Concept explainers
(a)
The gravitational force on the particle of mass
(a)
Answer to Problem 64P
The gravitational force on the particle of mass
Explanation of Solution
Given data:
Following figure shows the distribution of masses on the semi-circular arc of radius
Formula Used:
The expression for the gravitational force between the masses
Here,
Calculation:
Radius of the arc is
Choose the unit vector
The gravitational force between the masses
The gravitational force between the masses
The gravitational force between the masses
The gravitational force between the masses
Hence, net force on the particle of mass
Substitute the values and solve:
Conclusion:
Therefore, the gravitational force on the particle of mass
(b)
The gravitational field at center of curvature of the arc.
(b)
Answer to Problem 64P
The gravitational field at center of curvature of the arc is
Explanation of Solution
Given data:
Following figure shows the distribution of masses on the semi-circular arc of radius
Formula Used:
Gravitational field at a point is:
Here, net gravitational force is
Calculation:
The gravitational field at the center of curvature of the arc can be determined as follows.
Substitute
Conclusion:
The gravitational field at center of curvature of the arc is
Want to see more full solutions like this?
Chapter 11 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forwardA geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are sueful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for Earth in Appendis D.arrow_forwardTwo stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P11.50). Show that each star has a period given by T2=42d3G(M+m) Proceed as follows: Apply Newtons second law to each star. Note that the center-of-mass condition requires that Mr2 = mr1, where r1 + r2 = d.arrow_forward
- An Earth satellite has its apogee at 2500 km above the surface of Earth and perigee at 500 km above the surface of Earth. At apogee its speed is 730 m/s. What is its speed at perigee? Earth’s radius is 6370 km (see below).arrow_forwardEstimate the gravitational force between two sumo wrestlers, with masses 220 kg and 240 kg, when they are embraced and their centers are 1.2 m apart.arrow_forwardIf a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.arrow_forward
- Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass,m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(+)=gg2REtan , where is the angular velocity of Earth.arrow_forwardModel the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forwardWhat is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forward
- Circular orbits in Equation 13.10 for conic sections must have eccentricity zero. From this, and using Newton’s second law applied to centripeta acceleration, show that the value of in Equation 13.10 is given by Where is the angular momentum of the orbiting body. The value of is constant and given by this expression regardless of the type of orbit.arrow_forwardThe 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?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill