Question Video: Identifying the Origin of the Centripetal Force Physics • First Year of Secondary School

Video Transcript

A ball rolls along a horizontal circular path inside a hollow toroidal pipe, as shown in the diagram. Which of the following provides the centripetal force on the ball? (A) Tension in the pipe. (B) Gravitational force on the ball. (C) Friction of the ball with the surface of the pipe. (D) Normal reaction force on the ball.

Here, we are asked to identify the force that provides the centripetal force acting on the ball of the diagram. First, let’s recall the definition of centripetal force. The centripetal force 𝐹 of an object of mass 𝑚 that moves uniformly with speed 𝑣 along the circumference of a circle of radius 𝑟 is given by 𝐹 equals 𝑚𝑣 squared over 𝑟, where the term 𝑣 squared over 𝑟 is the centripetal acceleration.

Starting with option (A), we can observe that it is not a force of tension as it is not a force due to a string or other connector between two different objects. An example of this that would produce circular motion is a string that joins a ball to a point, forcing it to travel in a circle when in motion.

Option (B) suggests it is gravitational, but this is also not true. There is no mass in the center of the circumference that attracts the mass of the ball, like we expect in orbital systems. The Earth and Moon is an example of gravitational force maintaining a circular orbit.

Looking at option (C), we can also rule out that it is a friction force, because a frictional force would have to be in the opposite direction of the movement of the ball. Friction opposes motion. It cannot maintain a centripetal force.

This leaves us with option (D). A normal reaction force is a reaction force normal to, or in other words perpendicular to, a surface. The ball and the tube’s velocity at each point of contact in the tube suggests it is going to escape the circle it travels in, but it keeps running into the tube. The tube is exerting a force equal and opposite to the force of the ball being in constant contact with it.

The direction of the normal force would thus be normal to the point of contact between the ball and the tube, which would look like this. As the ball continues to travel, the normal reaction force will always be pointing towards the center of the circle, maintaining a centripetal force. Therefore, we can conclude that the correct answer is option (D), a normal reaction force on the ball.