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 13.5 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                meaure that the height of the rocket when the engine cuts off is 21.2 m. He also measures the rocket's peak height, which is 25.7 m. If the rocket has a mass of                0.663 kg, how much work is done by the drag force on the rocket during its ascent?

Explanation / Answer

Use the work energy theorem.

There are 3 different stages. There's lift-off, engine cutoff and peak height. Lets call these points 1, 2 and 3 respectively.

Use work energy between engine cut off and peak height first to determine kinetic energy at peak height.

KE2 + mgy2 = KE3 + mgy3

But KE3 = 0 since at peak height speed is zero.
Ke2 = mg(y3-y2)

Now that we have kinetic energy at point two, use the work energy theorem:

Ke1 + mgy1 + Wrocket + Wwind = KE2 + mgy2

KE1 = 0 since it begins at rest:
Wrocket + Wwind = KE2 + mg(y2-y1)

Wind work is negative, since F*D is negative. (The force acting on the object is opposite of direction of travel.)
Wr -Ww = KE2 + mg(y2-y1)

Solve for work due to wind:
Ww = Wr - KE2 -mg(y2-y1)
Ww = Fth*(y2-y1) - mg(y3-y2) - mg(y2-y1)
= Fth*(y2-y1) -mg(y3-y1). (Since y3-y2+y2-y1 = y3-y1)

= 13.5*21.2 - .663*9.81*25.7= 119.05J

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