An ant crawls on the surface of a ball of radius b in such a manner that the ant's motion is given in spherical coordinates by the equations r = b; phi = omega*t; theta = pi/2 * [1 + 1/4 * cos(400t)] Find the speed of the ant as a function of the time t. What sort of path is represented? by the above equations ?

An ant crawls on the surface of a ball of radius b in such a manner that the ant's motion is given in spherical coordinates by the equations r = b; phi = omegat; theta = pi/2 [1 + 1/4 * cos(400t)] Find the speed of the ant as a function of the time t. What sort of path is represented? by the above equations ?

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter13: Universal Gravitation

Section: Chapter Questions

Problem 32AP

See similar textbooks

Similar questions

We are presented with a particle of mass (m = 4.56 kg) which is in uniform circular motion going around a fixed point O. It had a radius of orbit (r = 3.63 m) and it experiences a net force of magnitude F = Br toward the fixed point O, where B = 2.75 Nm. What is the period of the particles orbit?
A car is traveling at constant speed of v= 16.8 m/s. It’s tired have a diameter of d=0.78 m. Randomized variables: v= 16.8 m/s d=0.78m Consider a point on the outer edge of the tire. What is the centripetal acceleration, ac at this point in m/s^2? If the car was traveling twice as fast, what would be the numerical value of the ration of the mew centripetal acceleration, an, to the old centripetal acceleration?
Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?
If a = (2, -4, 4), b = (4, 0, 3) and c = a × b, what is the magnitude of c?
A rod of length L0 moving with a speed v along the horizontal direction makes an angle 0 with respect to the x axis. (a) Show that the length of the rod as measured by a stationary observer is L = L0[1 (v2/c2)cos2 0]1/2. (b) Show that the angle that the rod makes with the x axis is given by tan = tan 0. These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)
Two particles A and B start from rest at the origin s = 0 and move along astraight line such that aA = (6t − 3) m/s^2 and aB = (12t2 − 8) m/s^2, where t is inseconds. Determine the distance between them and the total distance each hastravelled at t = 4s.
The flight from Cairo K = (30◦ N, 30◦ E) to Shanghai S = (30◦ N, 120◦ E) follows the shortest possible route, i.e. the surface of the Earth in the plane determined by the points O = origin = center of the Earth, K and S.a) Calculate the length of the route when the value 6,371 km is used for the radius of the Earth.b) How far north (latitude) does the airplane go during the trip?
A runner and his trainer are standing together on a circular track of radius 100 meters. When the trainer gives a signal, the runner starts to run around the track at a speed of 10 m/s. How fast is the distance between the runner and the trainer increasing when the runner has run 1/4 of the way around the track? A. 5.04 m/s B. 6.78 m/s C. 5.67 m/s D. 7.07 m/s
The gravitational force exerted by the Sun on the Earth holds the Earth in an orbit around the Sun. Let us assume that the orbit is perfectly circular. The work done by this gravitational force during a short time interval in which the Earth moves through a displacement in its orbital path is. a. ZERO b. positive c. negative d. dificult to determine
Car A is traveling at the constant speed of 48 km/h as it rounds the circular curve of 295-m radius and at the instant represented is at the position θ = 49°. Car B is traveling at the constant speed of 64 km/h and passes the center of the circle at this same instant. Car A is located with respect to car B by polar coordinates r and θ with the pole moving with B. For this instant determine vA/B and the values of r˙ and θ˙ as measured by an observer in car B. Find vA/B and vA/B. vA/B = ( ______i + ____j) m/s vA/B = ______ m/s
The gravitational force exerted by the earth on a unit massat a distance r from the center of the planet is where M is the mass of the earth,R is its radius, and G isthe gravitational constant. Is F a continuous function of r ?
1. Consider a bouncy ball and a metal cylinder on a 20 degree incline. Everyone knows a regular bouncy ball has a diameter of 2.5 cm and has a mass of 29 g, the cylinder is 5 cm long with a diameter 1 cm. 1. Use the conservation of energy approach to find the length of time theobjects in #1 take to roll down a 1.5 m incline at 200.t =_________________________ and ____________________________ If you could clearly circle the answers I need, that would be great!! Thanks!