A Physics Lesson from a Ketchup Bottle

It happens to all of us. We reach into the fridge and pull out the ketchup bottle only to that find the remainder of ketchup is clinging for dear life at the bottom of the bottle. There are two well known practices of getting the remainder of the ketchup out of the bottle. Either you place the bottle on its head and wait for gravity to do its job, or you shake the ketchup down. But, I'm here to tell you there is a third and more efficient way to get that last bit of ketchup out of the bottle.

Hold the bottom of the ketchup bottle and make sure the lid is secured tightly. Then swing your arm around in a quick circle a few times. When you stop all of the ketchup should be at the top of the bottle. How does this work? Centripetal and centrifugal forces!

Centripetal force is plainly defined at the force exerted on an object towards the center when moving in a circular motion. Centrifugal force is the opposing force exerted on an object to move it away from the center. Both of these forces are required to understand what is happening in our ketchup bottle.

It is helpful to break the bottle and the ketchup into their own force diagrams while maintaining the rotating reference frame. Since you are holding onto the bottle, your hand is exerting the centripetal force necessary to keep the bottle on its circular path. However, there is nothing holding onto the ketchup. Therefore, the centripetal force acting on the ketchup is zero. 

This causes an unbalanced force to act on the ketchup. Remember what Newton's First Law states? "An object at rest tends to stay at rest and an object in motion tends to stay in motion in the same direction and speed unless acted upon by an unbalanced force." Therefore, the ketchup accelerates away from the center of circular motion until it hits the lid, which subsequently exerts the centripetal force towards the center of the circular motion to stop the flow of ketchup.

Give this technique a "whirl" the next time you need to get the remaining bit of ketchup out of the bottle and impress your friends and family with your knowledge of Physics!