Since antiquity people have used the sling to increase the speed of a rock and send it swiftly in a specific direction. While the rock is being spun overhead, the force that keeps the rock moving in a circle is provided by the tensile strength of the sling material. Leather has a fairly high tensile strength. Assume that, for a certain sling, 8.00 x 102 N is the largest possible tension. If the rock in the sling is 0.40 m from the center of rotation and has a tangential speed of 6.0 m/s, what is the largest mass the rock can have?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Two objects of different mass start from rest, are pulled by the same magnitude net force, and are moved through the same distance. the work done on object 1 is 900 j. after the force has pulled each object, object 1 moves twice as fast as object 2. how much work is done on object 2?

Alandscaper is shopping for landscaping materials. she wants to use materials through which water flows easily. which materials should she choose? check all that apply. clay gravel granite rocks with cracks loosely packed soil