A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of the angle it slides.

A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of the angle it slides.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 6P: At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of...

See similar textbooks

Similar questions

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 ?
At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.
If a particle moving in one-dimensional motion about the x-axis starts from the originwith velocity vi and decelerates with constant acceleration - a, show that the particle will return to the origin in a time.
Assume that, at the initial instant to = 0, a particle is thrown with initial speed vo and with an initial angle θo, with respect to a direction parallel to the Earth's surface. In this way, in order to carry out an analytical study of its motion in a simpler way, consider a coordinate system xoy, with its origin at the particle's launch position, and with its positive x axis oriented in the direction of the horizontal motion of the particle and with its positive y-axis oriented vertically upward. In this sense, illustrate (make the force diagrams) the projectile launch, highlighting its main characteristics, and describe algebraically what is asked:
An object is projected straight upwards with an initial velocity U. If T is the time taken to return to the point of projection, H is the maximum height and g is the acceleration due to gravity, derive how to solve for: (a.) time of flight, T, and (b.) the maximum height, H, that the projectile can achieve.
A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) Find the magnitude of the velocity as a function of time
A particle is launched from the origin in R^3 with initial velocity v(0) = < 0, 8, 10 > and undergoes constant acceleration a = < 2, - 1, - 5 > due to the combined forces of gravity and wind. Where and at what time does the particle hit the "ground" (e.g. the plane z = 0)?
Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for t ≥ 0 arex = t − 2 sin t, y = 3 − 2 cos t Assuming that the plane flies in a room in which the floor is at y = 0, explain why the plane will not crashinto the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.] How high must the ceiling be to ensure that the plane does not touch or crash into it?
Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t) = t −1/2, moves arbitrarily far from the origin after sufficient time has elapsed.
What form does the trajectory of a particle have if the distance from any point A to point B is equal to the magnitude of the displacement from A to B?
A projectile is fired horizontally with speed v0 from the top of a cliff of height h. Itimmediately enters a fixed tube with length x, as shown in Figure. There is friction between the projectileand the tube, the effect of which is to make the projectile decelerate with constant acceleration ax. After theprojectile leaves the tube, it undergoes normal projectile motion down to the ground. Calculate the totalhorizontal distance, l, that the projectile travels. (g=9.8 m/s2) v0=5.5m/s ax=-2.5m/s2 x=4.5m h=12m
Two trains travel in the opposite direction, leaving each of the opposite stations which call station A and station B. The train A departs at a constant speed of 150[km/h], while the train B leaves from rest with constant acceleration of 1,5[m/s]. HOW far and at what time do the two trenes intersect? Consider that the two stations are separated by a distance of 10[km].