### Chapter 13, Problem 011In the figure, two spheres of mass \( m = 9.24 \) kg, and a third sphere of mass \( M \) form an equilateral triangle, and a fourth sphere of mass \( m_4 \) is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass \( M \)?(b) If we double the value of \( m_4 \), what then is the magnitude of the net gravitational force on the central sphere?#### Diagram DescriptionThe diagram provided is a geometric layout showing:- An equilateral triangle with three spheres at the vertices. - Two spheres at the base vertices are labeled with mass \( m \). - The third sphere at the top vertex of the triangle is labeled with mass \( M \).- A fourth sphere labeled \( m_4 \) is located at the center of the equilateral triangle.#### Interactive Response Fields- For part (a): - Input field for the numerical value of mass \( M \) and a dropdown menu for units.- For part (b): - Input field for the numerical value for the magnitude of the net gravitational force on the central sphere when \( m_4 \) is doubled and a dropdown menu for units.#### Additional Options- Open Show Work: An optional link is provided for students who wish to show their work for the question.#### Status Indicators- Question Attempts: Shows the current count of attempts, out of a maximum of 10, that the user has used.#### Actions- Save For Later: An option to save the current progress and return to it at a later time.- Submit Answer: An option to submit the final answer for evaluation.This problem is part of an educational resource aimed at enhancing understanding of gravitational forces in a geometric configuration. The challenge involves applying principles of gravitational force and equilibrium conditions.

Answered: Image /qna-images/answer/845e434b-8f20-415e-bce1-775c12f4cb27.jpg

Chapter 13, Problem 011 In the figure, two spheres of mass m = 9.24 kg. and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass mą is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere? M (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show Work Question Attempts: 0 of 10 used SAVE FOR LATER SUBMIT ANSWER

Chapter 13, Problem 011 In the figure, two spheres of mass m = 9.24 kg. and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass mą is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere? M (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show Work Question Attempts: 0 of 10 used SAVE FOR LATER SUBMIT ANSWER

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 87CP: (a) Show that tidal force on a small object of mass m, defined as the difference in the...

See similar textbooks

Related questions

Q: Sphere A with mass 80 kg is located at the origin of an xy coordinate system; sphere B with mass 60…

Q: Planet A has a mass of mA = 1.50 × 1024 kg and planet B has a mass of mB = 2.40 × 1023 kg. The…

A: The force of gravity between any two masses is given by the equation F=Gm1m2r2G is the universal…

Q: In the figure, a square of edge length 16.0 cm is formed by four spheres of masses m1 = 4.80 g, m2 =…

A: Net gravitational force is F = 10.56*10-15 i + 10.56*10-15 j Newton

Q: Many people mistakenly believe that the astronauts that orbit Earth are “above gravity.” Calculate g…

A: The acceleration due to gravity is given by The space shuttle territory is 200000 meters above the…

Q: The (Figure 1) shows three masses. Take m1 = 32 kg , m2 = 5.0 kg, and m3 = 18 kg.What is the…

Q: The figures show a hypothetical planetary system at two different times. The system has a star S and…

Q: Newton’s version of Kepler’s third law is P2 = 4 π2 / [G (M1 + M2)] · a3, where G is the…

A: From Newton’s version of Kepler’s third law

Q: Sphere A with mass 81 kg is located at the origin of an xy coordinate system; sphere B with mass 58…

Q: Each mass is 4.00 kg. Find the magnitude of the net gravitational force on mass A due to masses B…

Q: Newton’s version of Kepler’s third law is: P2 = 4 π2 / [G (M1 + M2)] × a3. The space shuttle orbits…

A: The space shuttle orbits 271 km above the earth

Q: The density inside a solid sphere of radius a is given by p=Po a/r, where Po is the density at the…

A: The given solid sphere can be considered as a collection of small divisions. Then we can replace…

Q: Sphere A with mass 89 kg is located at the origin of an xy coordinate system; sphere B with mass 58…

Q: Four masses are at the vertices of a square. Find the magnitude of the gravitational force on the…

Q: Planet X has a radius of 6.00×10^7 m and an unknown mass. When a woman of mass 65.0 kg weighs…

A: Given data: The radius of planet is r=6.00x107 m. The mass of woman is m=65 kg. The distance from…

Q: Three masses, MA = Mg = Mc = M are placed at the vertices of a right triangle ( ljE & ), as shown in…

A: Given data- Three masses MA=MB=MC=M The distance between masses in figure =R Let gravitational force…

Q: Europa orbits Jupiter at a distance of 6.7 x 108 m from Jupiter's cloudtops (the surface of the…

Q: The gravitational force between two people is found to be 5.9 x 10-11 N. What would the…

Q: Sphere A with mass 70 kg is located at the origin of an xy coordinate system; sphere B with mass 73…

Q: The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that…

A: Given, Rh = 2GM/c2 a. Gravitational acceleration is given byag=Gmr2dag=2Gmr3drSince, h<<48…

Q: A spacecraft travels along the straight line connecting the earth and the sun. At what distance from…

Q: A person's weight W varies inversely as the second power of the distance d from the center of a…

A: As weight varies inversely as the second power of the distance d from centre of the planet we can…

Q: Newton’s version of Kepler’s third law is P2 = 4 π2 / [G (M1 + M2)] · a3, where G is the…

A: Given data: The value of gravitational constant G is 6.67×10-11 m3/kg.s2 The average distance is…

Q: A planet of mass 5 ⨯ 1024 kg is at location <4 ⨯ 1011, −4 ⨯ 1011, 0> m. A star of mass 4 ⨯…

A: (a)The relative position vector pointing from the planet to the star is,Substitute the values,

Q: Planet X has four times the diameter and five times the mass of earth. What is the ratio gx:ge of…

A: Here we have to use a basic formula here.

Q: Two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere…

Q: Two lead spheres are separated by 0.207 m, centre-to-centre. One sphere has a mass of 5.53 kg. The…

A: Given data: Distance between spheres (r) = 0.207 m Mass of one sphere (m1) = 5.53 kg Gravitational…

Q: Sphere A with mass 92 kg is located at the origin of an xy coordinate system; sphere B with mass 65…

A: It is given that, mA=92 kgmB=65 kgmC=0.50 kgrA=0i^+0j^rB=0.25 i^rC=0.19 i^+0.18 j^G=6.64×10-11…

Q: The mass of a moon is MM and the mass of the planet it orbits is Mp. The distance between the center…

A: gravitational force is proportional to mass of objects and inversely proportional to distance2.

Q: two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere…

Q: The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that…

A: The expression for the gravitational acceleration if given as, ag=-GMr2⇒daa=2GMr3dr Since h≪48…

Q: The mean diameters of Mars and Earth are 6.9×10^3km and1.3×10^4km, respectively. The mass of Mars is…

A: (a) Density of mars ρM=MMV=MM4πRM33=3MM4πRM3 Density of Earth ρE=MEV=ME4πRE33=3ME4πRE3

Q: Consider the gravitational acceleration on the surface of the Moon and of Mars. a) What is the…

A: The formula for determining the magnitude of the acceleration due to gravity g at the surface of any…

Q: Square A and square B have equal massess, 0.260 kg. Additionally, a smaller square with a mass of…

Q: Four spheres form the corners of a square whose sides are 6 cm long. The masses of the spheres are…

Q: Two spherical masses m1 = 4.10 g and m2 = 3.90 g are located at coordinates (-5.00, -3.75) cm and…

Concept explainers

Gravitational force

In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.

Acceleration Due to Gravity

In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.

Question

100%

### Chapter 13, Problem 011

In the figure, two spheres of mass \( m = 9.24 \) kg, and a third sphere of mass \( M \) form an equilateral triangle, and a fourth sphere of mass \( m_4 \) is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero.

(a) What is the value of mass \( M \)?

(b) If we double the value of \( m_4 \), what then is the magnitude of the net gravitational force on the central sphere?

#### Diagram Description
The diagram provided is a geometric layout showing:
- An equilateral triangle with three spheres at the vertices.
- Two spheres at the base vertices are labeled with mass \( m \).
- The third sphere at the top vertex of the triangle is labeled with mass \( M \).
- A fourth sphere labeled \( m_4 \) is located at the center of the equilateral triangle.

#### Interactive Response Fields
- For part (a):
- Input field for the numerical value of mass \( M \) and a dropdown menu for units.

- For part (b):
- Input field for the numerical value for the magnitude of the net gravitational force on the central sphere when \( m_4 \) is doubled and a dropdown menu for units.

#### Additional Options
- Open Show Work: An optional link is provided for students who wish to show their work for the question.

#### Status Indicators
- Question Attempts: Shows the current count of attempts, out of a maximum of 10, that the user has used.

#### Actions
- Save For Later: An option to save the current progress and return to it at a later time.
- Submit Answer: An option to submit the final answer for evaluation.

This problem is part of an educational resource aimed at enhancing understanding of gravitational forces in a geometric configuration. The challenge involves applying principles of gravitational force and equilibrium conditions.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Two black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 1011 m), attract one another with a gravitational force of 8.90 1025 N. The combined mass of the two black holes is 4.00 1030 kg. What is the mass of each black hole?
A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?
Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2
Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
The Sun has a mass of approximately 1.99 1030 kg. a. Given that the Earth is on average about 1.50 1011 m from the Sun, what is the magnitude of the Suns gravitational field at this distance? b. Sketch the magnitude of the gravitational field due to the Sun as a function of distance from the Sun. Indicate the Earths position on your graph. Assume the radius of the Sun is 7.00 108 m and begin the graph there. c. Given that the mass of the Earth is 5.97 1024 kg, what is the magnitude of the gravitational force on the Earth due to the Sun?
The mass of the Earth is approximately 5.98 1024 kg, and the mass of the Moon is approximately 7.35 1022 kg. The Moon and the Earth are separated by about 3.84 108 m. a. What is the magnitude of the gravitational force that the Moon exerts on the Earth? b. If Serena is on the Moon and her mass is 25 kg, what is the magnitude of the gravitational force on Serena due to the Moon? The radius of the Moon is approximately 1.74 106 m.
(a) Find the magnitude of the gravitational force between a planet with mass 7.50 1024 kg and its moon, with mass 2.70 1022 kg, if the average distance between their centers is 2.80 108 m. (b) What is the acceleration of the moon towards the planet? (c) What is the acceleration of the planet towards the moon?
Planetary orbits are often approximated as uniform circular motion. Figure P7.9 is a scaled representation of a planets orbit with a semimajor axis of 1.524 AU. a. Use Figure P7.9 to find the ratio of the Suns maximum gravitational field to its minimum gravitational field on the planets orbit. b. What is the ratio of the planets maximum speed to its minimum speed? c. Comment on the validity of approximating this orbit as uniform circular motion.
For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
(a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?
Three billiard balls, the two-ball, the four-ball, and the eight-ball, are arranged on a pool table as shown in Figure P7.26. Given the coordinate system shown and that the mass of each ball is 0.150 kg, determine the gravitational field at x=2m, y=0.
When a star dies, much of its mass may collapse into a single point known as a black hole. The gravitational force of a black hole on surrounding astronomical objects can be very great. Astronomers estimate the strength of this force by observing the orbits of such objects around a black hole. What is the gravitational force exerted by a black hole on a 1-solar-mass star whose orbit has a 1.4 1010 m radius and a period of 5.6 days?