Assignment:
1. A solid block with mass 0.4 Kg floats on the surface of a tank of water (ρwater = 1000 Kg/m3); the part of the solid submerged in the water is one third of its total volume.
(i) Calculate the density of the solid.
(ii) Calculate the total volume of the solid.
2. An object has a weight of 24 N in the air and 22 N when fully submerged in water (ρwater = 1000 Kg/m3).
(i) Calculate the density of that object.
(ii) Calculate the mass of that object (take g = 10 m/s2).
(iii) Calculate the buoyancy force on that object when it is fully submerged in water.
(iv) Calculate the buoyancy force on that object when it is half submerged in water (i.e. when half f its volume is under water).
3. An ideal fluid flows at 2 m/s in a cylindrical pipe with diameter of 0.4 m.
(i) If the pipe splits in 4 branches, each with 0.1 m diameter, what will be the speed of the fluid in each branch?
(ii) If the pipe splits in 4 branches, all with the same diameter d, for what value of d will the speed of the fluid in each branch remain equal to 2 m/s?
4. A mass of 0.2 Kg is hung to a spring. When displaced by 0.04 m, the mass oscillates with a frequency of 50 Hz.
(i) Calculate the elastic constant of the spring.
(ii) Calculate the time it will take the mass to complete 5 full oscillations.
5. The picture below (bird view) depicts a spinning ball that travels in the direction of the arrow, through the air. Draw the trajectory the ball will follow.
