Please show the work/equations for these please! 1. What is the period of the or
ID: 1289941 • Letter: P
Question
Please show the work/equations for these please!
1. What is the period of the orbit of two equal mass stars (10^30 kg each) around their common center of mass (halfway between them)? Separation distance d=10^9 m. (ANSWER IS 1.7X10^4 s)
2. The earth and the moon (mass 7 x 10^22) are separated by 4 x 10^8m from center to center. what fraction of the distance from the center of the earth to the moon would you have move to find a place where the gravitational pull towards the earth would equal the gravitational pull toawrds the moon? (ANSWER IS 90%)
3. What is the absolute pressure under the water at a depth of 10m in a proof of fresh water at a seaside resort? (ANSWER IS 2X10^5 N/M^2)
4. A plane moves through air. this results in the air under the wing moving at speed v=50m/s. The air rushing over the wing moves at speed 60m/s. If the area of the wings is 200 m^2, what is the lift exerted on the plane? (ANSWER IS 1.3X10^5)
Explanation / Answer
1]
Given:-
Mass of each star= 1030kg
Distance d=109 m.
The centre of mass is th midway between the two stars since they have equal masses.Let R be the orbit radius for each star,thus the two star are separated by a distance 2R as showm in the below figure.
Here centripetal force balancec the gravitational force between two stars
mv2/R = Gm2/[2R]2
v2 = Gm/4R
v= [Gm/4R]1/2
We have the expression for period as, T= 2*pie *R/v
Hence we get T=2*pie *R/[Gm/4R]1/2 =4*pie[R3/Gm]1/2
Plugging the values, we get T=4*3.14*[(0.5*109)3/6.67*10-11*1030]1/2 = 1.7*104 s
2]
Force due to gravity= Gravitational force between earth and moon
Fg= FG
Let 'x' be the point where the gravitational pull towards the earth would equal the gravitational pull toawrds the moon
mg=GMm/[r]2
g=GM/r2
gE/gM= [x-RE]2/[RM-x]2
we get X= 1.2*108 m
3] Given :-
h=10m
We have the equation for Pabsolute= Po+rhosea water*g*h
Po is the atmospheric pressure= 1.013*105 N/m2
Density of sea water= 1027kg/m3
Plugging the values we get, Pabsolute= Po+rhosea water*g*h
we get Pabsolute=1.013*105 +[1027*9.8*10]= 2*105 N/m2
4]
Use Bernoulli's equation to find the pressure difference.
P1 + 1/2 rho v12 = P2 + 1.2 rho v22
(P1 -P2)= (1/2) rho (v22-v12) = (1/2) (1.29)(602-502 )= 709.5N/m2
Lift force exerted on the plane= (P1 -P2)* A= 1.4*105 N