Math Problem Statement
Solution
Let me solve this problem step-by-step:
Given Data:
- Mass of the airplane,
- Initial velocity,
- Final velocity, (since the plane stops)
- Stopping distance,
- Reverse thrust force,
We need to calculate:
- The deceleration ().
- The additional force of friction required to stop the plane ().
- The minimum coefficient of friction ().
1. Finding Deceleration ():
We can use the kinematic equation: Rearranging for : Substituting the values: Thus, the deceleration is .
2. Finding Additional Force of Friction ():
Using Newton's Second Law, the total force required to stop the plane is: Substituting the values:
The reverse thrust provides . The additional force of friction required is: Thus, (acting opposite to the motion).
3. Finding Minimum Coefficient of Friction ():
The force of friction is related to the normal force () and the coefficient of friction: Here, , where :
The minimum coefficient of friction is: Substituting the values:
Final Results:
- Deceleration of the airplane:
- Additional force of friction required:
- Minimum coefficient of friction:
Would you like further details on any step? Here are some follow-up questions for further exploration:
- How would the stopping distance change if the reverse thrust were doubled?
- What if the coefficient of friction was only —would the plane still stop in time?
- How would the problem change if the mass of the airplane were increased?
- Can you derive the deceleration formula from basic principles of kinematics?
- How does air resistance influence stopping forces in real-world scenarios?
Tip: Always check your units to ensure consistency throughout calculations.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Newton's Laws of Motion
Forces and Friction
Formulas
v_f^2 = v_i^2 + 2ad
F = ma
F_friction = μF_normal
Theorems
Newton's Second Law of Motion
Suitable Grade Level
Grades 11-12
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