Answer and discuss each problem in a detailed way.

An Ideal spring of negligible mass with force constant of 400 Nlm is placed on a frictionless horizonal table with one end xed at a wall next to the table. A billiard ball of mass 200 g is pushed against the spring, campressing the spring to some distanCe. After the system is released, the Spring returns to equilibrium with the billiard ball leaving the table's edge at 4.00 m/s and hits the floor 80 cm below. Using the principle of energy conservation, (a) determine the initial compression of the spring. (b) What is the speed of the ball when it hits the floor? A pendulum is formed from a Small rock with mass of 0.10 kg that is fastened to a massless string with length 0.750 m. It is swinging so as to make a maximum angle of 45.0 with the vertical. Air resistance is negligible. What is the tension in the string as it passes through the vertical