A Vulcan spaceship has a mass of 2.7*10^4 kg and a romulan spaceship is twice as

Question

A Vulcan spaceship has a mass of 2.7*10^4 kg and a romulan spaceship is twice as massive. Both have engines that generate the same total force of 8.3*10^6 N. Assume that the engines are fired for 6.7*10^1 s. What is the change in kinetic energy and change in momentum for both ships? Assume the the engines are fired for 6.7*10^1 m. What is the change in kinetic energy and change in momentum for both ships? A Vulcan spaceship has a mass of 2.7*10^4 kg and a romulan spaceship is twice as massive. Both have engines that generate the same total force of 8.3*10^6 N. Assume that the engines are fired for 6.7*10^1 s. What is the change in kinetic energy and change in momentum for both ships? Assume the the engines are fired for 6.7*10^1 m. What is the change in kinetic energy and change in momentum for both ships?

Explanation / Answer

Their accelerations are

a1 = F/m1 = 307.41 m/s^2
a2 = F/m2 = 153.7 m/s^2

Thus, their distances travelled for 67 s is

d1 = 1/2 a t1^2 = 689975 m
d2 = 344987 m

Thus, the work done on them is

W1 = Fd1 = deltaKE1 = 5.73*10^12 J
W2 = Fd2 = deltaKE2 = 2.86*10^12 J   [ANSWERS, CHANGE IN KE]

For the change in momentum,

J1 = J2 = F t = 5.56*10^8 N*s   [ANSWER]

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Here,

W1 = W2 = F d = 5.56*10^8 J   [ANSWER, delta KE]

t1 = sqrt(2d/a1) = 0.660 s
t2 = sqrt(2d/a2) = 0.9337 s

Thus,

J1 = F t1 = 5.48*10^6 N*s
J2 = F t2 = 7.75*10^6 N*s [ANSWER, change in momentum]

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