Math Problem Statement
Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor. (a) The 1800 kg tractor exerts a force of 1.95 104 N backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0.100 m/s2, what is the mass of the airplane in kilograms? (b) Calculate the force (in N) exerted by the tractor on the airplane, assuming 2000 N of the friction is experienced by the airplane.
Solution
Let's solve the problem step by step.
Part (a) - Finding the mass of the airplane:
We are given:
- The force exerted by the tractor on the pavement: .
- The total resistive forces acting on the system: .
- The acceleration of the system: .
- The mass of the tractor: .
Now, to find the mass of the airplane, we'll apply Newton's second law to the system as a whole. The net force acting on the system is given by the difference between the force exerted by the tractor and the resistive forces:
From Newton's second law , we can solve for the mass of the airplane :
Solving for :
So, the mass of the airplane is 169200 kg.
Part (b) - Finding the force exerted by the tractor on the airplane:
We are given:
- The friction experienced by the airplane: .
We need to find the force exerted by the tractor on the airplane. Using Newton's second law for the airplane alone:
Substituting the values we know:
Solving for :
Thus, the force exerted by the tractor on the airplane is 18920 N.
Let me know if you need any details or have further questions!
Here are 5 questions that expand upon this topic:
- How would the force change if the resistive forces acting on the system increased?
- What happens to the acceleration if the mass of the airplane increases while keeping the tractor's force constant?
- How does the system behave if the friction experienced by the airplane doubles?
- How would the tractor’s force change if the acceleration increased to 0.200 m/s²?
- What is the significance of knowing the force of friction in systems like this?
Tip: Always ensure to subtract resistive forces when calculating net force in problems involving motion!
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Math Problem Analysis
Mathematical Concepts
Newton's Second Law
Force
Friction
Mass
Acceleration
Formulas
F_net = F_tractor - F_resist
F_net = (m_tractor + m_airplane) × a
F_tractor on airplane = F_airplane × a + F_friction
Theorems
Newton's Second Law of Motion
Suitable Grade Level
Grades 10-12
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