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
diamong [38]
3 years ago
7

Two particles, each of mass m, are initially at rest very far apart.Obtain an expression for their relative speed of approach at

any instant as a function of their separation distance d if the only interaction is their gravitational attraction to each other.Express your answer in terms of some or all of the variables m, d, and gravitational constant G.
Physics
1 answer:
PSYCHO15rus [73]3 years ago
5 0

Answer:

|\Delta v |=\sqrt{\frac{4Gm}{d} }

Explanation:

Consider two particles are initially at rest.

Therefore,

the kinetic energy of the particles is zero.

That initial K.E. = 0

The relative velocity with which both the particles are approaching each other is Δv and their reduced masses are

\mu= \frac{m_1m_2}{m_1+m_2}

now, since both the masses have mass m

therefore,

\mu= \frac{m^2}{2m}

= m/2

The final K.E. of the particles is

KE_{final}=\frac{1}{2}\times \mu\times \Delta v^2

Distance between two particles is d and the gravitational potential energy between them is given by

PE_{Gravitational}= \frac{Gmm}{d}

By law of conservation of energy we have

KE_{initial}+KE_{final}= PE_{gravitaional}

Now plugging the values we get

0+\frac{1}{2}\frac{m}{2}\Delta v^2= -\frac{Gmm}{d}

|\Delta v |=\sqrt{\frac{4Gm}{d} }

=\sqrt{\frac{Gm}{d} }

This the required relation between G,m and d

You might be interested in
A wire is used as a heating element that has a resistance that is fairly independent of its temperature within its operating ran
dedylja [7]

Answer:

Double the current

Explanation:

The energy delivered by the heater is related to the current by the following relation:

E= I^{2}R t

let R * t = k ( ∴ R and t both are constant)

so E= k I^{2}

Now let:

E2= k I₂^2

E2= 4E

⇒ k I₂^2= 4* k I^{2}

Cancel same terms on both sides.

I₂^2= 4* I^{2}

taking square-root on both sides.

√I₂^2 = √4* I^2

⇒I₂= 2I

If we double the current the energy delivered each minute be 4E.

3 0
3 years ago
A 3.0 kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) ini
finlep [7]
<h2>Option 2 is the correct answer.</h2>

Explanation:

Elastic collision means kinetic energy and momentum are conserved.

Let the mass of object be m and M.

Initial velocity object 1 be u₁,  object 2 be u₂

Final velocity object 1 be v₁,  object 2 be v₂

Initial momentum = m x u₁ + M x u₂ = 3 x 8 + M x 0 = 24 kgm/s

Final momentum = m x v₁ + M x v₂ = 3 x v₁ + M x 6 = 3v₁ + 6M

Initial kinetic energy = 0.5 m x u₁² + 0.5 M x u₂² = 0.5 x 3 x 8² + 0.5 x M x 0² = 96 J

Final kinetic energy = 0.5 m x v₁² + 0.5 M x v₂² = 0.5 x 3 x v₁² + 0.5 x M x 6² = 1.5 v₁² + 18 M

We have

            Initial momentum = Final momentum

            24 = 3v₁ + 6M

            v₁ + 2M = 8

             v₁ = 8 - 2M

            Initial kinetic energy = Final kinetic energy

            96 = 1.5 v₁² + 18 M

            v₁² + 12 M = 64

Substituting  v₁ = 8 - 2M

           (8 - 2M)² + 12 M = 64    

           64 - 32M + 4M² + 12 M = 64    

            4M² = 20 M

               M = 5 kg

Option 2 is the correct answer.  

6 0
3 years ago
What is TRUE about a capitalist society?
Makovka662 [10]

The idea behind capitalism is that the free market of products and ideas is owned and driven by private citizens. A capitalist society is a social order in which private property rights and the free market serve as the basis of trade, distribution of goods, and development.

7 0
3 years ago
Read 2 more answers
How magnitude, distance and velocity affects motion?
levacccp [35]

Answer:

Velocity is the rate of motion in a specific direction. ... My velocity is 30 kilometers per hour that-a-way. Average speed is described as a measure of distance divided by time. Velocity can be constant, or it can change (acceleration).

Explanation:

Velocity is the rate of motion in a specific direction. ... My velocity is 30 kilometers per hour that-a-way. Average speed is described as a measure of distance divided by time. Velocity can be constant, or it can change (acceleration).

6 0
3 years ago
Emilio pushes a 100 kg freshman with 200 N of force. How much is the freshman accelerated?
ladessa [460]

Explanation:

F = MA

200 = 100 * A

A = 200/100

A = 2m/sec^2

<h3><em>hope </em><em>it </em><em>helps </em><em>you </em></h3>
8 0
3 years ago
Other questions:
  • Five hundred joules of heat are added to a closed system. The initial internal energy of the system is 87 J, and the final inter
    5·2 answers
  • How fast is a cat that runs 50 meters in 10 seconds?
    7·2 answers
  • A physical science test book has a mass of 2.2 kg what is the weight on mars??? please help
    5·1 answer
  • What efficiency of a car's engine when heat input is 200,000 joules and waste heat is 150,000 joules?
    10·1 answer
  • An object is placed 25 cm from a convex lens whose focal length is 10 cm. The image distance is ________ cm.
    7·1 answer
  • I need help on this question!
    11·1 answer
  • The physical quantity represented as rate of change of change in position in a
    12·1 answer
  • How is the density of water different from the densities of most other substances?
    8·1 answer
  • A dolphin leaps out of the water
    8·1 answer
  • Every summer I drive to Pennsylvania. It is 895 km to get there. If I average 100 km/hr, how much time will I spend driving?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!