The magnitude of the gravitational force between a particle of mass m1 and one of mass m2 is given by F(x) = G m1m2 / x2, where G is a constant and x is the distance between the particles. (Use any variable or symbol stated above as necessary.) (a) What is the corresponding potential energy function U(x)? Assume that U(x) → 0 as x → [infinity]. U(x) =

Answers

Answer 1

The corresponding potential energy function U(x) = -Gm1m2/x, where G is the gravitational constant.

The potential energy function corresponding to the given gravitational force function is represented by the equation U(x) = -Gm1m2/x, where G is the gravitational constant.

To find the potential energy function, we need to integrate the force function with respect to the distance x.

This integration results in the negative sign and the inverse relation in the potential energy function.

The property that U(x) approaches 0 as x approaches infinity means that the potential energy becomes negligible at large distances, which is consistent with the behavior of gravitational potential energy.


Related Questions

What symbol is used to represent internal energy in the first law of thermodynamics?

A. Q
B. W
C. U
D. V

Answers

Answer:

\Delta U = Q - W

aka—^

(ΔU = Q − W)

The symbol for Internal Energy Change isΔU. It is the sum of all the microscopic energies such as: translational kinetic energy. vibrational and rotational kinetic energy.

Answer:

C. U

Explanation:

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A sled of mass m is coasting on the icy surface of a frozen river. While it is passing under a bridge, a package of equal mass m is dropped straight down and lands on the sled (without causing any damage). The sled plus the added load then continue along the original line of motion. How does the kinetic energy of the (sled + load) compare with the original kinetic energy of the sled? A) It is 1/4 the original kinetic energy of the sled. B) It is 1/2 the original kinetic energy of the sled. C) It is 3/4 the original kinetic energy of the sled. D) It is the same as the original kinetic energy of the sled. E) It is twice the original kinetic energy of the sled.

Answers

Answer:B

Explanation:

Given

mass of Sled is m

another package of mass m is thrown on it

Suppose u be the initial velocity of sled

conserving momentum

[tex]mu=2mv[/tex]

[tex]v=\frac{u}{2}[/tex]

where v is the final velocity

Initial kinetic energy [tex]=\frac{1}{2}mu^2[/tex]

Final Kinetic Energy[tex]=\frac{1}{2}(2m)\cdot (\frac{u}{2})^2[/tex]

Final Kinetic Energy[tex]=\frac{1}{2}\times \frac{1}{2}mu^2 [/tex]

Final kinetic Energy is half of initial    

Which aspect of the scientific method occurs first?
a. hypothesis
b. data collection
c. experiment
d. observation

Answers

Answer:

The right option is d. observation

Explanation:

Observation: These is the state of being very alert about the what is happening around. Observation in science can be done using the sense organs such eyes to spot out differences, nose to smell the release of gases, ears to hear sound, skin to feel changes in temperature. Observation is the first scientific method. And it can be carried out anywhere.

Observation leads pattern, pattern leads to problems, problems leads to hypothesis, hypothesis leads to experiment, experiment leads to Theory.

Therefore the right option is d. observation

The correct answer is observation, which is in option d. In the scientific method, observation is the first step. It involves gathering information about a phenomenon or a specific aspect of the natural world through careful and systematic observation.

The process of observation allows scientists to identify patterns, make initial observations, and ask questions about the phenomenon they are studying. It serves as the foundation for scientific inquiry and guides the subsequent steps of the scientific method. After making observations, scientists then move on to formulating a hypothesis, which is a proposed explanation or prediction based on the observed data. The hypothesis is a tentative answer to the research question and serves as the starting point for further investigation.

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Two skaters skate toward each other, each moving at 3.3 m/s. Their lines of motion are separated by a perpendicular distance of 1.5 m. Just as they pass each other (still 1.5 m apart), they link hands and spin about their common center of mass. What is the rotational speed of the couple about the center of mass? Treat each skater as a point particle, each with an inertia of 51 kg.

Answers

Answer:

4.4 rad/s

Explanation:

When the 2 skaters is spinning with a distance of 1.5m, their rotation radius is half of that distance, which is 1.5/2 = 0.75m.

Then their moments of inertia, given that their mass being 51 kg, is (treating them as point mass particle):

[tex]I = Mr^2 = 2Mr^2 = 51*0.75^2 = 38.25 kg.m^2[/tex]

When they change from linear motion to rotational motion, their energy must be conserved:

[tex]E_L = E_r[/tex]

[tex]2*(0.5Mv^2) = 2*(0.5I\omega^2)[/tex]

[tex]\omega^2 = \frac{Mv^2}{I}[/tex]

[tex]\omega = v\sqrt{\frac{M}{I}}[/tex]

[tex]\omega = 3.3\sqrt{\frac{51}{38.25}} = 4.4 rad/s[/tex]

The rotational speed of the couple about the center of mass is: 4.4 rad/s

Meaning of Couple

A couple can be defined as an effect or force created by two parallel forces that are equal in masses but opposite in sense or opposite in direction and do not share the same line of action.

The couple can also be used to signify two individuals.

In conclusion, the rotational speed of the couple about the center of mass is: 4.4 rad/s

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Your pet hamster sits on a record player whose angular speed is constant. If he moves to a point twice as far from the center, then his linear speed
A) doubles.
B) halves.
C) remains the same.

Answers

Answer:

option A

Explanation:

given,                    

angular speed is constant

initial distance = r                

final distance (r')= 2 r

initial linear velocity = v

final linear velocity = v'

we know,                  

v = r ω......................(1)

where r is the distance

ω is the angular speed

now,            

v' = r' ω            

v' = 2 r ω        

v' = 2 v                

hence, the linear velocity doubles.

The correct answer is option A

If an alpha particle and a beta particle have the same energy, which particle will penetrate farther into an object?

Answers

Answer:

Beta particle

Explanation:

If an alpha particle and a beta particle have the same energy, beta particle will penetrate farther into an object than alpha particle because;

1. In air, beta particles can travel a few hundred times farther than alpha particles.

2. Beta particles have more penetrating power than alpha particles.

3. Alpha particle can be absorbed or stopped by an inch or less 1-2 centimeters of air or a thin piece of tissue while beta particles can be stopped or absorbed by a thin layer of Aluminium.

4. Alpha particles loose all of their energies in a small volume easily that beta particles.

5. Beta particles can traveled a longer distance between 2-3 meters at a speed nearly equal to that of light than alpha particles which travel a distance between 2-4 cm at a speed approximately five percent the speed of light.

If you are going 30 miles an hour in good condition, it will take how many feet to stop .

Answers

Answer:

158400 feet per hour

Explanation:

First we find:

How many feet are in miles per hour?

Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour.

For example, 30 miles per hour times 5,280 feet per mile is 158,400 feet per hour.

Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) The plate starts to spin? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?

Answers

Answer:

Explanation:

(a) When the plate starts to spin:

Its angular velocity increases, so the angular acceleration is non zero. As the direction of velocity keeps on changing every instant so the linear acceleration is also non zero.

(b) When the plate rotates at constant angular velocity:

Its angular velocity is constant so the angular acceleration is zero. As the direction of velocity keeps on changing every instant so the linear acceleration is also non zero.

(c) When the plate sows to halt:

Its angular velocity decreases, so the angular acceleration is non zero( but negative). As the direction of velocity keeps on changing every instant so the linear acceleration is also non zero.

A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then:
A. his angular velocity doublesB. his angular velocity remains about the sameC. his angular velocity is halvedD. the direction of his angular momentum vector changesE. his rotational kinetic energy increases

Answers

Answer:

Explanation:CE

Let after the fall of weight from hands , the moment of inertia reduces from 2I to I. Since no external torque is acting on the system , angular momentum will be conserved.

I₁ ω₁ = I₂ ω₂

2I ω₁ = I ω₂

2ω₁ =  ω₂

So , angular velocity will be doubled.

Option A is correct.

Measurements of how orbital speeds depend on distance from the center of our galaxy tell us that stars in the outskirts of the galaxy. True or False

Answers

Answer:

True

Explanation:

Measurements of how orbital speeds depend on distance from the center of our galaxy tell us that stars in the outskirts of the galaxy. True or False

stars in the outskirt orbit the galactic center

the object mean orbital speed depends only on the Earth's mass and the semi-major axis (half the longest diameter) of the object's orbit. worthy of note. the orbital speed changes depending on where in the orbit the object is. It will be greatest when closest to Earth and least when furthest from Earth.

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