After graduating with a physics degree, you get a job with the Naval Surface War
ID: 3308745 • Letter: A
Question
After graduating with a physics degree, you get a job with the Naval Surface Warfare Center in Dahlgren, VA. The Navy wants a new airplane launcher for their aircraft carriers and you are on the design team. The launcher is effectively a large spring that pushes the plane for the first 5 meters of the 20 meter long runway. During that same time, the plane's jet engines supply a constant thrust of 5.4 x 104 N for the entire length of the runway. The 2,000 kg planes need to have a velocity of 45 m/s by the end of the runway. What should be the spring constant for the launcher?
Im asking for the solution in much detail, including a physics diagram of the problem, the eqautions needed for the problem laid out and the solution laid out. Please help thank you.
Explanation / Answer
Work done by thrust force = F.d
= (5.4 x 10^4) (20)
= 1.08 x 10^6 J
Work done by spring force,
= k d^2 /2
= k (5^2/2)
= 12.5 k
{ where k is spring constant.}
APplying work energy conservation,
Work done by spring forcer + work done by thrust force = change in KE
(1.08 x 10^6) + (12.5k) = 2000 (vf^2 - vi^2 )/2
(1.08 x 10^6) + (12.5k) = (1000)(45^2 - 0) = 2.025 x10^6
k = 75600 N/m
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