Determine the takeoff speed of the airplane

Question

A 10000 lb airplane is launched from a catapult. The spring of the catapult (k_s = 150 lb/in) is initially compressed 10ft. and then released. During the launching, the airplane engine exerts a constant horizontal force of 2000 lbs. Assuming the friction to be negligible, determine the takeoff speed of the airplane at the instant when the spring reaches its undeformed position.

Answer 1

This is a work-energy problem.

Step 1) Step collect all the information given

k = 150 lb/in = 1800 lb/ft

m = 10,000/g = 310.6 slugs

d = 10 ft

T = 2000 lb

Step 2) Determine the Equation

E_k = W + E_s = 0.5mv² = Td+0.5kx²

Step 3) Evaluate the Equation

0.5*310.6 *v² = 2000*10+0.5*1800*10² ∴ v = 26.6 ft/s

Answer:

The airplane's velocity when the spring is fully expanded is 26.6 ft/s