A mechanical centrifuge features a horizontal rotating arm with a heavy sample container secured at the outer end. During high-speed operation, the retaining bracket holding the container abruptly breaks, eliminating the inward force. According to the principles of circular motion and inertia, which of the following best describes the immediate trajectory of the sample container?
- AIt will fly directly outward along the radius, straight away from the center of the centrifuge.
- BIt will snap inward toward the center hub as an equal and opposite reaction to the break.
- It will travel in a straight line tangent to the circular path at the exact point of the break.Answer
- DIt will continue to curve but accelerate, because removing the restraining force inversely increases its acceleration.
Answer
The sample container will travel in a straight line tangent to the circular path.
The correct answer accurately describes the tangent path. When the inward centripetal force provided by the bracket is suddenly removed, there is no longer a net force acting on the container to pull it into a circular path. Due to inertia (Newton's First Law), the container will continue moving in a straight line at its current instantaneous velocity. Because the velocity vector is always tangent to the circular path at any given moment, the object will fly off in a straight, tangent line.
Step-by-Step Solution
Key Concept
Tangential Velocity and Inertia in Circular Motion