5 Examples of Solving Centripetal Force Problems - IB Physics

This paragraph introduces the concept of centripetal force and its application in physics problems. It outlines five different scenarios to illustrate how centripetal force operates in various situations. The explanation begins with horizontal circular motion, emphasizing that in a perfect horizontal circle, all vertical forces cancel out, simplifying the problem to forces in the x-direction. The paragraph also touches on vertical circular motion, noting that the net force must lie in the plane of the circle. Three initial situations are introduced, starting with an object on a horizontally spinning surface, where friction provides the centripetal force. The explanation includes a free body diagram and a force table to demonstrate the relationship between gravitational force, normal force, and friction.

The second paragraph delves into horizontal uniform circular motion with three distinct examples. The first scenario considers an object on a spinning horizontal surface, where the centripetal force is provided by friction. The paragraph explains how the force of friction is calculated and how it equates to mv^2/r. The second situation introduces an individual holding a bar while spinning, adding an applied force to the equation, which reduces the reliance on friction. The third example discusses a car turning, where the road's friction serves as the centripetal force. A banked road is then introduced as a design feature to reduce the dependency on friction, with a detailed explanation of the forces involved and how the normal force's components contribute to the centripetal force.

This paragraph presents a scenario where a ball attached to a wire is spinning in a horizontal circle, introducing the concept of tension at an angle. The explanation involves calculating the radius of the ball's path based on the wire's length and the angle of the wire. A free body diagram illustrates the forces acting on the ball: tension and gravity. The force of tension is then broken down into its components, and a force table is used to show how these components relate to the centripetal force mv^2/r. The paragraph concludes by demonstrating how to use the equations derived from the force table to find missing variables in the problem.

The fourth paragraph explores vertical circular motion, starting with a car going over a hill, which is conceptualized as part of a larger circular path with a 'radius of curvature.' The forces acting on the car are identified as gravity and the normal force, with the net centripetal force calculated as the difference between these two forces. The discussion then moves to a trough, where the normal force exceeds gravity, and the centripetal force is the sum of the normal force and gravity. The paragraph culminates with a complex example of a car navigating a loop-de-loop, requiring an understanding of the forces at play at various points along the loop to maintain circular motion.

The final paragraph focuses on determining the minimum velocity required for a car to successfully navigate a loop-de-loop. It explains that the centripetal force must equal the force of gravity at the top of the loop to maintain motion. As the car's velocity decreases, the centripetal force also decreases, necessitating adjustments in the other forces to maintain equilibrium. The paragraph describes the forces at the bottom, side, and top of the loop and how they contribute to the centripetal force. It concludes by emphasizing that the minimum velocity is when the centripetal force equals the force of gravity, and provides insights into the relationship between normal force, centripetal force, and gravity at different points of the loop.