Newton’s Third Law: A Verification with Buoyancy Forces

Barry Feierman - April 2013 SEPS/AAPT Drexel University

Newton’s Third Law is the “law of interaction”. For every force that acts on one object, there is an equal force (equal is size, opposite in direction) that acts on a second object. Thus, this law is often called the “Law of Action and Reaction”. This law will be tested using buoyancy forces and a Vernier Force plate and Vernier Dual-Range Force meter.

A metal can filled with soup has a density overall slightly greater than water. When the can is lowered into a big beaker of water, the can will sink. But as it sinks, it has an upward (buoyant) force acting on it from the water. The pressure on the bottom of the can from the water pushing the CAN upwards is greater than the pressure on the top of the CAN from the water, pushing the can downwards, since the bottom of the can is at a greater depth in the fluid, the water. Pressure in a fluid increases linearly with depth. Thus, there is an imbalance on the forces acting on the CAN by the WATER. This difference in pressure causes an upwards “buoyancy” force on the can. For more details, consult Archimedes’ Principle relating the buoyant force to the weight of the “displaced” fluid.

However, from the point of view of the water in the beaker, what is happening? If the water exerts an upwards force on the CAN, then does the CAN exert an equal and opposite DOWNWARDS force on the water and beaker (Newton’s Third Law)? If so, then the water (and the beaker) should “weigh more” when the CAN is lowered into the WATER. In fact, if the CAN loses N newtons of weight due to the buoyancy of the water, then the BEAKER of WATER should GAIN the same N newtons of force. We will test this idea using two Vernier force sensors, Logger Pro software, a soup CAN, and a large BEAKER and some water.

A Vernier Dual-Range Force Meter (0-50N) is used to “weigh” a can of soup when suspended in air. For the moment, ignore the buoyancy effect of the air since it is so small. The CAN of soup is attached to the force sensor by some string. A Vernier Force Plate Meter (0-850N) is used to measure the weight of a large beaker filled partially with water. We will record the weight of the CAN both before and after lowering it into the large beaker of water. We will record the apparent CHANGE in the can’s weight due to the buoyancy of the water.

We will also record the weight of the BEAKER of WATER before and after lowering the CAN into the water. We will find the apparent CHANGE in weight of the Beaker of Water due to the buoyant effect it has on the can of soup.

Our experiment will use Vernier’s Logger Pro to record data for 20 seconds at 50 samples per second. If the CAN of soup loses a weight N newtons, and if the BEAKER of water gains the same weight N newtons, then it looks like Newton’s Third Law is confirmed.

We will now examine each graph in more detail. Here is the graph for the CAN of soup as it is lowered into the water in 20 seconds.

Before can is lowered W = 9.8 N

After can is lowered under water W = 1.0 N

Loss in weight when can is under water = 8.8 N with a margin of error (std dev) of +/- 0.1 N

Here is the graph for the BEAKER of WATER before and after the CAN of soup is lowered into the water.

Beaker of water before can is lowered: W = 30.6 N

Beaker of water after can is lowered: W = 39.5 N

Gain in weight of Beaker and Water: W = 8.9 N

The Vernier Force Plate sensor readings have a standard deviation of +/- 0.3 N

Finally, we ADD the weight of the CAN of soup to the weight of the Beaker of Water by adding the force values of the two Force Sensors.

Notice that the SUM of the two force sensors remains constant: W = 40.5 N both before, during, and after the can of soup is lowered into the beaker of water.

Have we verified Newton’s Third Law by studying buoyancy of a soup can while lowered into a beaker of water?

Barry Feierman [email protected]