- Potential of a Uniform Spherical Shell As an example, let us find the potential function for a uniform spherical shell. Solution: we have Phi =-Gint (dM)/(s)=-Gint (2pi rho R^2sinTheta dTheta )/(s) From the relation between s and Othat we used in Equation 6.2.5, we find that the pre- ceding equation may be simplified to read Phi =-G(2pi rho R^2)/(rR)int _(r-R)^r+Rds=-(GM)/(r) where M is the mass of the shell . This is the same potential function as that of a single particle of mass M located at O. Hence , the gravitational field outside the shell is the same as if the entire mass were concentrated at the center. It is left as a problem to show that, with an appropriate change of the integral and its limits, the potential inside the shell is constant and , hence, that the field there is zero.
- Which letter shows the ball when it has the maximum potential energy? G D A
- EXAMPLE 6.7.1 Potential of a Uniform Spherical Shell As an example, let us find the potential function for a uniform spherical shell. Solution: By using the same notation as that of Figure 6.2.1, we have Phi =-Gint (dM)/(s)=-Gint (2pi rho R^2sinTheta dTheta )/(s) __ g is the local acceleration of a mass m due to gravity.On the surface of Earth, its value is 9.8m/s^2 and is primarily due to the mass of the Earth. CHAPTER (Gravitation and Central Forces From the relation between s and 0 that we used in Equation 6.2.5, we find that the pre- ceding equation may be simplified to read Phi =-G(2pi rho R^2)/(rR)int _(r-R)^r+Rds=-(GM)/(r) (6.7.13) where M is the mass of the shell . This is the same potential function as that of a single particle of mass M located at O. Hence , the gravitational field outside the shell is the same as if the entire mass were concentrated at the center. It is left as a problem to show that, with an appropriate change of the integral and its limits, the potential inside the shell is constant and hence, that the field there is zero.
- 15. Enumere los planetas loviales en orden decreciente de distancia al Sol. 16. ¿Qué objeto del Sistema Solar tiene slempre un foco? __ __ 17. Qué planetaes más grande: Urano o Neptuno? __ 18. ¿Cual es el objeto más grandeque no es un planeta en la tabla de datos? __ 19. Compare la excentricidad de Plutón con los datos de excentricidad de los planetas yasteroides enumerados en esta tabla de datos. ¿Aqué categoria pertenece más de cerca Plutón? Reclamo: Plutón deberia ser un __ __ 20. ¿Qué dos planetas tienen la duración del día más similar? __ y __ 21. ¿Qué dos planetas tienen las órbitas con formas más similares? __ y __ 22. ¿Qué variable tiene una relación directa con la distancia media al Sol? __ because 23. ¿Cuáles dos objetos del Sistema Solar están más probablemente a la misma distancia del Sol? __ 24. ¿Qué planeta tiene aproximadamente la mitad del tamaño de la Tierra? __ 25.¿Qué edad tendrias en Mercurio? Pista: si tienes 15 años, ¿cuántos dias llevas vivo? Toma esa cantidad de de revolución. __ 26. Desaffo: Si los planetas tienen una forma esférica axial, zpor qué los inacion adal, goor questions de la superficie curva de un planeta? __
- ultiple Choice (10 marks) entity the letter of the choice that best completes the statement or answers the question __ 13. The speed of any mechanical wave as it propagates through a medium is dependent mainly on the a. frequency of the wave source d. type of medium through which it travels b. wavelength e. amplitude C. period of the wave __ 14. If a sound has an intensity of 3.0W/m^2 Find its intensity if the observer were to move three times as far away from the source. a. 0.33W/m^2 d. 27W/m^2 b. 1.0W/m^2 e 3.0times 10^2W/m^2 C. 9.0W/m^2 __ 15. Which of the following is not an application of the reflection of sound? a. Ultrasound imaging d. resonance b SONAR e. they are all applications of reflection C. echolocation __ 16. Which statement best describes what will occur at the barrier between th medium, shown below? incident pulse __ a. The reflected pulse will be in upright and the transmitted pulse will be inverted. b. The reflected pulse will be inverted and the transmitted pulse will be upright C. Both the reflected and transmitted pulses will be upright. d. Both the reflected and transmitted pulses will be inverted e. All of the wave energy will be reflected and inverted, and there will be no transmission. 17. An ambulance is approaching a stationary observer. For the observer , the apparent frequency of the siren compared to the actual frequency of the siren a. increases or decreases depending on the speed of the ambulance b. resonates C. decreases d. stays the same e. increases 8. A person tuning a guitar strikes a tuning fork with a frequency of 384 Hz simultaneously as a guitar string is plucked. If 15 beats are heard in 5.0 s, the frequency of the string is a. 369 Hz d. 381 Hzor 387 Hz
