12. The astronaut orbiting the Earth in Figure on side is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 600km above the Earth's surface, where the free-fall acceleration is 8.21m/s2. Take the radius of the Earth as 6400km. Determine the speed of the satellite and the time interval required to complete one orbit around the Earth, which is the period of the satellite. 13. The figure on side represents the total acceleration of a particle moving clockwise in a circle of radius 2.50m at a certain instant of time. For that instant, find (a) the radial acceleration of the particle, (b) the speed of the particle, and (c) its tangential acceleration. 14. A ball swings counterclockwise in a vertical circle at the end of a rope 1.50m long. When the ball is 36.9 past the lowest point on its way up, its total acceleration is (22.5i^+20.2j^)m/s2. For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball. 15. Two objects are connected by a light string that passes over a frictionless pulley as shown in Figureon side. Assume the incline is frictionless and take m1= 2.00kg,m2=6.00kg, and = 55.0. (a) Draw free-body diagrams of both objects. Find (b) the magnitude of the acceleration of the objects, (c) the tension in the string, and (d) the speed of each object 2.00s after it is released from rest. 16. A 5.00kg block is placed on top of a 10.0kg block (Fi gure) ). A horizontal force of 45.0N is applied to the 10kg block, and the 5.00kg block is tied to the wall. The coefficient of kinetic friction between all moving surfaces is 0.200. (a) Draw a free-body diagram for each block and identify the action-reaction forces between the blocks. (b) Determine the tension in the string and the magnitude of the acceleration of the 10.0kg block. 17. A 9.00kg hanging object is connected by a light, inextensible cord over a light, frictionless pulley to a 5.00 . kg block that is sliding on a flat table (Figure) . Taking the coefficient of kinetic friction as 0.200 , find the tension in the string. 18. A space station, in the form of a wheel 120m in diameter, rotates to provide an "artificial gravity" of 3.00m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of the wheel's rotation in revolutions per minute that will produce this effect. 19. A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in Figure The length of the arc ABC is 235m, and the car completes the turn in 36.0s. (a) What is the acceleration when the car is at B located at an angle of 35.0 ? Express your answer in terms of the unit vectors i^ and j^. Determine (b) the car's average speed and (c) its average acceleration during the 36.0s interval. 20. A roller-coaster (as shown figure) has a mass of 500kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point (B) involves only up-and-down motion (as seen by the riders), with no motion to the left or right. (a) If the vehicle has a speed of 20.0m/s at point (A), what is the force exerted by the track on the car at this point? (b) What is the maximum speed the vehicle can have at point (B) and still remain on the track? Assume the roller-coaster tracks at points (A) and (B) are parts of vertical circles of radius r1=10.0m and r2=15.0m, respectively. 21. An object of mass m1= 4.00kg is tied to an object of mass m2= 3.00kg with String 1 of length =0.500m. The combination is swung in a vertical circular path on a second string, String 2, of length =0.500m. During the motion, the two strings are collinear at all times as shown in Figure At the top of its motion, m2 is traveling at v=4.00m/s. (a) What is the tension in String 1 at this instant? (b) What is the tension in String 2 at this instant? (c) Which string will break first if the combination is rotated faster and faster