a cylindrical metal strut that forms part of a landing gear of a jet aircraft has a diameter of 24mm and is 0.35m long.during landing the maximum compressive force reaches a value of 50kn
Assuming that the elastic limit of the strut is not exceeded calculate the reduction in length of the strut under this compressive force
the young modulus for the metal is 80GNm-2
please help i found that the area is : 4.52 x 10^-4 m2
To calculate the reduction in length of the strut under the compressive force, you need to use Hooke's Law, which states that the strain (change in length) of an object is directly proportional to the applied stress (force per unit area).
First, calculate the area of the strut:
Given that the diameter is 24 mm, we can find the radius by dividing it by 2:
Radius = 24 mm / 2 = 12 mm = 0.012 m
To find the area of the circular cross-section of the strut, use the formula:
Area = π * radius^2
Area = π * (0.012 m)^2
Now, we can calculate the area:
Area = 3.14 * (0.012 m)^2 = 0.00452 m^2 (rounded to 5 significant figures)
The maximum compressive force (stress) is given as 50 kN. To convert it from kilonewtons to newtons:
50 kN = 50,000 N
Now, we can use Hooke's Law to calculate the strain (change in length) of the strut:
Stress = Young's modulus * Strain * Area
Rearranging the equation:
Strain = Stress / (Young's modulus * Area)
Given:
Young's modulus = 80 Giga Newtons per square meter (80 GN/m^2)
Area = 0.00452 m^2
Stress = 50,000 N
Substituting the values into the formula:
Strain = 50,000 N / (80 GN/m^2 * 0.00452 m^2)
Calculating the strain:
Strain = 0.00309 (rounded to 5 decimal places)
The strain represents the fractional change in length, so to calculate the reduction in length, multiply the strain by the original length of the strut.
Given:
Length of the strut = 0.35 m
Reduction in length = Strain * Length of the strut
Reduction in length = 0.00309 * 0.35 m
Calculating the reduction in length:
Reduction in length = 0.00108 m (rounded to 5 decimal places)
Therefore, the reduction in length of the strut under this compressive force is approximately 0.00108 meters.