How large is the force that the catapult must exert on the jet?

Question

On aircraft carriers, catapults are used to accelerate jet aircraft to flight speeds in a short distance. One such catapult takes a 17,600-kg jet from 0 to 68 m/s in 2.6 s. (Assume the catapult acts in the positive horizontal direction. Indicate the direction with the sign of your answer where appropriate.)

How far does the jet travel while it is accelerating?

How large is the force that the catapult must exert on the jet?

Answer 1

assuming positive x as in the direction of motion and initial x=0

X₀ = 0m , V₀ = 0 t₀ =0 ,

X_f = ? V_f = 68 m/s , t = 2.6s

A) distance traveled

first average acceleration:

a= ΔV/Δt = (68m/s - 0m/s) / (2.6s - 0s) = 26.15 m/s²

to find X we have to assume acceleration is constant (which wont be in real life the acceleration will slow down toward the end)

ΔX = 0.5 a * t²+V₀t = 0.5 * 26.15 m/s² * 6.76 s² + 0 = 88.4 m

B) Force of Catapult

Fnet = m*a = 17600 kg * 26.15 m/s2 = 460240 N

(also you can calculate directly from change of momentum which is technically here the same thing:

Fnet = ΔP/Δt =(mVfinal-0)/tf = 17600kg * 68m / 2.6s = 460240 N)

Note that infact

Fnet = F_catapult - F_drag - F_friction

and at 152 Miles per Hour you cant neglect the drag so the value is the minimum of the catapult force.

F_catapult = 4.6*10⁵N + F_drag + F_friction