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Chapter 2: Problem 8

How does an object move when it is subject to a steady centripetal force? How does it move if that force suddenly disappears?

Short Answer

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#tag_title# Summary When an object is subject to a steady centripetal force, it moves in a circular path at a constant speed due to the force continuously changing the direction of the object's velocity. If that centripetal force suddenly disappears, the object will continue moving in a straight line with its instantaneous speed and direction at the moment the force disappeared, following a linear path tangent to the circle at that point. This behavior is due to Newton's first law of motion.

Step by step solution

01

Centripetal force and its effect on motion

Centripetal force is the net force acting towards the center of a circular path that keeps an object moving in a circle. This force is always perpendicular to the object's velocity. This means that the force doesn't do work on the object, but it causes a continuous change in the direction of the object's velocity, maintaining the circular motion. The centripetal force can be calculated using the formula: F_c = m * a_c = (m * v^2) / r, where F_c is the centripetal force, m is the mass of the object, a_c is the centripetal acceleration, v is the speed of the object, and r is the radius of the circular path. So, when subjected to a steady centripetal force, an object follows a circular path at a constant speed.
02

Removal of centripetal force

When the centripetal force suddenly disappears, there is no longer a force acting towards the center of the circle to maintain the circular motion. In this case, the object will continue moving in a straight line with its instantaneous speed and direction at the moment the force disappeared. This happens because of Newton's first law of motion, which states that an object in motion stays in motion at a constant velocity unless acted upon by an external force. Since the centripetal force is no longer present, the object follows a linear path tangent to the circle at the point where the force disappeared.

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