Please solve the following problems. You must show all work. 

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 and the one on the right is 43 degrees. Find the tension in each wire if the street light has a mass of 60.0 kg. 

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.

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?

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? 

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?

Notes on this week’s homework;

On number 1, it isn’t very clear, but I’m going to solve the problem as if the angles are given relative to the horizontal. You can draw the one on the left as if the wire is 32 degrees above horizontal on the left, and the right is 43 degrees above horizontal on the right.

It may not be obvious reading number 2, but the way the problem is written, M1 is on the right and M3 is on the left.

For problems 5 and 8, you have to assume the water is flowing through a small hole. If the hole was large, we would need to use differential equations to solve the problem. I assume nobody wants to do that.