Calculating Thrust for Rocket Propulsion

Given Data

• Mass of the rocket: 15,000 kg
• Acceleration of the rocket: 2.5 m/s²

Problem

Determine the amount of force (thrust) required to propel the rocket upwards.

Key Concepts

• Weight of the rocket: Acts downward.
• Thrust (Propelling Force): Acts upward, opposing the weight.

Approach to Solution

Free Body Diagram

• Consider forces acting on the rocket:
  • Downward force: Weight (mg)
  • Upward force: Thrust (F_thrust)

Newton's Second Law of Motion

• Formula: ( F_{net} = ma )
• For a system at rest or moving with constant velocity, ( F = mg ), but the rocket is accelerating._

Equation Derivation

• Net force (acting upward): [ F_{thrust} - mg = ma ]_

Solving for Thrust

• Rearranging the equation: [ F_{thrust} = m(g + a) ]
  • ( g ) is acceleration due to gravity (9.8 m/s²).
  • ( a ) is given (2.5 m/s²).
  • ( m ) is given (15,000 kg)._

Calculation

• Substitute the values into the equation: [ F_{thrust} = 15,000 \times (9.8 + 2.5) ]
• Calculate to find the thrust required to propel the rocket upwards._

Conclusion

• The calculated thrust represents the force needed to propel the rocket with the given acceleration.

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