Please show your work on all questions

1. A street light is supported by two wires and each makes a different angle from each other. The one on the left is 32 degrees from the vertical and the one on the right is 43 degrees from the vertical. Find the tension in each wire if the street light has a mass of 60.0 kg. See notes in week 5 announcement on this problem.

2. There are three masses m1 = 2.0 kg, m2 = 5.0 kg and m3 = 7.0 kg. The mass are all affixed to a massless rod of length 15cm. m1 and m3 are at the ends and m2 is 10 cm from left where m1 is. Calculate the center of mass of the system and specify from which end it is from.

3. A pair of hedge trimmers are 45 cm long from the pivot to the end of the handles. If the person applies of a force of 15 N on each handle and the blades are 3.5 cm long, how much force is applied to the branch?

4. A 245 kg person lays on board that is supported only on the ends and that has a mass of 12.0 kg. If the person and the board are both 205 cm long and the person’s center of mass is 38 cm from the left side, what is the force on either side where the board is supported?

5. A large tank of water is full and has a depth of 10.0 m. What is the pressure at the bottom of the tank? What would the velocity of the water be if the tank was opened at the bottom? Hint: open vessels are subject to atmospheric pressure.

6. A Two balloons of identical volume (radius 11.5 m) are filled with gas. The first with helium, the second with hydrogen (H2) gas. Each balloon and cage have a mass of 750 kg. What is the lift created by each one? Which one lifts better? Hint: find the volume or air displaced by balloon and assume the balloon to be a sphere. Find the Buoyancy force on the balloon: it is the same no matter what the gas you use. Why? Calculate the total weight of each case. Lift = B-W.

7. A irregular piece of metal has a dry mass of 5.7 kg. Once it is submerged it has an apparent mass of 2.4 kg. What is the density of the piece of metal?

8. If water leaves a tank of water at a velocity of 16.7 m/s, how tall is the tank?