A rocket of mass 5 kg accelerates upward at a constant 4 g\'s for 5 sec starting

Question

A rocket of mass 5 kg accelerates upward at a constant 4 g's for 5 sec starting from rest. Assume the mass of the fuel is negligible so the mass of the rocket can be considered constant throughout the acceleration, (a) How much energy is imparted to the rocket during the first second? (b) How much energy is imparted to the rocket during the last second? (c) Is chemical energy that drives the rocket being expended at the same rate during the first second as during the hist second? (d) Explain why answers a and b are not the same. Where does the extra energy go?

Explanation / Answer

a) using Fnet = ma

F - mg = ma = 4mg

F = 5mg

and during first second,

d = ut + at^2 /2

d = 0 + (4x9.8)(1^2) /2

d= 19.6 m

Energy Emparted = work done = F.d = 5 mg (19.6)

= 5 x 19.6 x 5 x 9.8 = 4802 J

b) for last second.

d = d_5 - d_4 = (4 x 9.8 ) (5^2 - 4^2)/2 =176.4 m

W = F.d = 5 x 5 x9.8 x 176.4 = 43218 J

c) now energy transfer rate is different.

for last minute energy was transferred more rapidly.

d) energy over transferred over a displacement will be same not for some time interval.

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