1. Two objects are connected by a light rope in between and are placed on a table. The mass of object 1 is m; = 2.00 kg and object 2 has a mass m, = 3.00 E kg. Both objects have the same coefficients of kinetic friction gy = 0.100 with the table top. A horizontal force F=8.00N is applied to object 1 in the direction parallel to the rope. As a result, the two objects move together at the same acceleration on the table. a) Find the frictional forces acting on object 1 and object 2, respectively. (You should draw a clear force diagram representing this system. You may use g = 9.80 m/s') (4 pts.) Light rope b) Find the acceleration of the system. (4 pts.) ) Find the tension in the rope. (2 pts.) 4. A skier of mass m starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates. The crest of the second hill is circular in shape with a radius of curvature equal to r. Let the initial height of the starting point from the top of the second hill be h (see figure). a) Neglect friction and air resistance, find the speed of the skier when he/she just reaches the top of the second hill in terms of the initial height h and the free fall acceleration g. (6 pts.) b) Also Neglect friction and air resistance and assuming the skier can reach the top of the second hill, find the normal force (from the ground) acting on the skier, in terms of the initial height h and the radius of curvature r, at the top of the second hill. (6 pts.) c) If the radius of curvature is r = 36 m, what must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill? (3 pts.) 6. Starting from rest, a 93-kg firefighter slides down a fire pole. The average frictional force exerted on him by the pole has a magnitude of 810 N, and his speed at the bottom of the pole is 3.4 m/s. How far did he slide down the pole? (You may use g = 9.80 m/s) (10 pts.) 3. A car is making a turn on an unbanked curve on a horizontal level road. What is the force responsible for providing the centripetal force and keeping the car from sliding off? (Choose one. 2 pts.) [ 1 The weight of the car. The normal force acting by the ground on the car. " Canter of eurahing [ 1 The friction between the tires of the car and the ground. 4 [ 1 The centrifugal force. / Car A uses tires for which the coefficient of static friction is 1.1 on a particular unbanked curve. The maximum speed at which the car can negotiate this curve is 25 m/s. Car B uses tires for which the coefficient of static friction is 0.85 on the e same curve. What is the maximum speed at which car B can negotiate the curve? = (You may use g =9.80 m/s') (8 pts.) 2. a) What is the weight of an object by definition? (2 pts.) b) It is the year 2124 and mankind is planning to migrate to Mars. It is necessary to know all the details of the planet. The average distance of planet Mars from the Sun is 229,000,000 km. Previous space probes have already determined the free fall acceleration on the surface of Mars to be 3.71 m/s'. Based on astronomical observations of the periods of the moons of Mars and their distances from the planet, Mars' mass is found to be 6.417x10%* kg. What is the radius of planet Mars? (You may use G=6.67x10"" N-m'/kg') (6 pts.)