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# Linear Inertia: Resistance to Change in Linear Motion (page 2)

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Author: Janice VanCleave

### Try New Approaches

As the angle between ramp B and the surface decreases, the decelerating force on the ball decreases. How does the decrease in the decelerating force affect the distance the ball rolls up ramp B? Determine this by repeating the investigation three times, decreasing the angle of ramp B only to 40°, 20°, and 0°. Add an extension to ramp B if necessary. Using your results, explain how Galileo's results from a similar experiment made him aware that without an incline or friction, the ball would roll forever. In other words, how did Galileo determine that objects have inertia?

### Design Your Own Experiment

1.
1. Mass is the amount of matter in an object and is a measure of inertia. As mass increases, inertia of an object increases. (Matter is the substance of which physical objects consist; anything that takes up space and has mass.) Design a way to determine the mass of an object by measuring its inertia. One way is to design and calibrate an inertia balance, which is an instrument that determines mass due to the periodic motion (the motion of an object, such as a back-and-forth motion, that is repeated in each of a succession of equal time intervals) of the balance. This can be done using a thin hacksaw blade and coins. To avoid being cut, cover the teeth of the blade with a strip of masking tape. Then tape the blade to the edge of a table. Fill an empty plastic 35-mm film canister about one-fourth full with modeling clay. Push the clay down so it is secure and its surface is relatively flat. Tape the canister to the free end of the blade. Push a cotton ball into the canister. Calibrate the balance (blade ÷ canister) using a standard mass, such as a penny.
2. First determine the time of 25 oscillations with no pennies. Place the cap on the canister. Then cause the balance to vibrate (repeatedly swing or move back and forth) by pulling it to one side and releasing. Using a stopwatch, determine the time of 25 oscillations. Begin timing the oscillations as soon as you let go of the blade. One oscillation is when the film canister swings out then returns to its original position. Calculate the period (T), which is the time it takes a vibrating object to complete one vibration or oscillation (to swing or move back and forth) using this formula:

T = period (time/oscillations)

For example, if it takes 10 seconds for 25 oscillations, the period would be:

T = 10 sec/25 oscillations
= 0.4 sec/oscillation

Record the period in an Inertia Data table like Table 8.2. Repeat the procedure four times and average the results. Then place one penny in the canister and repeat the procedure. Continue the procedure, adding one coin at a time until a total of 10 coins are used.

3. Use a food scale to determine the mass in grams of one penny by measuring the mass of one hundred pennies and dividing by 100. Then use the mass of one penny to calculate the mass of each number of pennies from one to ten. Use the mass of each number of pennies and the period (T) for each number to create a mass vs. period graph with mass on the x-axis and period (T) on the y-axis.
4. The mass of an object, such as other coins or a metal washer that will fit in the canister, can be determined by measuring its time for 25 oscillations, calculating its period (T), and comparing this period to mass on the mass vs. period graph from part b.
5. Another way to determine the mass of an object is to use the relationship between mass and period, which can be expressed by this equation:
6. in which m1 is the unknown mass and m2 is the known mass (penny). T1 and T2 are their respective periods. To determine the unknown mass, the equation can be written as:

### Get the Facts

Galileo was one of many great scientists whom Sir Isaac Newton (1642—1727) said he was influenced by when he formed his ideas about motion. Newton described three laws of motion, the first being the law of inertia. How does inertia affect objects at rest? How does inertia affect the direction and the speed of an object in motion? For more information, see Robert Garner, Experiments with Motion (Springfield, N.J.: Enslow, 1995), pp. 7-17.

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