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The centripetal force of an object moving in a circle varies jointly with the mass of the object and the square of its velocity and
inversely as the radius of the circle. A 7-gram object moving in a circle with a radius of 25 centimeters and at velocity of
20 centimeters per second has a centripetal force of 112 dynes. Find the radius of the circle (in cm) on which of a 17-gram
object moving in a circle travels with velocity of 40 centimeters per second and the force on the object is 5,440 dynes. ​

Respuesta :

MathPhys

Answer:

5 cm

Explanation:

Centripetal force varies directly with mass and the square of velocity, and inversely with radius.  If k is the constant of proportionality:

F = k m v² / r

When m = 7 g, v = 20 cm/s, and r = 25 cm, then F = 112 dynes.  Solving for k:

112 = k (7) (20)² / 25

k = 1

When m = 17 g, v = 40 cm/s, and F = 5440 dynes:

5440 = 1 (17) (40)² / r

r = 5

The radius is 5 cm.

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