Question

The magnitude of the centripetal force acting on an object traveling in a horizontal circular path will decrease and if the

Answer 1

The magnitude of centripetal force will decrease if the radius of the circular path increases, as the force is inversely proportional to the radius of curvature while being directly proportional to the square of the velocity and the mass of the rotating body.

Step-by-step explanation:

The magnitude of the centripetal force acting on an object traveling in a horizontal circular path is influenced by several factors, including the mass of the object, its velocity, and the radius of the path. Newton's second law implies that the centripetal force, which is always directed towards the center of rotation, is essential in maintaining circular motion. If we use the formula Fc = mv2/r, where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius, it is clear that the centripetal force is directly proportional to both the mass and the square of the velocity, but inversely proportional to the radius.

Therefore, an increase in the radius of the circular path would result in a decrease in the centripetal acceleration and thus, a decrease in the centripetal force, as centripetal acceleration (ac = v2/r) is directly proportional to the square of the object's velocity and inversely proportional to the radius of curvature (r).

Answer 2

The radius of the path is increased

Step-by-step explanation:

The centripetal force is represented by the equation:

`F=(mv^2)/(r)`

where
`F` is the centripetal force,
`m` is the mass of the object on the circular path,
`v` is its velocity and
`r` the radius of the circle

From the equation we can observe that the centripetal force and the radius of the circular path are inversely proportional: if the radius increases the force decreases, and if the radius decreases the force increases.

Thus, the complete sentence is:

The magnitude of the centripetal force acting on an object traveling in a horizontal circular path will decrease and if the radius of the path is increased