Two identical pucks of mass m rotate together on a frictionless, horizontal table. Puck 1 is distance d from the center of rotation, and puck 2 is distance 2d from the center of rotation. They are attached by a string along the radial arm of circular motion. If they rotate together at a frequency  f, what are the tensions of the two strings?

Children playing pirates have suspended a uniform wooden plank with mass M = 13.4 kg, length ℓ = 2.40 m, and angle θ = 35.0°, as shown in the figure. Sophia, with a mass of m = 21.6 kg, is made to "walk the plank" and is d = 1.5 m from reaching the end of the plank. What is the tension acting on the rope at the end (i.e value of F3)?

The figure shows a container of mass m₁ = 1.7 kg connected to a block of mass m₂ by a cord looped around a frictionless pulley. The cord and pulley have negligible mass. When the container is released from rest, it accelerates at 1.0 m/s² across the horizontal frictionless surface. What are (a) the tension in the cord and (b) mass m₂? (a) Number (b) Number i Units Units m₁ mq >

A girl swings a 0.190 kg rock attached to a taut string in a circle around her head; her hand holds the end of the string above her head, and the string angles down slightly. The string is massless and 0.680 m long. A coordinate system lies with its origin at the location where the string comes out of the girl's hand. The positive z-axis points vertically upwards, the positive y- axis points horizontally towards the right, and the positive x-axis points out of the screen. At a certain instant, the rock makes 3.25 revolutions per second (rev/s) in a counterclockwise direction, as seen from above. The string is inclined at an angle of 0 = 12.4° below the xy-plane, and the projection of the string onto the xy- plane makes an angle o = 36.8° with the positive x-axis. What is the tangential velocity vector v in meters per second (m/s) at this instant? Report your answer using ijk unit vector notation. i = v, i + vyj+ vz k m/s