 University of Virginia
Physics Department

## Newton's Second Law: F = ma

A Physical Science Activity

2003 Virginia SOLs

• PS.1
• PS.10

Objectives

Students will

• understand how motion depends on force;
• investigate the relationship between force, mass and acceleration as described by Newton's Second Law.

Motivation for Learning

Discrepant Event - Softball vs. Whiffle Ball

Materials
• Softball
• Softball with eyescrew in top
• Whiffle ball (same size as softball)
• String 0.75 m long
• Ring stand

Procedure

1. Tie one end of the string to the ring stand and the other end to the eyescrew on the softball.
2. Set the ring stand on a table. Adjust the height of the ball so that it hangs barely above the surface.
3. Place the whiffle ball at the edge of the table. Adjust the position of the ring stand so that, when the softball is swung, it will contact the whiffle ball and knock it off of the table.
4. Rotate the softball so that the eyescrew is at 90° and release it so that it hits the whiffle ball. Measure the distance traveled by the whiffle ball from the edge of the table.
5. Replace the whiffle ball with the softball. Repeat step 4. Measure the distance traveled by the softball. It should not travel as far as the whiffle ball.
6. Ask the class to explain the difference in the distance traveled by the two balls. How does this relate to Newton's Second Law?
7. Explain the relationship between mass and acceleration if the force is held constant. Background Information

In this experiment, the students will attempt to verify Newton's Second Law. This law states that a force on an object will cause it to accelerate in the direction of the force. The greater the force exerted on an object, the greater its acceleration. For any given force, the greater the mass of an object, the smaller its acceleration. This is written as:

 F = ma

In the experiment, a force will be applied to a cart using rubber bands. One student will hold the cart in place while the other attaches the rubber band. When the cart is released, it should move forward. Please remind the students to take care in releasing the cart, so that they do not impact its initial acceleration.

The distance traveled in this case will be directly proportional to its initial acceleration. Therefore, the greater the cart's initial acceleration, the farther it should move. Friction (another force) will eventually slow down and stop the carts. By measuring the total distance traveled, the students can determine the relationships between force and acceleration and between mass and acceleration. They are asked to plot their data. The resulting graph should look like this: The empty carts will travel greater distances for the same force than the carts containing a mass. The plot on the graph closer to the y-axis should represent the carts with the mass, while the plot farther away should represent the empty carts. This can be explained by the inverse relationship between mass and acceleration.

Special Note

In the following student procedure, it might be argued that using the unit of rubber bands might not be good pedgogy. In particular, what does 1 1/3 rubber band mean? You could have a spring scale present and have the students calibrate the length of rubber band pull in terms of Newtons. Once this is done, then one rubber band would correspond to a certain number of Newtons. ### Student Activity

To print out the Student Copy only, click here.

Materials

• Cart (20-25 cm long) -- available from Frey Scientific Catalog (1-888-222-1332); item number SO4480. • 10-32 x 1 1/4 " bolt and nut
• 3 large rubber bands
• 500 g mass
• Ruler
• Meter stick
• Masking tape
• Graph paper (8x11)

Procedure

1. Screw the bolt and nut through a hole at one end of the cart, so that the long end of the bolt forms a post at one end of the cart (see diagram below).
2. Place the cart on an open surface at least 5-6 m long (perhaps the floor). Mark its starting point on the surface with a piece of masking tape.
3. While one person holds the back of the cart, another should hook a rubber band around the front post.
4. Extend the rubber band about 35 cm in front of the car.
5. The person holding the back of the cart should let go, allowing the cart to roll forward.
6. Measure the distance the cart travels. Record this on the data table.
7. Replace the cart at its starting point. Repeat steps 2-5 with two rubber bands and then with three rubber bands.
8. Replace the cart at its starting point. Place the 500 g mass inside the cart.
9. Hold the cart, attach one rubber band and repeat steps 3-6. Repeat with two and three rubber bands.
10. Plot your data on a piece of graph paper. Label the y-axis (vertical) "Distance traveled" in units of meters. Label the x-axis (horizontal) "Force." The force unit will be the number of rubber bands attached to the cart. Draw two separate lines-one using the data from the empty carts, and another for the carts containing the 500 g mass.

Data Sheet

To print out the Data Sheet only, click here.

 Cart Type Distance Cart with one rubber band Cart with two rubber bands Cart with three rubber bands Cart with 500 g/ one rubber band Cart with 500 g/ two rubber bands Cart with 500 g/ three rubber bands

Questions

1. How is distance related to force in this experiment? To mass?

2. Describe the relationship between distance and acceleration. How would an increase or decrease in one value affect the other?

3. State Newton's Second Law in your own words. Do your results agree with this law? Why or why not?

Students with Special Needs

All students should be able to participate in this activity.

Click here for further information on laboratories with students with special needs. Assessment

Data sheet to be completed during the laboratory.