If the pilot cannot exceed 6.0 gg , or 6.0 times the normal acceleration of gravity, what is the tightest circle (smallest radius) in which the plane can turn?

Express your answer using two significant figures.

The problem asks for the smallest radius \( r \) in which the plane can turn, given that the pilot cannot exceed a maximum acceleration of \( 6.0 \, g \), where \( g \) is the acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \)).

The centripetal acceleration \( a_c \) for an object moving in a circular path is given by:

\[
a_c = \frac{v^2}{r}
\]

where \( v \) is the speed of the plane, and \( r \) is the radius of the turn. The maximum centripetal acceleration the pilot can handle is \( a_c = 6.0 \, g = 6.0 \times 9.8 \, \text{m/s}^2 \).

Thus,

\[
6.0 \times 9.8 = \frac{v^2}{r}
\]

Solving for \( r \), we get:

\[
r = \frac{v^2}{6.0 \times 9.8}
\]

To find the radius, we need the speed of the plane, \( v \). Could you provide the speed of the plane, or is there any other detail missing?

Once you provide this, I can complete the calculation.

Would you like to clarify anything or continue? Here are some related questions:

1. How does centripetal acceleration vary with speed?
2. What role does mass play in circular motion at constant speed?
3. What other factors limit a plane’s turning radius?
4. How is “g-force” experienced differently by pilots and passengers?
5. Why does increasing speed increase the turning radius?

**Tip:** Remember that the turning radius increases with speed at a given level of centripetal acceleration.

If the pilot cannot exceed 6.0 gg, or 6.0 times the normal acceleration of gravity, what is the tightest circle (smallest radius) in which the plane can turn? Express your answer using two significant figures.

Learn how to calculate the smallest turn radius of a plane where the pilot cannot exceed 6.0 times the acceleration due to gravity (6.0 g). This problem involves concepts like centripetal force, circular motion, and Newton's laws, and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation