# Toy Airplane Twirling Speed Calculation

## Centripetal Force Formula Application

**Explanation:** The question is asking us to determine how fast a child can twirl a 2 lb toy airplane on a 10 lb test fishing line before it breaks. To solve this, we will use the formula for centripetal force, which is given by **F = mv ^{2}/r**, where F is the force (in pounds) exerted by the line, m is the mass of the airplane converted into slugs (1 lb = 1/32.2 slugs), v is the tangential velocity in feet per second, and r is the radius of the circle in feet (half the diameter).

**Solving for v:**

Convert the mass to slugs: **m = 2 lb * (1/32.2 slugs/lb) = 0.06211 slugs.**

Find the radius of the circle: **r = diameter/2 = 5 ft / 2 = 2.5 ft.**

Insert the values into the centripetal force equation and solve for v: **10 = 0.06211 * v ^{2}/2.5.**

Multiply both sides by 2.5: **25 = 0.06211 * v ^{2}.**

Divide both sides by 0.06211: **402.25 = v ^{2}.**

Take the square root of both sides: **v = √402.25.**

Find the velocity: **v ≈ 20.06 feet per second.**

Therefore, a child can twirl the airplane at a speed of up to approximately 20.06 feet per second before the 10 lb test fishing line breaks.