Newton's Third Law of Motion: Action-Reaction

Sir Isaac Newton (1642–1727), the famous British scientist credited with discovering gravity, also gave us three laws describing motion. Newton's first law of motion states that a force is needed to change the motion of an object. In other words, a force either starts an object moving or causes a moving object to stop. His second law of motion explains how the force needed to accelerate (change in velocity) an object depends on the mass of the object. His third law explains that forces act in pairs.

In this project, you will demonstrate Newton's third law of motion, that every action has an equal and opposite reaction due to the action of forces in pairs. You will also determine how pairs of forces that are equal but in opposite directions can produce motion.

Getting Started

Purpose: To demonstrate Newton's third law of motion.

Materials

• pencil
• 5-ounce (150-ml) paper cup
• 40 to 50 pennies
• 12-inch (30-cm) piece of string
• handheld spring scale

Procedure

1. Use the pencil to make two holes across from each other just beneath the rim of the cup. Place the coins in the cup.
2. Loop the string through the holes, then tie the ends of the string between the holes.
3. Hold the scale and adjust it so that it reads zero.
4. While holding the scale, attach the cup so that the cup hangs freely. Observe the reading on the scale.

Results

The cup pulls the scale down so that the measurement on the scale indicates the weight of the cup and the coins.

Why?

Newton's third law of motion states that for every action, there is an equal and opposite reaction due to pairs of forces. In other words, Newton realized that if one object applies a force on another, the second object applies an equal force but in the opposite direction on the first object. You can be sure that two forces are action-reaction pairs of forces if the reverse description of one force describes the other force. In Figure 6.1, the three identified action-reaction pairs of forces are: A/A₁; B/B₁; C/C₁. The description of force A is "the hand acts on the scale," and the description of force A₁ is "the scale acts on the hand." One description is the reverse of the other, so the forces are equal in magnitude, but in opposite directions. Thus forces A and A₁ are action-reaction pairs.

Try New Approaches

The scale attached to the cup measures the downward force of the cup (the action). How can the upward force of the hand (the reaction) be measured? Repeat the experiment, using two scales. First hang one scale from the other. So that the weights of the scales are not considered, while holding the top scale (A), adjust the scales so each reads zero. Attach the cup to the bottom scale (B) as before. Scale A measures the upward force (the reaction), and scale B measures the downward force (the action).

Science Fair Hint: A diagram showing the action-reaction pairs can be used as part of a project display.

Design Your Own Experiment

1. Every force on an object causes the object to be compressed to some degree. Design an experiment to demonstrate that an object compresses until the action-reaction forces are equal. For example, fill a 3-ounce (90-ml) cup with coins. Lay two similar-size books about 10 inches (25 cm) apart on a table. Support the ends of a thin, flexible, plastic ruler on the books. Set the cup of coins in the center of the ruler.



Science Fair Hint: Make a diagram showing the compression of the ruler and the action-reaction pairs of forces, such as in Figure 6.3. Three legends describing the force pairs of the books and the cup can be added to the drawing. For example:

Force Pairs, Book A

• Ruler acts on book A.

Book A acts on ruler.

• Book A acts on table.

Table acts on book A.

• Table acts on Earth.

Earth acts on table.

2. Unaccompanied forces do not exist. Since all forces are in pairs of equal strength and acting in opposite directions and acting on different objects, what causes motion? A resultant force is the single force that has the same effect as the sum of two or more forces acting simultaneously on an object. When forces simultaneously act on an object and the resultant force is zero, the forces are said to be balanced forces and produce no acceleration. Acceleration is a change in velocity (speed and direction of a moving object) per unit of time. When the resultant force of a group of forces acting simultaneously on an object is not equal to zero, the forces are said to be unbalanced forces. Newton's first law of motion explains that an unbalanced force acting on the object is needed to cause acceleration. In this law, the resultant force is the net force (the sum of all forces acting simultaneously on an object).

Design an experiment to demonstrate that a pair of action-reaction forces are unbalanced because they act on different objects. One way is with two identical balloons. Inflate one of the balloons and tie a knot in its open end. Lay the balloon on a table and observe any motion of the balloon. Repeat using an inflated balloon that is not tied.

Science Fair Hint: Prepare a diagram representing the action-reaction forces for the open and closed balloon, such as in Figure 6.4. Add the calculations for determining the net force of the gas inside the balloon on the balloon, represented by forces A as well as the net force of the balloon on the gas inside the balloon, represented by forces B. The equation for net force is:



The calculation for determining the net force of the gas on the balloon in the closed balloon is:



The equation representing the net forces of the gas acting on the open balloon is:





In the closed balloon, the action reaction pairs are A₁B₁, A₂/B₂, A₃/B₃. and A₄/B₄. As shown by the calculations, the net force of the gas acting on the balloon is zero. Therefore there is no unbalanced force, and thus no motion of the balloon caused by the gas acting on it. In the open balloon, the action reaction pairs are also A₁B₁. A₂/B₂, and A₃/B₃. As shown by the calculations, the net force of the gas acting on the balloon is equal to force A₁↑. While A₁↑ and B₁↓, are action-reaction pairs acting in different directions, they each act on different objects, thus are unbalanced forces. The unbalanced force of A₁↑ acting on the balloon, causes the balloon to move in the direction of this force. Use the net force equation to calculate the net force of the balloon on the gas inside the open and closed balloon to determine why the gas moves out of the open balloon.

Get the Facts

1. The use of steam as a source of power can be traced back to a toy invented by a Greek engineer named Hero of Alexandria (20?-62?). This toy turned as a result of action-reaction forces. For information about the construction of Hero's toy and how the action-reaction forces were produced, see Struan Reid and Patricia Fara, Inventors (fulsa, Okla.: EDC, 1994), p. 10.
2. A Hero's engine can be made from a soda can. For information about building this simple Hero's engine and making predictions about its movement, see Robert Ehrlich, Why Toast Lands Jelly-Side Down (Princeton, N.J.: Princeton University Press, 1997), pp. 69-71.

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