Landing Airplane Wheel Homework: Solving (a)-(e)

In summary, the conversation discusses the analysis of a landing airplane wheel in terms of its mass, radius, and moment of inertia. The goal is to calculate the velocity of the wheel when it stops slipping, the length of the skid mark it would leave on the runway, and the amount of energy lost to friction. This involves considering the force and coefficient of friction between the wheel and the ground, as well as the initial and final kinetic energies of the wheel. The conversation also mentions comparing the energy loss to the product of the force of gravity and the length of the skid mark, and suggests using a distance multiplied by the friction force to calculate the energy loss.
  • #1
diracy
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Homework Statement


Consider a wheel of a landing airplane. The wheel has mass M, radius
R, and moment of inertia around its axis [itex]\alpha[/itex]MR^2.
The wheel lands on the ground with horizontal
velocity v, but does not rotate before it touches the ground.
(a) Calculate the velocity of the wheel when it stops slipping. Assume that the wheel presses on
the ground with force Mg and the coecient of friction is . Once the wheel no longer slips it
moves with constant velocity. (b) Find the length of the skid mark this wheel would leave on the
runway. (c) Compute the amount of energy lost to friction by subtracting the nal kinetic energy
of rotation and linear motion from the kinetic energy of the wheel before it hit the ground. (d)
Compare the energy loss to Mg times the length of the skid mark. (These two should not be
the same!) (e) Figure out how to calculate the energy loss by multiplying the friction force by a
distance. Figuring out which distance it is requires some thought if you haven't seen this before

Homework Equations


The Attempt at a Solution



I was able to do (a), (b), and (c) but I am stuck with d and e. Can someone give me some guidance?
 
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  • #2
any help here?
 

Related to Landing Airplane Wheel Homework: Solving (a)-(e)

1. How do you determine the weight of an airplane wheel for landing?

The weight of an airplane wheel for landing is determined by several factors such as the type and size of the aircraft, the number of wheels needed for proper support, and the weight capacity of the wheels. This information is usually provided by the manufacturer and can also be calculated using mathematical equations based on the specific aircraft's specifications.

2. What is the purpose of solving for the weight of an airplane wheel for landing?

The weight of an airplane wheel for landing is a crucial factor in ensuring the safety and stability of the aircraft during takeoff and landing. By accurately calculating the weight, the proper amount of force and pressure can be applied to the wheels, preventing any potential accidents or malfunctions. It also helps in determining the overall weight and balance of the aircraft, which is essential for flight performance.

3. How do you account for variations in the weight of an airplane wheel for landing?

There are several factors that can cause variations in the weight of an airplane wheel for landing, such as weather conditions, cargo weight, and passenger weight. To account for these variations, aircraft manufacturers typically provide a range of acceptable weights for the wheels, taking into consideration these factors. Pilots also use weight and balance calculators to ensure the aircraft is within the safe weight limits before takeoff.

4. Do all airplanes use the same type and weight of wheels for landing?

No, different types and sizes of aircraft require different types and weights of wheels for landing. Smaller airplanes may only require single or dual wheels, while larger commercial aircraft may need multiple sets of wheels for proper support. The weight of the wheels also varies depending on the weight capacity of the aircraft and the type of terrain it will be landing on.

5. Why is it important to follow the manufacturer's recommended weight for landing airplane wheels?

It is crucial to follow the manufacturer's recommended weight for landing airplane wheels to ensure the safety and stability of the aircraft. These weight recommendations are carefully calculated and based on the aircraft's specifications and performance capabilities. Deviating from these recommendations can result in improper weight distribution, causing the aircraft to be unbalanced and leading to potential accidents.

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