Calculating Thrust Required to Propel a Rocket

Problem Statement

• Objective: Determine the thrust needed to propel a rocket upward.
• Given:
  • Mass of the rocket: 15,000 kg
  • Acceleration required: 2.5 m/s²

Forces Acting on the Rocket

• Weight (W): Acts downward
• Thrust (F_thrust): Acts upward, propelling the rocket
• Acceleration Due to Gravity (g): 9.8 m/s²

Key Concepts

• Newton's Second Law of Motion: F = ma
  • The net force (F) is the sum of all forces acting in one direction.
  • When the rocket is accelerating, use this law to determine the equation of motion.

Calculating Net Force

• Equation:
  • Net Force, F_net = F_thrust - mg
    • F_net is the difference between the upward thrust and downward weight
    • F_thrust and mg act in opposite directions (upward and downward respectively)

Solving for Thrust

• Formula: F_thrust = m(g + a)
  • m: Mass of the rocket (15,000 kg)
  • g: Acceleration due to gravity (9.8 m/s²)
  • a: Acceleration of the rocket (2.5 m/s²)
• Calculation: Substituting the given values to find thrust.

Conclusion

• The thrust force required is calculated using the given formula.
• This force allows the rocket to accelerate upward with the specified acceleration.

Additional Notes

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