Active Physics160

Chapter 2 Physics in Action

Physics WordsNewton’s second law of motion: the acceleration of an object is directly proportional to the unbalanced force acting on it and inversely proportional to the object’s mass. The direction of the acceleration is the same as the direction of the unbalanced force.

NEWTON’S SECOND LAW OF MOTIONEvidence for Newton’s Second Law of Motion

In the Investigate, you observed that it was difficult to push on an object with a constant force because the object would move faster and faster. This observation that a constant force produces an acceleration is very important in physics.

You also found that if you pushed on a more massive object with the same force, it did not accelerate as much. This observation that the acceleration decreases with an increase in mass is also very important.

Based on observations from investigations similar to yours, Isaac Newton wrote his (Newton’s) second law of motion: The acceleration of an object is directly proportional to the unbalanced force acting on it and is inversely proportional to the object’s mass. The direction of the acceleration is the same as the direction of the unbalanced force.

You saw the evidence for Newton’s second law in the Investigate. When you pushed an object with a small force, the object had a small acceleration. The speed of the object increased, but not very quickly. When you pushed the object with a large force the object had a large acceleration. Newton’s second law states this: “The acceleration of an object is directly proportional to the unbalanced force acting on it.” This is a mathematical way of saying that the larger force produces a larger acceleration. As the force gets larger, the acceleration gets larger — a direct proportion. In this Investigate, the force was a push.

You also found that the same force on a small mass produced a larger acceleration than it did on a large mass. Newton’s second law states this, “The acceleration of an object is… inversely proportional to the object’s mass.” This is a mathematical way of saying that the larger the mass, the smaller the acceleration. As the mass gets larger, the acceleration gets smaller — an inverse proportion. To achieve a big acceleration, you need to apply a large force to a small mass.

In one of the most important science books of all time, Principia, Isaac Newton wrote his second law of motion. It is interesting both historically and in terms of understanding physics to read Newton’s second law in his own words:

“The change in motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”

Physics Talk

Active Physics165

Section 3 Newton’s Second Law: Push or Pull

Determining the Number of Significant Figures in a Measurement

There are guidelines that you can use to determine the number of significant figures in a measurement.

All nonzero numbers are considered to be significant figures. In the measurement 152.5 m, all the digits are significant. The measurement has four significant figures.

Zeros may or may not be significant, depending on their place in a number.

• A zero between nonzero digits is a significant figure. In the measurement 308 g, the zero is significant. The measurement has three significant figures.

• A zero at the end of a decimal number is considered significant. In the measurement 1.50 N, the zero is significant. The measurement has three significant figures.

• A zero at the beginning of a decimal number is not significant. In the measurement 0.023 kg, the zeros are not significant. The measurement has two significant figures.

• In a large number without a decimal point, the zeros are not significant. In the measurement 2000 kg, the zeros are not significant. The measurement has one significant figure. However, if the zeros in 2000 were significant, it would be written as 2000. or in exponential notation as 2.000 × 103.

Significant Figures in Calculations

There are also guidelines that you can use when making your calculations.

Adding and Subtracting

When adding or subtracting, the final result should have the same number of decimal places as the measurement with the fewest decimal places.

Multiplying and Dividing

When multiplying or dividing, the result should have no more significant digits than the factor having the fewest number of significant digits.

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