1. A satellite of mass 1200 kg moves uniformly at the height of 380 km in a circ

ID: 1291418 • Letter: 1

Question

1. A satellite of mass 1200 kg moves uniformly at the height of 380 km in a circular orbit around the Earth. Find

a) the gravitational force on the satellite;

b) the speed of the satellite;

c) the period for the satellite around the Earth.

(The mass of he Earth: Mearth = 5.98 x 1024 kg; the radius of the Earth: Rearth = 6370 km . )

2. The volume rate of a flow in a horizontal pipe is 4.0 L/s. The diameters of the pipe at points A and B are 2.0 cm and 5.0 cm, respectively. Find

a) the speeds of the flow at points A and B;

b) the difference in pressure between the two points, i.e. Pb - Pa

a) F = GMm/r^2

F = (6.67e-11*5.98e24*1200)/(6370000+380000)^2

F = 10505.11 N

b) v = sqrt(GM/r) = sqrt(6.67e-11*5.98e24)/(6370000+380000)

v = 7687.08 m/s = 7.68 km /s

T = (2*pi*r)/V = (2*3.14*(6370000+380000))/7687.08

T = 5514.45 s = 1.532 hours

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continuity equation

a) at point A

area*va = 4

pi*1e-4*va = 4e-3

va = 12.74 m/s

at point B

area*vb = 4

pi*2.5*2.5*1e-4 = 4e-3

vb = 2.04 m/s

bernoullis pricilple

Pa + 0.5*rho*va^2 = Pb + 0.5*rho*vb^2

Pb - Pa = 0.5*rho*(va^2 - vb^2)

Pb -Pa = 0.5*rho*((12.74*12.74)-(2.04*2.04)) = 79.073*rho pascals

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