A0.504 kg metal cylinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger. the cylinder comes to rest some distance above the plunger. the plastic tube has an inner radius of 5.37 mm and is frictionless. neither the plunger nor the metal cylinder allow any air to flow around them. if the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cylinder by a factor of 2.31, what is the initial acceleration a of the metal cylinder?

Explanation:

Given:

m=0.504kg

r=5.37mm

metal cylinde factor=2.31

we know that

Upward force = Downward force

Net force

the altitude of these satellites above the surface of the earth;

35790 km ( SI units )

22243.63 miles ( U.S. customary unit )

Explanation:

Given the data in the question;

Time taken by the satellite to complete on revolution is 23.934 hours

= 23.934 × 60 × 60 = 86162.4 seconds

now, let h represent altitude, r represent Orbit radius, v represent Orbit speed.

we know that

v² = GM/r

= gR²/r

= (9.81m/s² × ( 6.37 × 10⁶ m)²) / r

v = 19.95 × 10⁶ / √r   let this be equation

also;

time t = 2πr/v

86162.4 s = 2πr/v let this be equation 2

a) Determine the altitude of these satellites above the surface of the earth in both SI and U.S. customary units

we substitute v in equation into equation 2

so

86162.4 s = 2πr / (19.95 × 10⁶ / √r)

r = 42.16 × 10⁶ m

so, altitude h = r - R

h = 42.16 × 10⁶ m - 6.37 × 10⁶ m

h = 35790000 m

convert to kilometer

h = 35790000 / 1000

h = 35790 km

Convert to miles

h = 35790 / 1.609

h = 22243.63 miles

Therefore, the altitude of these satellites above the surface of the earth;

35790 km ( SI units )

22243.63 miles ( U.S. customary unit )