The Greatest Acceleration a Man Can Give to an Airplane
What is the greatest acceleration the man can give the airplane when pulling the cable at an angle of 6.8° above the horizontal?
Answer:
The greatest acceleration the man can give the airplane, when pulling the cable at an angle of 6.8° above the horizontal, is approximately 0.259 m/s^2.
Understanding the Calculation:
To find the exact numerical values, let's break down the equations and calculations:
- Calculate the maximum tension in the cable:
- Calculate the maximum acceleration:
Tension_horizontal = μ * m_man * g * cos(6.8°)
Given values are: μ = 0.98, m_man = 82 kg, g = 9.8 m/s^2, and the angle = 6.8°
Plugging in these values, we get:
Tension_horizontal ≈ 790.275 N
a = (Tension_horizontal - μ * m_man * g) / m_man
Plugging in the calculated tension and values, we get:
a ≈ 0.259 m/s^2
Therefore, based on the calculations, the greatest acceleration the man can give the airplane when pulling the cable at an angle of 6.8° above the horizontal is approximately 0.259 m/s^2.