Toy Airplane Twirling Speed Calculation

How fast can a child twirl a 2 lb toy airplane above their head before a 10 lb test fishing line breaks? To find the maximum speed at which a child can twirl a 2 lb airplane on a 10 lb test fishing line without breaking it, the centripetal force formula is applied. After converting the mass to slugs, finding the radius of the circle, inserting values into the formula, and solving for the velocity, it is found that the child can twirl the airplane at approximately 20.06 feet per second.

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.

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