A small object with mass 3.60 kg moves counterclockwise with constant angular speed 1.40 rad/s in a circle of radius 2.55 m centered at the origin. It starts at the point with position vector 2.551 m. Then it undergoes an angular displacement of 9.15 rad. (a) What is its new position vector? m (b) In what quadrant is the object located and what angle does its position vector make with the positive x-axis? ---Select--- ✓ at (c) What is its velocity? m/s (d) In what direction is it moving? (Give a negative angle.) ° from the +x direction. (e) What is its acceleration? m/s² (f) What total force is exerted on the object? N

A spring with unstretched length of 14.3 cm has a spring constant of 4.63 N/m. The spring is lying on a horizontal surface, and is attached at one end to a vertical post. The spring can move freely around the post. The other end of the spring is attached to a puck of mass m. The puck is set into motion in a circle around the post with a period of 1.32 s. Assume the surface is frictionless, and the spring can be described by Hooke's law. (a) What is the extension of the spring as a function of m? (Assume x is in meters and m is in kilograms. Do not include units in your answer.) x = Your answer cannot be understood or graded. More Information x Find x (in meters) for the following masses. (If not possible, enter IMPOSSIBLE.) (b) m = 0.0700 kg x Use your result from part (a), and insert the given value for m. m (c) m 0.140 kg × Use your result from part (a), and insert the given value for m. m (d) m = 0.180 kg x Use your result from part (a), and insert the given value for m. m (e) m =…

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 860 kg. It has strayed too close to a black hole having a mass 98 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. 100 m- 10.0 km Black hole (a) Determine the total force on the spacecraft. The total force is determined by the distance from the black hole to the center of gravity of the ship which will be close to the midpoint. N (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in acceleration grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.) N/kg 2.56e+12