To solve this problem, we will apply the concepts related to the linear deformation of a body given by the relationship between the load applied over a given length, acting by the corresponding area unit and the modulus of elasticity. The mathematical representation of this is given as:
Where,
P = Axial Load
l = Gage length
A = Cross-sectional Area
E = Modulus of Elasticity
Our values are given as,
l = 3.5m
D = 0.028m
E = 200GPa
Replacing we have,
Therefore the change in length is 1.93mm
Answer:
F = 4.48N
Explanation:
In order to calculate the net gravitational force on the rocket, you take into account the formula for the gravitational force between two objects, which is given by:
(1)
G: Cavendish's constant = 6.674*10^-11 m^3kg^-1s^-2
r: distance between the objects
You have a rocket at the middle of the distance between Earth and Moon, then, you have opposite forces on the rocket.
If you assume the origin of a system of coordinates at the rocket position, with the Moon to the left and the Earth to the right, you have:
(2)
Me: mass of the Earth = 5.98*10^24 kg
Mm: mass of the Moon = 7.35*10^22 kg
m: mass of the rocket = 1200kg
r1: distance from the rocket to the Earth = 3.0*10^8m
r: distance between rocket and Moon = 3.84*10^8m - 3.0*10^8m = 8.4*10^7m
You replace the values of the parameters in the equation (2):
The net force exerted over the rocket is 4.48N