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 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 meaure that the height of the rocket when the engine cuts off is 10.2 m 10.2 m . He also measures the rocket's peak height, which is 14.7 m 14.7 m . If the rocket has a mass of 0.663 kg 0.663 kg , how much work is done by the drag force on the rocket during its ascent?

Answer 1

Answer:

The work done by the drag force is given by 29.96 J

Explanation:

Given :

Thrust force $F = 12.3$ N

Displacement $d = 10.2$ m

Mass of rocket $m = 0.663$ Kg

From work energy theorem,

  $W = \Delta K$

 $W_{t} - Wd - W_{g} = KE$

Where $W_{t} =$ thrust work $W_{g} =$ gravitational work

$KE = 12.3 \times 10.2 -Wd - 0.663 \times 9.8 \times 10.2$

$KE = 59.2 -Wd$

After cutoff kinetic energy is converted into potential energy,

$KE = Wd' + mg\Delta h$

Put value of KE

$59.2 -Wd = Wd' + 0.663 \times 9.8 \times 4.5$

Work done by drag force is given by,

$Wd'+Wd = 59.2 -29.23$

                 $= 29.96$ J

Therefore, the work done by the drag force is given by 29.96 J