1)A curve has a radius of 20 meter and a banking angle of 30 degrees. Assuming a static coefficient of friction 0.7 of the car's tires to the road. a) Draw the free body diagram of the car on the bank? b) What is the speed you can safely use for the cat to not slide up or down the embankment? c) What would happen if the car's speed was lower than your answer from part B? d) What would happen if the car's speed was higher than your answer from part B? e) Assuming there is no friction, could the car still get around the curve? If so, what is the precise speed required? If not explain.

2) A400g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R=60 cm. Calculate: a) its gravitational potential energy at A relative to B. b) its kinetic energy at B. c) its speed at B? d) its potential energy at C relative to B. e) its speed at C.

3)Two objects of masses =0.56 kg and =0.88 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k=280 N/m is placed between them as in Figure P6.28a. Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of 9.8 cm. If the objects are released from rest, find the final velocity of each object.

4)An object of mass 1 = 4 is connected by a light cord to an object of mass 2= 3 on a frictionless surface. The pulley rotates about a frictionless axle and has a moment of inertia of 0.500 kg/m 2 and a radius of 300 cm.Assuming that the cord does not slip on the pulley: (a)Find the acceleration of the two masses. (b)Find the net torque on the pully. (c) Find the tensions T1 and T2. (d) Find the acceleration of pulley.

5)Two astronauts, each having a mass of 75.0 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate: (a) the magnitude of the angular momentum and the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (b) What is the new angular momentum of the system? (c) What are their new speeds? (d) What is the new rotational energy of the system? (e) How much work is done by the astronauts in shortening the rope? 16) A uniform beam with weight of 60 N and length of 3.2 m is hinged at its lower end, And a horizontal force F of magnitude 50N at its upper end. The beam is held vertical by a cable that makes angle 25 degrees with ground and is attached to the beam at height h=2 m: a) Draw FBD. b) The tension in the cable. c) What is the x-component of the force on the beam from the hinge. d) What is the y-component of the force on the beam from the hinge.