Chapter 4 Part 1 Force, Inertia, Mass, Newton's First Two Laus

Prof. Clements Notes/Hints for Physics Courses

Chapter 4 Open Stax College Physics or Most Introductory Physics Courses

DYNAMICS: FORCE AND NEWTON'S LAWS OF MOTION

Terms you should know at the end of this unit: dynamics, force, mass, inertia, inertial reference frame, internal force, external force, net force, system, weight

This chapter starts our discussion of Dynamics of motion. Dynamics is the study of what causes changes to take place in the motion of an object. The central concept in the chapter is Force. Force is a vector quantity. Newton developed a coherent set of laws that describe motion and describe how force causes a change in the motion of an object. These laws are concise statements that have a very wide range of applications for objects moving at slow speeds (< 5% of the speed of light). You should know that Newton made his contributions to physics in the last half of the 1600’s.

The development of a sun-centered solar system model and the detailed orbits of the planets influenced the development of Newton’s laws and Newton’s Law of Gravitation. I will not delve too deeply into the study of planet orbits. You should know that astronomy had a major influence on the development of physics theories. This relationship between astronomy and physics continues to this day.

The material in this chapter is foundational for future chapters. You should work through example problems in each section and work problems at the end of the chapter in your textbook that have answers in the back of your text on in the student solution guide. If you have trouble understanding this chapter you may have trouble understanding future chapters. See your instructor, or a class mate, when questions arise.

Force Concepts

force … a push or a pull

Think about circumstances where you experienced a force. You experiencing forces at this moment (force of gravity, upward force of chair on your body, etc.)

net force … The vector sum of all forces which act on one object. The vector sum will be done using the methods of chapter 3. You will need to find the X and Y components of the net force. If necessary, you should review right triangles and trig functions.

There are two categories of force: internal and external. Examples of internal force are forces between atoms or molecules in a solid or the force at the link between two railroad cars. Internal forces do not affect the motion of an object and we will be able to ignore them. External forces do affect the motion of the object. You will need to be able to sketch "free-body" diagrams that show the object and all of the external forces that act on the object. You must ignore any forces that do not act on the object of interest.

Newton’s First Law of Motion Inertia, Mass, Weight

The Greek natural philosophers believed that a constant push was required in order for an object to maintain a constant velocity. This was due to their lack of understanding of the force due to friction. Galileo and Newton understood friction and did have a correct understanding of the law of inertia.

Newton’s First Law … An object has a constant velocity unless there is a non-zero net force acting on the object.

Inertia is a measure of the resistance of an object to a change in its velocity.

The velocity an inertial reference frame (coordinate system) must be constant but the velocity does not have to be zero.

Mass is a measure of the inertia of a body. In the metric system the fundamental unit of mass is the kilogram.

Mass and Weight are different types of physics quantities. Mass is a measure of the inertia of an object. Weight is a measure of the gravitational force on an object. Mass and weight are proportional to each other but the quantities have different units and different numerical values (on Earth).

Newton’s Second Law of Motion

You may wish to do a search on YouTube for:

newtons second law demonstration

The word "system" is used often in physics. The system will often have more than one object in the system. Forces that exists between members of the system are internal forces and will be ignored because they do not affect the motion of the overall system. Forces that act on the system from outside the boundaries of the system are the external forces that must be considered. People riding in a car are inside the system of (car + people). The forces the people may apply to the seat or floor do not change the motion of the system.

Imagine what happens to the acceleration of a system if the external force becomes larger while the mass is constant.

The acceleration increases.

Imagine what happens to the acceleration of a system if the mass (inertia) becomes larger while the net force is constant.

The acceleration decreases.

This leads to the following form of the second law: F_NET = ma F_NET is the net external force (the sum of all of the external forces that act on the object of interest). A force of 1 Newton will give a 1 kg object an acceleration of 1 m/s² . The unit of force in the English system is the pound.

The direction of the acceleration is always the same as the direction of the net force.

Newton's Second Law has been verified by experiments.

Suppose two cars, with different masses, have the same velocity before the brakes are applied. Why is a larger braking force required to stop a larger car in the same distance that a smaller car is stopped?

You should think about the value of the acceleration for both cars. The fourth kinematic equation V² = V_o² + 2 * a * (X – X_o) , shows us that the acceleration value is the same for both cars since the velocities and displacement values are equal. F_NET = ma tells us that the Force will be larger for the car that has the larger mass.

Weight The downward force that accelerates objects towards the Earth is called weight. Weight is a vector that points toward the center of the Earth.

Objects that have more mass have more weight near the surface of the Earth.

Objects that have greater weight do not have greater acceleration values towards the Earth. They have the same acceleration values.

One way to calculate weight is to use W = m * g where g is the value of the acceleration due to gravity. You will see another way to calculate weight when Newton's Law of Gravity is discussed. Try these algebra steps: 1) Write F = ma, 2) replace F with W, 3) replace W with m*g , 4) solve for the acceleration, a.

F = ma

W = ma

mg = ma Cancel the mass values, m.

g = a Objects of any mass accelerate towards the Earth with the same value, -9.8 m/s² .

(Note: there is a subtle, but very important, concept regarding mass. There are two types of mass: gravitational mass and inertial mass. Experiments have verified that the two mass values are identical to the full number of decimal places that can be detected.)

Objects that have greater weight do not greater acceleration values towards the Earth.

An astronaut who has a mass of 70 kg will have different weights on the Earth, the Moon, and Mars. Remember, W = mg. The value of g is different for the Earth, Moon, and Mars.

Astronauts on the International Space Station (in orbit about 240 miles ( above the surface of the Earth) do not have zero weight . They are not weightless because “g” is not zero at this location. They are apparently weightless. This may be discussed more in the chapter that discusses gravity.

Calculate the weight in Newtons, and in pounds, for an astronaut on Earth who has a mass of 70 kg. W = mg W = 70 kg * 9.8 m/s² W = 686 Newtons 1 pound/4.448 N → 154 lb

Calculate the weight in Newtons, and in pounds, for an astronaut in the International Space Station who has a mass of 70 kg. 'g” is about 8.7 m/s² at this location.

W = mg W = 70 kg * 8.7 m/s² W = 609 Newtons 1 pound/4.448 N → 137 lb

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