A string under a tension of 53.9 N is used to whirl a rock in a horizontal circle of radius 2.59 m at a speed of 21.8 m/s. The string is pulled in and the speed of the rock increases. When the string is 1.23 m long and the speed of the rock is 54.8 m/s, the string breaks. What is the breaking strength (in newtons) of the string

During physical science, ms. greene challenged her students to produce an energy transformation. james and jill wrapped a 4-inch nail with a coil of fifty turns of wire. they connected one end of the coil to one terminal of a knife switch. they connected the other terminal of the knife switch to the battery. finally, they connected the end of the coil to the other terminal of the battery. james held the tip of a 1-inch nail near the flat end of the 4-inch nail. jill closed the knife switch quickly and then opened it. the 1-inch nail was pulled toward the 4-inch nail. what is the best explanation of why the nail moved? a) electrical energy was converted to mechanical energy in the 1-inch nail. b) the 4-inch nail became an electromagnet and the magnetic force attracted the 1-inch nail. c) the electric current in the 4-inch nail was converted to mechanical energy in the 1-inch nail. d) the 4-inch nail had a positive charge and the 1-inch nail had a negative charge. opposites attracted.

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.

How is coal extracted from mountaintop removal mines? a. dynamite is used to create underground tunnels where miners go to extract the coal. b. dynamite is used to break apart rocks and then draglines are used to remove the broken rock and reach the coal. c. coal in mountaintops is extracted by digging strips in the landscape to reach the coal. d. placer deposits in mountain river bottoms are removed by