PHYS 131 Tutorial 1 Please note that these questions are meant for you to work on during tutorials with your group members. Be sure to show all your work. 1. The picture shows three identical beakers, partially filled with water, with three cubes of equal volume fully or partially immersed in water. The water levels for A, B and C are the same in the figure. A B C Rank the volume of water in each beaker. Explain your reasoning. A. VA = VB = Vc B. VA = VC < VB C. VA = Vc > VB D. VA < VB < VC E. VA > VB > VC - the cubes in A and C are fully submerged regardless of its position in the water - for B, the cube is only partially submerged . has more Volume since it is the same neight as A and C
2. A cylinder holds 80 g of water, which comes up to a height of 4 cm. An irregularlytishaped stone is then placed into the water, resulting in the water level rising to 6 cm. The figure shows the cylinder of water before and after the stone is lowered into the water. 4 cm 6 cm L h = 2cm = 0-02cm a) If the mass of the stone is 100 g, what is the stone's average density (in units g/cm3)? m= ev before store Vdisplaced = m - e 80g 1g/cm3 @ water = 1g / cm 3 with stone = 80 cm3 e = m = 100g = 2.5g/cm3 V (20) (2) Vcylinder = Tr2h = 80 base base = 80/4 = 20cm b) If we lower another piece of this same stone with mass 50 g into the cylinder (which already holds the 100 g piece), what will the new water level in the cylinder be (in cm)? e = m V 50g V= m -- 2.5g/cm3 = 20 cm 3 Vdisplaced = Ah h = v = 20 = 1cm 20 A 20 new height = 7 cm
3. A cube with a mass of 440 g and side length of 6 cm is placed on an inclined plane with angle shown in the figure. 60° 30' -- 52 FN 30 x mg cos 30' = x a) What is the density of the block in units kg/m3? Show your work. e = m -. 0.440Kg = 2037Kg/m3 (0. 06) } b) What is the pressure exerted by the cube on the slope? [Hint: Recall that pressure is the component of force perpendicular to the surface per unit area.] P = = - mg cos 30' - (0.440Kg)(9.8m/s2) cos 30 ( 0.06 m) 2 (0.06m) 2 = 1037.31 Pa c) If you shift the block higher up the inclined plane (to the right in the picture), does the pressure increase, decrease, or stay the same? Why? Explain in words. Stay the same as the angle of incline stays the same , hence the F ( mg