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 = mv2/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 * v2/2.5.
Multiply both sides by 2.5: 25 = 0.06211 * v2.
Divide both sides by 0.06211: 402.25 = v2.
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.