Question

Consider an object in uniform circular motion.

A.) If the trajectory and the mass of the object are unchanged, but the centripetal force is doubled, is the object's speed multiplied by a factor of 1, square root of 2, 2, or 4?

B.) If the mass of the object is halved and the radius of the circle quadrupled, while keeping the mass of the object the same, is the object's speed multiplied by a factor of1, square root of 2, 2, or 4?

C.) If the centripetal force is halved and the radius of the circle quadrupled , while keeping the mass of the object the same, is the object's speed multiplied by a factor 1, square root of 2, 2, 0r 4?

D.) If the centripetal force is furnished by a hook holding the object, describe, in one sentence, the direction and the magnitude of the force exerted by the object on the hook, assuming the object has mass m, the radius of the circle is R, and the speed of the object is v.

Answer 1

centripetal force,F= mv^{​​​​​2}/r

where, m is the mass of the object,v is the speed and r is the radius of circular motion

A. F' = 2F=mv'^{​​​​​​​​2}/r

v' = sqrt(2Fr/m)

v= sqrt(Fr/m)

v' = √2 v

B.

m'=m/2

r'=4r

F'= (m/2)v'^{​​​​​2}​​​​/4r

v' = sqrt(8Fr/m)

v= sqrt(Fr/m)

v' = 2√2v

C.

F'=F/2

r'=4r

v'=sqrt(2Fr/m)

v=sqrt(Fr/m)

v'= √2v

D.

F=mv_{​​​​​}^{​​​​​2}​​​​/r outwards