please answer questions 1-6 on a seperate sheet of paper with explanations!

1. An 8-g bullet is fired into a 2.5-kg block that is initially at rest at the edge of a frictionless table of height 1 m, as shown in the figure below. The bullet remains in the block, and after impact the block lands d=2 m from the bottom of the table. Determine the initial speed of the bullet. M = 2.5kg 8 8 M 2 m 2. A big letter G with a volume of 0.0004 my is fully submerged in water. Two strings hold the G in place, as shown, and they each have a tension of 1.5 N. The density of water is 1000 kg/m. (a) Draw a free-body diagram of the G. (b) Find the magnitude of the byouant force exterted on the G by the water. (c) What is the mass of the G? (d) What is the density of the G? (e) The two strings are cut simultaneously. Find the acceler- G ation of the G (direction and magnitude) right after the 530 530 strings are cut. 3. A stick that is 1-m long is placed under water in an aquarium. The stick has a volume of 0.001 m3 and a mass of 0.5 kg. One side of the stick is fixed to the aquarium wall, and the other side is tied down by a string, as shown in the figure. The density of water is 1000 kg/m". (a) What is the buoyant force exerted on the stick? (b) Draw an extended free-body diagram of the stick. (Hint: The buoyant force acts at the geometric center of the stick.) (c) Find the tension in the string. /30 4. As show in the figure, a 3-kg block is released from the top of the slope and hits a spring. Both the slope and the ground are frictionless. The spring constant k is 400 N/m. (a) Find the maximum distance Ar that the spring was compressed. (b) The block was stuck with the spring after it hit the spring, and oscillated back and forth. Find the period and frequency of the oscillation. 2.0 m 30 5. A 1.5-kg block moves to the right and hit a 2-kg block that is initially at rest on a horizontal surface. After the collision, the 1.5-kg block slides to the left with a speed of -5 m/s, and the 2-kg block slides to the right for 7.5 m before coming to rest. The coefficient of kinetic friction between the block and the surface is 0.6. (a) What is the frictional force exerted on the 2kg-block when it is sliding? (b) What is the speed of the 2-kg block immediately after its being hit by the 1.5-kg block? (c) What was the speed of the 1.5-kg immediately before the collision? C 6. A uniform horizontal beam with a length of 8 m and a weight of 300 N is attached to a wall by a pin connection at point P. Its far end is supported by a cable that makes an angle of 53 with the horizontal, and a 650-N person stands 2 m from the wall, as shown in the figure. (a) Draw a free-body diagram of the beam. (b) Draw an extended free-body diagram of the beam. (c) Find the tension in the cable. (d) Find the force exerted by the wall on the beam. 53.0 8.00 m