1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sdas [7]
3 years ago
9

4. Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 7.3 times tha

t of particle B. The period of particle B is 2.5 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to
Physics
2 answers:
HACTEHA [7]3 years ago
3 0

Answer:

Explanation:

Acceleration of particle A is 7.3 times the acceleration of particle B.

Let the acceleration of particle B is a, then the acceleration of particle A is

7.3 a.

Let the period of particle A is T and the period of particle B is 2.5 T.

Let the radius of particle A is RA and the radius of particle B is RB.

Use the formula for the centripetal force

a=r\omega ^{2}=r\times \frac{4\pi^{2}}{T^{2}}

So, r = a\frac{T^{2}}{4\pi^{2}}

The ratio of radius of A to the radius of B is given by

\frac{R_{A}}{R_{B}}=\frac{a_{A}\times T_{A}^{2}}{a_{B}\times T_{B}^{2}}

\frac{R_{A}}{R_{B}}=\frac{7.3 a\times T^{2}}{a\times 6.25T^{2}}

RA : RB = 1.17

KiRa [710]3 years ago
3 0

Answer:

The ratio of he radius of the motion of particle A to that of particle B is closest to 1.16.

Explanation:

Let a_A,a_B\ and\ r_A,r_B are accelerations of particle and radius of A and B respectively. It is given that :

a_A=7.3\times a_B\\\\\dfrac{a_A}{a_B}=7.3\\\\and\\\\T_B=2.5\times T_A\\\dfrac{T_B}{T_A}=2.5

The centripetal acceleration is given by the formula as :

a=\dfrac{v^2}{r}

r is the radius of motion

Since, v=\dfrac{2\pi r}{T}

a=\dfrac{4\pi ^2r}{T^2}

For A

a_A=\dfrac{4\pi^2 r_A}{T^2_A}.........(1)

For B

a_B=\dfrac{4\pi^2 r_B}{T^2_B}...........(2)

Dividing equation (1) and (2) we get :

\dfrac{a_A}{a_B}=\dfrac{T^2_B\times r_A}{T^2_A\times r_B}

\dfrac{r_A}{r_B}=\dfrac{a_A\times T^2_A}{a_B\times T^2_B}

Now using given conditions :

\dfrac{r_A}{r_B}=\dfrac{7.3}{(2.5)^2}\\\\\dfrac{r_A}{r_B}=1.16

So, the ratio of he radius of the motion of particle A to that of particle B is closest to 1.16.

You might be interested in
The equation for the speed of a satellite in a circular orbit around the earth depends on mass. Which mass?
katovenus [111]
<h3><u>Question: </u></h3>

The equation for the speed of a satellite in a circular orbit around the Earth depends on mass. Which mass?

a. The mass of the sun

b. The mass of the satellite

c. The mass of the Earth

<h3><u>Answer:</u></h3>

The equation for the speed of a satellite orbiting in a circular path around the earth depends upon the mass of Earth.

Option c

<h3><u> Explanation: </u></h3>

Any particular body performing circular motion has a centripetal force in picture. In this case of a satellite revolving in a circular orbit around the earth, the necessary centripetal force is provided by the gravitational force between the satellite and earth. Hence F_{G} = F_{C}.

Gravitational force between Earth and Satellite: F_{G} = \frac{G \times M_e \times M_s}{R^2}

Centripetal force of Satellite :F_C = \frac{M_s \times V^2}{R}

Where G = Gravitational Constant

M_e= Mass of Earth

M_s= Mass of satellite

R= Radius of satellite’s circular orbit

V = Speed of satellite

Equating  F_G = F_C, we get  

Speed of Satellite V =\frac{\sqrt{G \times M_e}}{R}

Thus the speed of satellite depends only on the mass of Earth.

6 0
4 years ago
In what direction must a force be applied so that the forces on the 1 kg object are balanced
choli [55]

Answer:

towards the object

Explanation:

7 0
3 years ago
A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a un
Kamila [148]

Answer:

<em>a) 6738.27 J</em>

<em>b) 61.908 J</em>

<em>c)  </em>\frac{4492.18}{v_{car} ^{2} }

<em></em>

Explanation:

The complete question is

A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a uniform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr2.

Part (a) If such a flywheel of radius r1 = 1.1 m and mass m1 = 11 kg can spin at a maximum speed of v = 35 m/s at its rim, calculate the maximum amount of energy, in joules, that this flywheel can store?

Part (b) Consider a scenario in which the flywheel described in part (a) (r1 = 1.1 m, mass m1 = 11 kg, v = 35 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r2 = 2.8 m and mass m2 = 16 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel?

Part (c) Return now to the flywheel of part (a), with mass m1, radius r1, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed vcar. Enter an expression for the mass of the car, in terms of the quantities defined here.

moment of inertia is given as

I = \frac{1}{2}mr^{2}

where m is the mass of the flywheel,

and r is the radius of the flywheel

for the flywheel with radius 1.1 m

and mass 11 kg

moment of inertia will be

I =  \frac{1}{2}*11*1.1^{2} = 6.655 kg-m^2

The maximum speed of the flywheel = 35 m/s

we know that v = ωr

where v is the linear speed = 35 m/s

ω = angular speed

r = radius

therefore,

ω = v/r = 35/1.1 = 31.82 rad/s

maximum rotational energy of the flywheel will be

E = Iw^{2} = 6.655 x 31.82^{2} = <em>6738.27 J</em>

<em></em>

b) second flywheel  has

radius = 2.8 m

mass = 16 kg

moment of inertia is

I = \frac{1}{2}mr^{2} =  \frac{1}{2}*16*2.8^{2} = 62.72 kg-m^2

According to conservation of angular momentum, the total initial angular momentum of the first flywheel, must be equal to the total final angular momentum of the combination two flywheels

for the first flywheel, rotational momentum = Iw = 6.655 x 31.82 = 211.76 kg-m^2-rad/s

for their combination, the rotational momentum is

(I_{1} +I_{2} )w

where the subscripts 1 and 2 indicates the values first and second  flywheels

(I_{1} +I_{2} )w = (6.655 + 62.72)ω

where ω here is their final angular momentum together

==> 69.375ω

Equating the two rotational momenta, we have

211.76 = 69.375ω

ω = 211.76/69.375 = 3.05 rad/s

Therefore, the energy stored in the first flywheel in this situation is

E = Iw^{2} = 6.655 x 3.05^{2} = <em>61.908 J</em>

<em></em>

<em></em>

c) one third of the initial energy of the flywheel is

6738.27/3 = 2246.09 J

For the car, the kinetic energy = \frac{1}{2}mv_{car} ^{2}

where m is the mass of the car

v_{car} is the velocity of the car

Equating the energy

2246.09 =  \frac{1}{2}mv_{car} ^{2}

making m the subject of the formula

mass of the car m = \frac{4492.18}{v_{car} ^{2} }

3 0
3 years ago
How does friction help soccer players
Lena [83]
When soccer players run they are using friction to propell themselves
7 0
3 years ago
Read 2 more answers
180 J of work is done when lifting a box up to a shelf that is 3 m high. What is the mass of the box?
ale4655 [162]

Explanation:

Work done= MGH

180=m×10×3

180/30=m

m=6kg

4 0
3 years ago
Other questions:
  • A special vehicle of length 50 m is designed to take passengers at extremely high speeds between different places on earth.
    14·1 answer
  • A circuit contains a resistor in series with a capacitor, the series combination being connected across the terminals of a batte
    13·1 answer
  • A 39.7 n object is in free fall. what is the magnitude of the net force which acts on the object? answer in units of n.
    15·1 answer
  • A snail at position 3 cm moves to position 20 cm in 8 seconds.
    6·1 answer
  • Learning Goal: To practice Problem-Solving Strategy 30.1 Electromagnetic Induction. A coil of wire contains N turns and has an e
    6·1 answer
  • A juggler has three objects in the air simultaneously. The masses of the objects are m, 2m, and 3m. At a particular instant, the
    13·1 answer
  • What is the total amount of force needed to keep a 6.0 kg object moving at speed
    8·2 answers
  • What is an earthquake​
    8·2 answers
  • Which nucleus completes the following equation?
    10·1 answer
  • Jack is a transgender male who is sexually attracted to males. Based on what you know about sex
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!