Question

im having problems with my physics homework. Im not that good at physics and would like to know what the awnsers are and a step by step apprach for i can completley understand and comprehend it. Thank you!

1) Define Pressure. 1) Use the expression for hydrostatic pressure to estimate the height of the atmosphere above sea level. Presume that the density of air and "e" remain constant. 11) Now presume that "g" is still a constant but the density of air varies and is defined by the function d d, Exp(-ay), where do is a constant and so also is a .y is height measured from the sea level. Derive an expression for the atmospheric pressure at any heighty. ill) Knowing the actual pressure and density at sea level can we find a value for a ?! 2) i) What is angular momentum? ii) Prove that for a centrally directed force (towards the center) angular momentum is conserved. ill) The rotational inertia of a collapsing spinning star drops to 1/3 its initial value. What is the ratio of the new rotational speed to the old rotational speed? What is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy? 3) 1) what is Archimedes principle and what could we use it for? ii) A big cube of ice is dropped into a glass of water. The ice floats and the level of the water in the glass rises by a small amount 'y. The ice is then allowed to melt. Will the level of water in the glass increase, decrease or remain the same? Prove your answer mathematically. iii) A block of wood floats in water with 2/3 of its volume V submerged and in oil with 0.90V submerged. Find the density of the wood and that of the oil? 4) A heavy box in the form of a cube with edge length 1.5m rests on a ramp that makes an angle with the horizontal. The center of mass of the box is at the geometrical center of the box. As the angle of the ramp is increased from zero gradually, an angle will be reached at which the box will either tip over (rotate about its center of mass) or start to slide. i) Write an equation for translational equilibrium. ii) Write a condition for rotational equilibrium. Make the axis of rotation to be through the center of mass, and note that the normal force will act at the front edge of the box. iii) If the coefficient of static friction between the box and the ramp is 0.7, will the box slide or tip over first? What angle will that happen?

Answer 1

i Pressure force applied per unitare P- f Bolet us imagine a point depth he inside a a point P Ugud od of I noensity Let us assume an imaginary a cylinder of cross-section area A C Voluone of cylinder VE AXL 2. Mass of liquid (m) - VP- ALP Weight a n (W)- Ahlg force is applied at Pressure applied al ponte P= fa AhPg. A - AO Ils ponte

to Now this experession for pressure can be used determine I height I above sea level If we imagine ourselves submerged in above sea level A of the sea of ais than Pressure at sea level apo "a beigbl e P P = h (5 from a botels stup of intal lesglu dy at a you uch della Weight of bu stup (W) - A dy dg Pressure (de) dy dg & Pressure of y height conlumn c d e (ay) = P² dp = EMTOS

Ая dog eaque 7 Dato If we know 2 4 for - Torque day [- ] Pasane of them we know a a centrally directed force applied (9) F smo No lorque oorneau nenews applied no mangul us changed AUG TWTFSS

Bunnse - 5.20 .M. Sunset - 5.53 PM. ( THURSDAY Angular Momentum (17. sxmo m- mass 2 mur W - anglue angular a mxrwxr ( velocity mwin s radius 150 ma from Conservation of Momentum Iywne Iz wz o I, QE XWR on W2 = 3 = 3:1 a New rotational energy old a I, X )