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1.3 Newton's second law of motion  (Page 4/7)

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Mass and weight

In this activity you will use a scale to investigate mass and weight.

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  • 1 scale
  • 1 table ( [link] )
  • Organisms: This lab uses organisms that can pass on diseases.

  1. What do bathroom scales measure?
  2. When you stand on a bathroom scale, what happens to the scale? It depresses slightly. The scale contains springs that compress in proportion to your weight—similar to rubber bands expanding when pulled. Newton’s 1st law : F n e t = 0   o r     ( ∑ F = 0 )
  3. The springs provide a measure of your weight (provided you are not accelerating). This is a force in newtons (or pounds). In most countries, the measurement is now divided by 9.80 to give a reading in kilograms, which are units of mass. The scale detects weight but is calibrated to display mass.
  4. If you went to the Moon and stood on your scale, would it detect the same “mass” as it did on Earth? How about:
    1. Mars
    2. Venus
    3. Saturn

This table shows the differences in mass and weights on different planets.
Planet Mass Weight: ( F n e t = 0   o r     ( ∑ F = 0 ) )
Mars 12 kg 5N
Venus 20 kg 90N
Saturn 1 kg 13N

[link]

Explain that, even though a scale gives a mass, it actually measures weight. Scales are calibrated to show the correct mass on Earth. They would give different results on the Moon, because the force of gravity is weaker on the Moon.

Only net external force impacts the acceleration of an object. If more than one force acts on an object and you calculate the acceleration by using only one of these forces, you will not get the correct acceleration for the object.

Newton’s second law of motion

This video reviews Newton's second law of motion ( F n e t = 0   o r     ( ∑ F = 0 ) ) and how net external force and acceleration relate to one another and to mass. It also covers units of force, mass, and acceleration and goes over a sample problem.

Newton's other laws:

  • Newton's first law of motion
  • Newton's third law of motion

[link]

Suppose that the net external force (push minus friction) exerted on a lawn mower is 51 N parallel to the ground. The mass of the mower is 240 kg. What is its acceleration?

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Strategy

Since F n e t and m are given, the acceleration can be calculated directly from Newton’s second law: F n e t = m a .

Solving Newton’s second law for the acceleration, we find that the magnitude of the acceleration, a, is a = F n e t m . Entering the given values for net external force and mass gives a = 51 N 240 k g . Inserting the units k g · m / s 2 for N yields a = 51   k g · m / s 2 240   k g = 0 . 21   m / s 2 .

Prior to manned space flights, rocket sleds were used to test aircraft, missile equipment, and physiological effects on humans at high accelerations. Rocket sleds consisted of a platform mounted on one or two rails and propelled by several rockets.

Calculate the magnitude of force exerted by each rocket, called its thrust T, for the four-rocket propulsion system shown below. The sled’s initial acceleration is 49 m/s2, the mass of the system is 2100 kg, and the force of friction opposing the motion is 650 N.

Sample problem testing table
Types of Links URLs
External link http://upload.wikimedia.org/wikipedia/commons/0/00/Herrenhaustag_MI_Juni_2009_205.jpg
Internal link http://cnx.org/contents/b3c1e1d2-839c-42b0-a314-e119a8aafbdd@8.53:49/Concepts_of_Biology

Strategy

The system of interest is the rocket sled. Although forces act vertically on the system, they must cancel because the system does not accelerate vertically. This leaves us with only horizontal forces to consider. We’ll assign the direction to the right as the positive direction. See the free-body diagram in the figure.

We start with Newton’s second law and look for ways to find the thrust T of the engines. Because all forces and acceleration are along a line, we need only consider the magnitudes of these quantities in the calculations. We begin with

F n e t = m a
where F n e t is the net external force in the horizontal direction. We can see from the image above that the engine thrusts are in the same direction (which we call the positive direction), whereas friction opposes the thrust. In equation form, the net external force is
F n e t = 4 T - f

  • Newton’s second law tells us that F n e t = m a , so we get
  • m a = 4 T - f
  • After a little algebra we solve for the total thrust 4T:
  • 4 T = m a + f
  • which means that the individual thrust is
  • T = m a + f 4
  • Inserting the known values yields
  • T = ( 2100 k g ) ( 49   m / s 2 ) + 650 N 4 = 2 . 6 * 10 4 N

Practice problems

Ptolemy vs. copernicus

Before the discoveries of Kepler, Copernicus, Galileo, Newton, and others, the solar system was thought to revolve around Earth as shown in Figure 04_03_solar_img (a). This is called the Ptolemaic (the P is silent) view, for the Greek philosopher who lived in the second century AD. This model is characterized by a list of facts for the motions of planets with no cause and effect explanation. There tended to be a different rule for each heavenly body and a general lack of simplicity.

Figure 04_03_solar_img (b) represents the modern or Copernican model . In this model, a small set of rules and a single underlying force explain not only all motions in the solar system, but all other situations involving gravity. The breadth and simplicity of the laws of physics are compelling. As our knowledge of nature has grown, the basic simplicity of its laws has become ever more evident.

Nicolaus Copernicus (1473 – 1543) first had the idea that the planets circle the Sun about 1514. It took him almost 20 years to work out the mathematical details for his model. He waited another 10 years or so to publish his work. It is thought he hesitated because he was afraid people would make fun of his theory. Actually, the reaction of many people was more one of fear and anger. Many people felt the Copernican model threatened their basic belief system. About 100 years later, the astronomer Galileo Galilei was arrested and put under house arrest for saying he thought the Earth traveled around the Sun. In all, it took almost 300 years for everyone to admit that Nicolaus had been right all along.

Astronomers:

  1. Copernicus
    1. Planets circle the Sun
    2. Didn't share his ideas out of fear
  2. Galileo
    1. 100 years later
    2. Put in prison

[link]

Section summary

  • Acceleration is a change in velocity, meaning a change in speed, direction, or both.
  • An external force acts on a system from outside the system, as opposed to internal forces, which act between components within the system.
  • Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to the system’s mass.
  • In equation form, Newton’s second law of motion is F n e t = m a or ∑ F = m a . This is sometimes written as a = F n e t m     o r     a = ∑ F m .
  • The weight of an object of mass m is the force of gravity that acts on it. From Newton’s second law, weight is given by W = m g

Key equations

Newton's second law of motion

F n e t = m a     o r     ∑ F = m a

Solving for acceleration

a = F n e t m     o r     a = ∑ F m

Solving for weight

W = m g
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Practice Key Terms 3

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Source:  OpenStax, Updated tutor hs physics content - legacy. OpenStax CNX. Mar 16, 2015 Download for free at https://legacy.cnx.org/content/col11768/1.4
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