Concept explainers
In Fig. 13-21, a central particle of mass M is surrounded by a square array of other particles, separated by either distance d or distance d/2 along the perimeter of the square. What are the magnitude and direction of the net gravitational force on the central particle due to the other particles?
Figure 13-21 Question 1.
To find:
The magnitude and direction of the net gravitational force acting on the central particle due to the other particles
Answer to Problem 1Q
Solution:
The net gravitational force acting on the central particle due to the other particles is
and is directed towards left.
Explanation of Solution
1) Concept:
Observing the figure, we can cancel out the equal and opposite forces. The sum of the remaining forces will be the net force acting on the central particle M.
2) Given:
Thefigure of system of particles is given.
3) Formulae:
The Gravitational force of attraction between two bodies of masses M and m separated by distance R is,
4) Calculations:
From the given figure, we can infer that the gravitation force due to each particle on one of the sides of the square is cancelled by the gravitational force due to one of the particles on the opposite side of the square with the same mass except particle 3M. Particle 3M would exert force on M, but there is no force on the opposite side which can cancel this force.
So, the net force acting on the central particle M is due to the particle 3M which is
As we know the gravitational force is an attractive force, the force on particle M by particle 3M is pointing towards the left.
Conclusion:
Using the formula for gravitational force, we can find the net force acting on the particle due to the system of particles.
Want to see more full solutions like this?
Chapter 13 Solutions
Fundamentals Of Physics Extended, 10e Wiley E-text Reg Card With Webassign Plus 2 Semester Set
Additional Science Textbook Solutions
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
Mathematical Methods in the Physical Sciences
Physics for Scientists and Engineers, Technology Update (No access codes included)
Life in the Universe (4th Edition)
EBK FUNDAMENTALS OF THERMODYNAMICS, ENH
Physics for Scientists and Engineers
- A uniform solid sphere of radius R produces a gravitational acceleration of ag on its surface. At what distance from the sphere’s center are there points (a) inside and (b) outside the sphere where the gravitational acceleration is ag/3?arrow_forwardOne model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M= 4.1 * 1024 kg and R = 6.0 *106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?arrow_forwardtwo point particles are fixed on an x axis separated by distance d. Particle A has mass mA and particle B has mass 3.00mA. A third particle C, of mass 75.0mA, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero?arrow_forward
- A certain spherical planet is made up of two types of material: in the inner core (from the center to radius r = 2R), the mass density is p1; in the outer core (r = 2R to r= 5R), the mass density is p2 = 1/2 p1. Using Gauss’s law, determine the gravitational field at r = 3R in terms of the variables provided.arrow_forwardTwo identical uniform spheres A and B, with mass M=M= 1.00 [kg], are placed 0.500 [m] away from another spherical mass C with mass m=m= 0.300 [kg] as shown: If mass C is released from rest, what is its net acceleration? Assume that only the gravitational forces from spheres A and B act on C. State also the direction if it is upward or downward.arrow_forwardTwo spherical asteroids have mass 1= 1.00 x 10^20 kg and mass 2= 3.00 x 10^20 kg. The magnitude of the force of attraction between the two asteroids is 2.20 x 10^9 N. Calculate the distance between the two asteroids?arrow_forward
- a square of edge length 20.0 cm is formed by four spheres of masses m1 = 5.00 g, m2 = 3.00 g, m3 = 1.00 g, and m4 = 5.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.50 g?arrow_forwardAt the Sun’s surface, the gravitational force between the sun and a 5.00 kg mass of hot gas has a magnitude of 1370 N. Assuming that the sun is spherical and has a mass of 2 x 1030 kg, what is the sun’s mean radius?arrow_forwardA uniform solid sphere of radius R = 0.74 km produces a gravitational acceleration of ag on its surface. At what distance from the sphere's center are there points a) inside and b) outside the sphere where the gravitational acceleration is ag/5?arrow_forward
- Assume the earth is a uniform sphere of mass M and radius R. As strange as it may sound, if one can dig a long tunnel from one side of the Earth straight through the center and exit the other end, any object falling into the tunnel will appear at the other end (i.e. the opposite side of the Earth) in just 2530 s (42.2 min). Call that time t. Let t be a function of G, M, and R, where G = 6.67 x 10^-11 m3 kg−1 s−2 is the Universal Gravitational Constant, M = 5.98 x 10^24 kg, and R = 6400 km. (a) From dimensional analysis alone find the expression for t, up to a numerical constant c.(b) Determine the value of c by using the above values in the expression found in part (a).arrow_forwardWhat is the gravitational field intensity at a distance of 8.4 x 107 m from the centre of Earth?arrow_forwardChapter 11 67. A nonuniform thin rod of length L lies on the x axis. One end of the rod is at the origin, and the other end is at x=L. the rod's mass per unit length λ varies as λ=Cx, where C is a constant.(Thus, an element of the rod has mass dm=λ dx.) (a) Determine the total mass of the rod. (b)Determine the gravitational field due to the rod on the x axis at x=x0, there x0 >L.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning