Robert has just bought a new model rocket, and is trying to measure its flight c

Question

Robert has just bought a new model rocket, and is trying to measure its flight characteristics. The rocket engine package claims that it will maintain a constant thrust of 12.3 N until the engine is used up. Robert launches the rocket on a windless day, so that it travels straight up, and uses his laser range-finder to measure that the height of the rocket when the engine cuts off is 12.4 m. He also measures the rocket's peak height, which is 16.9m. If the rocket has a mass of 0.663 kg, how much energy is dissipated by the drag froce on the rocket during its ascent?

Explanation / Answer

Given that,

Thrust = Ft = 12.3 N ; engine cut off = He = 12.4 m ; peak height = Hp = 16.9 m ; M = 0.663 kg

We need to find the work done by drag force on the rocket during ascent. Let it be Wd.

As the engine is putting Ft force to lift the rocket for cut off height He, so the work done by the engine will be:

We = Ft x He = 12.3 x 12.4 = 152.52 J

This energy gets converted to KE, PE and a fraction of this is lost due to air drag.

When the rocket reaches the peak height of its flight, at this time the kinetic energy become zero because its velocity becomes zero(Remember velocity of projectile at its peak height is zero). At this time all the energy that the rocket has the gravitational potential energy PE.

PE = M g Hp = 0.663 x 9.81 x 16.9 = 109.92 J

Drag Force will then be:

Wd = We - PE = 152.52 J - 109.92 J = 42.6 J

Hence, Work done by the drag force = Wd = 42.6 Joules.

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