an indicator of a chemical change. For example, changing the color of a metal does not change its physical properties. However, in a chemical reaction, a color change is usually an indicator that a reaction is occurring.

How to find frequency.

Answers

Answer:

Divide the number of times an event occurs by the duration of time to calculate frequency. For instance, Anna divides the number of webpage clicks (236) by the time spent on the site (one hour, or 60 minutes). She discovers that she gets 3.9 clicks every minute.

Explanation:

does this help?

What does a larger interquartile range mean.

Answers

IQR measures the spread of the middle half of your data. It is the range of the middle 50% of your sample
Larger values indicate that the central portion of your data spread out further.

flat mirror: draw ray diagram for an object placed at F

Answers

Answer:

...

Explanation:

I'm doing this for points sorry

Hi all, can u please help me in this. I would very appreciate it :)

Write four questions and below the answers about water and air resistance.

Answers

Questions And Answers About Air Resistance.

Question 1: What is Air resistance?

Answer: Air resistance is a force that is caused by air. The force acts in the opposite direction to an object moving through the air. A lorry with a flat front will experience high air resistance while a sports car with a streamlined shape will experience lower air resistance, allowing the car to go faster.

Question 2: What causes air resistance?

Answer: Air resistance, also known as drag, is a force that is caused by air, the force acts in the opposite direction to an object moving through the air. It is where air particles hit the front of the object slowing it down. The more surface area, the more air particles hit it and the greater the resistance.

Question 3: How can air resistance be overcome?

Answer: Two ways to reduce air resistance are stated: reducing the area in contact with air (by the cyclist ducking down or cycling behind someone else) and by being more streamlined (wearing smoother surfaces or a more streamlined helmet).

Question 4: What happens when air resistance increases?

Answer: As it gains speed, the object's weight stays the same but the air resistance on it increases. There is a resultant force acting downwards. Eventually, the object's weight is balanced by the air resistance. There is no resultant force and the object reaches a steady speed – this is known as the terminal velocity.

Questions And Answers About Water Resistance.

Question 1: What is Water resistance?

Answer: Water resistance is a type of force that uses friction to slow things down that are moving through water. ... Water resistance occurs because of the particles in the liquid. As an object moves through a liquid, it collides with the particles which cause it to slow down.

Question 2: What causes water resistance?

Answer: Water resistance doesn't have to be just water, however, it can happen to objects moving through any type of fluid. Water-resistance happens because of the particles in water or the fluid. As the object moved through it collides with the particles which try to slow it down.

Question 3: How is water resistance useful?

Answer: Like friction and air resistance, it SLOWS THINGS DOWN, trying to stop them from moving. Water resistance can also be useful at times. When you are swimming and you push against the water with your hands, the water-resistance pushes back and helps you to move forward. This also happens when you use oars to row a boat.

Question 4: Does water-resistant mean waterproof?

Answer: The technical definition of water-resistant is that it's able to resist the penetration of water to a certain degree, but not entirely. Waterproof technically means that it's impermeable to water, no matter how much time it spends in the water.

Hope This Helps...:)

Which state of matter has molecules that move the most?

liquid

solid

gas

They are all the same.

Answers

Answer:

gas

Explanation:

in gaseous state molecules move the most because force of attraction between atoms are least in gaseous state

the first qstn plsss​

Answers

answer:

the first one  

Explanation:

i think it is this one because 4k is bigger than 2k . also it is asking which one has the lager magnitude so it is the first one

An eraser is tied to a string swung in a horizontal circle. Identify the type of force which causes this object to travel along a circular path.

Answers

Answer:

A centripetal force

Explanation:

The type of force in the given scenario is tension. The correct option is c.

What is tension force?

Tension is defined in physics as the pulling force conveyed axially by a string, cable, loop, or similar material, or by every end of a rod, truss member, or similar three-dimensional object.

Tension can also be defined as the action-reaction pair of forces acting at each end of said elements.

Newton's second law states that the tension in the rope must equal the weight of the backed mass.

Tension, the normal force, and friction are all examples of contact forces.

Since the weight is not moving, the acceleration is zero. Even if the acceleration is not zero, this equals zero.

Thus, the correct option is c.

For more details regarding tension force, visit:

https://brainly.com/question/2287912

#SPJ2

Your question seems incomplete, the missing options are:

a) gravityb) appliedc) tensiond) normal

PLEASE ANSWER NEED HELP!!!!!!!! PLEASE THE CORRECT ANSWER!!!!!!

Lamar has been feeling a little sluggish. He is not sick, but he has been working a lot, and even though he goes for a run every morning, he is not getting the same benefits out of it that he used to. His friend suggests that he try acupuncture, but Lamar does not know much about it or why it would be helpful. What is the BEST explanation that you could give Lamar?
A.
Acupuncture is designed to make everyone feel energized and alert.
B.
Acupuncture focuses on rewiring the nervous system more effectively.
C.
Acupuncture is designed to help the energy in the body flow more efficiently.
D.
Acupuncture is very unscientific and completely rejected by Western medicine.


PLEASE NO LINKS OR I WILL REPORT YOU

Answers

Answer:

The correct answer is a.

A particle is constrained to move round a circle radius 382400km and makes a single revolution in 27.3 days. (i). Find the velocity in ms-1. (ii). Find its acceleration

Answers

The velocity and acceleration of the particle moving round the circle is;

Velocity = 162.12 m/s

Velocity = 162.12 m/sAcceleration = 6.873 × 10^(-5) m/s²

We are given;

Radius of circle; 382400 km = 382400000 m

Time; t = 27.3 days = 27.3 × 86400 s = 2358720 s

Now, formula for velocity is;

Velocity = distance/time

Thus;

I) velocity = 382400000/2358720

Velocity = 162.12 m/s

II) Acceleration is centripetal acceleration and is given by the formula;

a = v²/r

a = 162.12²/382400000

a = 6.873 × 10^(-5) m/s²

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Omar rubs a balloon with wool, giving the balloon a
charge of -8.9x10-14 C. What is the force between
the balloon and a metal sphere that is charged to
25 C and is 2 km away?

Answers

Answer:

-8.9×10-14=-89-14=-103°C

25°C=2km

-103°C=? Less

=-103/25×2km

=-8.24km

How many sulfur atoms are there in 25 molecules c4h4s2?.

Answers

There are 50 atoms (twice the amount of the molecules)

if you have 3 moles of iron, how many grams of iron do you have?

Answers

Answer:

55.84 look at periodic table

so 55.84*3= 167.52gFe

if the velocity of gas molecules is doubled the its kinetic energy will be

Answers

Answer: Quadrupled

Explanation:

Because when it’s doubled they are going to make another pair so 2+2=4

PLEASE ANSWER NEED HELP!!!!!!!! PLEASE THE CORRECT ANSWER!!!!!!

Reba knows that if she exercises it will help her body, but she is less sure how this will bring positive changes to other aspects of her life. What is the BEST way to explain this connection to Reba?
A.
When you are healthy, everything is automatically better.
B.
Exercise will lead her to meditate, allowing her to improve her mind and body.
C.
She will definitely lose a lot of weight, and thinner people are always happier.
D.
Exercise reduces stress and boosts confidence, which can create positive change.

PLEASE NO LINKS OR I WILL REPORT YOU

Answers

D.

Exercise reduces stress and boosts confidence, which can create positive change.

the answer is D exercise reduces stress and boosts confidence which can create positive change. lmk if this helps

In motion pictures, what do you call the lens manipulation where the focus quickly changes from one subject to the next in a motion picture

Answers

Answer:

A film transition is a technique used in the post-production process of film editing and video editing by which scenes or shots are combined. Most commonly this is through a normal cut to the next shot. Most films will also include selective use of other transitions, usually to convey a tone or mood, suggest the passage of time, or separate parts of the story. These other transitions may include dissolves, L cuts, fades (usually to black), match cuts, and wipes.

Explanation:

i select true helllpppp me

Answers

This is true! The The Coriolis effect describes the pattern of deflection taken by objects not firmly connected to the ground as they travel long distances around Earth.

a metal wire has a resistance of 13.00 at a temperature of 25.0 degree celsius

Answers

Explanation:

what exactly are you asking for?

Change.
Wax melting is an example of a chemical reaction.
True or false

Answers

i believe it is a physical change not chemical


1. You walk along a long straight school corridor for 55
m, then you turn around and walk 30 m in the
opposite. Finally, you turn again and walk 39 m in
the original direction and stop. What is your
displacement from your starting point?

Answers

Explanation:

14 m is the displacement and towards the north

How fast is an object going if it travels from San Diego to Anaheim in 1.25 hours (hr)? The distance from San Diego to Anaheim is 93 miles (mi).

a) 74.4 mi/hr

b) 116.25 mi/hr

c) 0.013 mi/hr

d) 84.25 mi/hr

e) None of the answers

Answers

Answer:

74.4 mph

Explanation:

Since we have the distance in miles and the time it took in hours, we can divide the two to get miles per hour.

speed = mi/hr

speed = 93/1.25

speed = 74.4 mph

A block with a mass of 6.0 kg is
held in equilibrium on an incline
of angle θ = 30.0° by a horizontal
force, F, as shown in the figure.
Find the magnitudes of the
normal force on the block and of F. (Ignore friction.)

Answers

(a) The normal force on the block is 50.92 N.

(b) The horizontal force on block keeping it in equilibrium is 29.4 N.

The given parameters;

mass of the block, m = 6 kgangle of inclination, θ = 30.0°

The normal force on the block is calculated as follows;

[tex]F_n = W \times cos(\theta)[/tex]

where;

W is the weight of the block

[tex]F_n = mg \times cos(\theta)\\\\F_n = 6 \times 9.8 \times cos(30)\\\\F_n = 50 .92 \ N[/tex]

The horizontal force on block keeping it in equilibrium is calculated as follows;

[tex]F- F_x = 0\\\\F-mgsin\theta= 0\\\\F = mgsin\theta\\\\F = 6 \times 9.8 \times sin(30)\\\\F = 29.4 \ N[/tex]

Learn more here:https://brainly.com/question/24860178

The launch speed of a projectile is three times the speed it has at its maximum height.what is the elevation angle at launch?

Answers

Answer:

Given: a projectile of initial launch velocity(V) and launch angle ∅ and no air resistance. At the maximum height, the projectile would have a zero contribution of speed from the vertical component(Vy) Therefore, if we say Vx=Vcos∅ is the only speed the projectile has at the instant of maximum height then we can replace Vx with 1/5V and write 1/5V=Vcos∅. Solving for the the launch angle ∅, gives Inverse Cos(1/5)=78.5 degrees.

Which key phrase below would imply that an object has no (0) initial velocity?
1) smoothly
2) in motion
3) backwards
4) from rest
5) uniformly


I assume number 4.​

Answers

The key phrase which describes zero (0) initial velocity is from rest.

When the velocity of an object at initial time is zero (0), it implies that the change in the displacement of the object with time is zero

[tex]v= \frac{\Delta x}{\Delta t} \\\\v_0 = 0[/tex]

Generally, when an starts its motion from rest, the initial velocity of the object will be zero. As the object acquires more momentum, the velocity increases with time.

Thus, we can conclude that the key phrase which describes zero (0) initial velocity is from rest.

Learn more about initial velocity here:https://brainly.com/question/19365526

A 1300-kg car is traveling with a speed of 16.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 38.9 m?

Answers

Answer:

F=ma,a=0.329m/second squared,m=1300kg,F=1300*0.329=4277N

Pliss help...

Di bawah ini manakah yang termasuk organ-organ sistem peredaran darah pada manusia adalah...
a. jantung - ginjal - paru-paru
b. jantung-pembuluh darah - darah
c. jantung - ginjal - hati
d. jantung - paru-paru​

Answers

Answer:

I think it is A

Explanation:

Below, what belongs to the organs of the circulatory system in humans is...

a. heart - kidneys - lungs

b. heart-blood vessels - blood

c. heart - kidney - liver

d. heart - lungs

Di bawah ini manakah yang termasuk organ-organ sistem peredaran darah pada manusia adalah...

a. jantung - ginjal - paru-paru

b. jantung-pembuluh darah - darah

c. jantung - ginjal - hati

d. jantung - paru-paru

=================================

Opsi > A

a. jantung - ginjal - paru-paru

b. jantung-pembuluh darah - darah

c. jantung - ginjal - hati

d. jantung - paru-paru

a race car traveling at 44m/s slows at a constant rate to a velocity of 22m/s over 11 seconds , how far does it move during this time

find distance and acceleration
FAST PLEASE !!

Answers

Answer:

-1.2×10^2 m

I hope this helps you

lonic Naming Practice
Write the name of the following chemical compound:
Na3Cl1

Answers

Answer:

sodium chloride. .....

Ionic naming practice: Na3Cl1= Sodium Chloride

A 25 kg chair initially at rest on a horizontal floor requires a 165 N horizontal force to set it in motion. Once the chair is in motion, a 127 N horizontal force keeps it moving at a constant velocity.​

Find the coefficient of static friction between the chair and the floor.​















b. Find the coefficient of kinetic friction between the chair and the floor.​

Answers

a. The coefficient of static friction between the chair and the floor is 0.67.

b. The coefficient of kinetic friction between the chair and the floor is 0.52.

Given the following data:

Mass of chair = 25 kgHorizontal force A = 165 NHorizontal force B = 127 N

Scientific data:

Acceleration due to gravity = 9.8 [tex]m/s^2[/tex]

a. To find the coefficient of static friction between the chair and the floor:

Mathematically, the force of static friction is given by the formula;

[tex]F_s = uF_n = umg[/tex]

Where;

Fs represents the force of static friction.μ represents the coefficient of static friction.[tex]F_n[/tex] represents the normal force.g is the acceleration due to gravity.mμ is the mass of an object.

Making μ the subject of formula, we have:

[tex]u=\frac{F_s}{mg}[/tex]

Substituting the given parameters into the formula, we have;

[tex]u=\frac{165}{25 \times 9.8} \\\\u=\frac{165}{245}[/tex]

μ = 0.67

b. To find the coefficient of kinetic friction between the chair and the floor:

Note: The normal force would be the same as above.

[tex]u_k = \frac{F_k}{F_n} \\\\u_k = \frac{127}{245}\\\\u_k =0.52[/tex]

Read more on force of static friction here: https://brainly.com/question/25686958

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