a) The average net force acting on the jet during its launch is [tex]F_L=\frac{mv^2}{2d}[/tex]
b) The launch force is [tex]2.23\cdot 10^5 N[/tex]
c) The ratio of the launch force to the weight is 1.7
Explanation:
a)
The acceleration of the jet while travelling through the flight deck can be found by using the suvat equation:
[tex]v^2-u^2=2ad[/tex]
where
v is the final velocity
u = 0 is the initial velocity (the jet starts from rest)
a is the acceleration
d is the length of the flight deck
Solving for a,
[tex]a=\frac{v^2}{2d}[/tex]
Moreover, according to Newton's second law of motion, the force acting on the jet is equal to the product between its mass (m) and its acceleration (a):
[tex]F=ma[/tex]
Substituting the previous expression we found for the acceleration, we get:
[tex]F=\frac{mv^2}{2d}[/tex]
b)
Now we can find the numerical value of the magnitude of the force by susbstituting the data that we have.
We have:
v = 53 m/s (final velocity of the jet)
m = 13317 kg (mass of the jet)
d = 84 m (distance through which the jet has moved during the launch)
Substituting into the equation
[tex]F_L=\frac{mv^2}{2d}[/tex]
we find:
[tex]F_L = \frac{(13317)(53)^2}{2(84)}=2.23\cdot 10^5 N[/tex]
c)
First of all, we need to find the weight of the jet, which is given by
[tex]F_G = mg[/tex]
where
m is the mass of the jet
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
For this jet, we have
m = 13317 kg
So its weight is
[tex]F_G = (13317)(9.8)=1.31\cdot 10^5 N[/tex]
And therefore, the ratio of the launch force to the weight of the jet is
[tex]\frac{F_L}{F_G}=\frac{2.23\cdot 10^5}{1.31\cdot 10^5}=1.7[/tex]
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