1. A mechanic releases a small object with a density of 1.5 g/cm​3​ and a volume of 1.0 cm​3​ into a large vat of motor oil whose density is 888.1 kg/m​3​. The container is 12.0 m deep wit

1. A mechanic releases a small object with a density of 1.5 g/cm​3​ and a volume of 1.0 cm​3​ into a large vat of motor oil whose density is 888.1 kg/m​3​. The container is 12.0 m deep with a diameter of 1.8 m. What will the magnitude and direction of its acceleration be if it is released from rest (a) when it is 50% submerged? (b) at a depth of 1.0m (c) at a depth of 1.6m.  

 2. What is the density of a solid salad dressing ingredient if, in a container of salad dressing, it is at rest such that 45% of its volume is immersed in the extra virgin oil layer and the rest of its volume is immersed in the water layer?  

3. You have a 6.0-in diameter plastic cup of water filled to the brim, and an identical plastic cup of water containing one ice cube of volume 1.1 in​3​. The water level in the glass of water with ice is also filled to the brim, but part of the ice floats above the water level.  

a. A very small, hole forms from 3 in. from the top of the cup. What is the speed of the water leaving the hole when the hole first forms? What is the speed of the water leaving the hole after the water level has decreased by 1 in. from its original level at the brim of the cup? Note: this problem could be solved by using Torricelli’s theorem, but do not use this method. Instead use the fundamental physics principle: Bernoulli’s equation. To do so, assume that the speed of the water at the top of the water level is negligible. This is a reasonable assumption because the water level drops pretty slowly in the cup if the hole is small. 

 b. What is the longest vertical straw you could possibly drink this water through? Assume the straw is placed in the cup so that the bottom of the straw touches the the top of the water level.   

4. Oil (⍴=900 kg/m​3​) flows through a tube with values of various physical quantities given in the image. What does the top pressure gauge in the image read? By what factor do the cross-sectional areas of the tubes differ between the bottom and the top?