Question

An aircraft carrier uses a device called a catapult to help accelerate jets to the speed needed for take off. The flight decks on these carriers have length d = 84 m. A jet with a mass of m = 13317 kg can be accelerated from rest to a speed of v = 53 m/s by the end of the flight deck.
a. Select the correct symbolic expression for the magnitude of the average net force, FL, acting on the jet during its launch.
i. FL=mv/d
ii. FL=mv^2/2d
iii. FL=mv/2d
iv. FL=mv^2/d
v. FL=mvd
vi. FL=v^2/2d

b. Calculate the numerical value of the magnitude of the force F in Newtons?
c. What is the numerical value of the ratio R of the launch force FL to the jet's weight?

Answer 1

a) The average net force acting on the jet during its launch is $F_L=\frac{mv^2}{2d}$

b) The launch force is $2.23\cdot 10^5 N$

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:

$v^2-u^2=2ad$

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,

$a=\frac{v^2}{2d}$

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):

$F=ma$

Substituting the previous expression we found for the acceleration, we get:

$F=\frac{mv^2}{2d}$

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

$F_L=\frac{mv^2}{2d}$

we find:

$F_L = \frac{(13317)(53)^2}{2(84)}=2.23\cdot 10^5 N$

c)

First of all, we need to find the weight of the jet, which is given by

$F_G = mg$

where

m is the mass of the jet

$g=9.8 m/s^2$ is the acceleration of gravity

For this jet, we have

m = 13317 kg

So its weight is

$F_G = (13317)(9.8)=1.31\cdot 10^5 N$

And therefore, the ratio of the launch force to the weight of the jet is

$\frac{F_L}{F_G}=\frac{2.23\cdot 10^5}{1.31\cdot 10^5}=1.7$

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