An aircraft accelerating has a velocity of 40 m/s at an instant. It has 600kN weight and an upward lift force of also 600kN. It has an engine thrust in the forward direction of 500kN and air resistance opposing with 200kN force. At what rate is its kinetic energy increasing?
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Answer:
Now we deal with the case where the mass of an object is changing. We analyze the motion of a rocket, which changes its velocity (and hence its momentum) by ejecting burned fuel gases, thus causing it to accelerate in the opposite direction of the velocity of the ejected fuel (see (Figure)). Specifically: A fully fueled rocket ship in deep space has a total mass
m
0
(this mass includes the initial mass of the fuel). At some moment in time, the rocket has a velocity
→
v
and mass m; this mass is a combination of the mass of the empty rocket and the mass of the remaining unburned fuel it contains. (We refer to m as the “instantaneous mass” and
→
v
as the “instantaneous velocity.”) The rocket accelerates by burning the fuel it carries and ejecting the burned exhaust gases. If the burn rate of the fuel is constant, and the velocity at which the exhaust is ejected is also constant, what is the change of velocity of the rocket as a result of burning all of its fuel.