Reading Guide Chapter 4

This chapter starts our discussion of Dynamics: The study of what causes changes to take place in the motion of an object. The central concept in the chapter is that of Force. Force is a vector quantity. Newton developed a coherent set of laws that describe motion and how force causes a change in the motion of an object. 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. We 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 to our work in future chapters. You should work through the example problems in each section and work odd numbered problems at the end of the chapter. If you have trouble understanding this chapter you may have trouble understanding future chapters this semester. See me or someone in the TLC when questions arise.

4.1 Force

*force … a push or a pull

In what circumstances have you experienced a force? Are you experiencing any forces at this moment?

*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.

The four Fundamental Forces are 1) gravity 2) electromagnetic 3) strong nuclear and 4) weak nuclear.

 

4.2 Newton’s First Law of Motion

The Greek natural philosophers believed that a constant push was required in order for an object to maintain a constant velocity. This is 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.

*What is inertia?

*TRUE or FALSE The velocity of an inertial reference frame (coordinate system) may be different from zero.

In class we will view this videodisk: Cinema Classics 1A Chapter 72

4.3 Mass

* mass is a measure of the inertia of a body kilogram

Mass and Weight are different types of physics quantities. Mass is a measure of inertia. Weight is a measure of the gravitational force.

 

4.4 Newton’s Second Law

In class we will view this videodisk: Cinema Classics 1A Chapters 74 and 75

In this chapter mass will be a constant in any one problem. This leads to the following form of the second law: FNET = ma 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.

*What is true regarding the direction of the acceleration and the direction of the net force?

*Why is a larger braking force required to stop a larger car in the same distance that a smaller car is stopped?

4.5 Newton’s Third Law

Can you think of a force in the universe that does not have another force associated with it that is equal in magnitude but opposite in direction?

* True or False . There are no isolated (unpaired) forces in the universe.

Whenever one object exerts a force on a second object, the second exerts an equal and oppositely directed force on the first.

The name "Action Reaction" for Newton’s Third Law is misleading in that there is no time delay for the appearance of the "reaction" force. The two forces have equal magnitudes at all times.

*TRUE or FALSE The "action reaction" forces always act on different objects.

True or False: The apparent weight (measured by a bathroom scale) of a person riding in an elevator which is accelerating upward at 1 m/s2 is smaller than the weight of the same person standing in the elevator as it moves upward at a constant rate of 3 m/s.

In class we will watch the Videos: Cinema Classics 1A Chapter 76, 78

4.6 Weight - The Force of Gravity; The Normal Force

*True or False: Mass and weight are the same quantities.

F = mg

Contact force: a force that occurs between two objects when they are touching

True or False There is only one force in contact force situations.

Normal force: a contact force that is perpendicular to the suface

4.7 Solving Problems Free-Body Diagrams

A free body diagram is a drawing of an object that shows all of the forces which act on the object. A free body diagram focuses our attention on a single part of a system of objects.

*True or False Tension in a rope is a force.

In systems where there is more than one object you should start your analysis by finding the net EXTERNAL force acting on the system and the total mass of the system. Then you will be able to calculate the acceleration of the system. After this step you will draw the free body diagram for section of the system and calculate the tension in the connection between the masses.

* True or False The acceleration of the objects in an Atwood’s machine is less than 9.8 m/s2.

 

 

*Make a drawing which shows two objects of different mass (m1 > m2) at 10 meters off of the ground. Assume that both objects are released at the same time with Vo = 0 m/s. Which object will strike the ground first, the more massive or the less massive object? Support your conclusion by solving for the accelerations of the two objects. This is a symbolic solution, not a numerical solution.

 

 

 

 

 

 

In class we will work this problem: A person has a mass of 80 kg. What is the person’s weight in newtons as shown on a metric bathroom scale on the surface of the earth? b) The person is riding in an elevator which is moving upward at a constant velocity of 10 m/s. The person is standing on a metric bathroom scale. What is the scale reading? c) The elevator is accelerating upwards at 2 m/s2. What is the bathroom scale reading? d) The elevator is accelerating downwards at 9.8 m/s2. What is the scale reading?

 

 

4.8 Friction Inclines

Make a drawing that shows a 5 kg object on a frictionless plane which is inclined at 25 degrees to the horizontal. Show all of the forces that act on the object. a) Find the magnitude of the normal force and the magnitude of the force acting on the object in a direction of "down the plane". b) Now suppose that a 3 kg object is connected with a string at the upward side of the 5 kg object. The string passes over a pulley at the top of the ramp and the 3 kg object hangs vertically from the string. The 3 kg object does not touch the ground. The system starts at rest. Calculate the acceleration of the 3 kg object. Let the up-the-plane direction be the positive direction. c) Calculate the tension in the string.

 

 

 

 

 

 

 

 

 

The force of friction is a result of the microscopic interaction of surfaces. We will not explore the details of this interaction. Instead we will use the simple model presented in the text (page 96) to calculate the force of friction.

*True or False The force of friction always opposes motion.

True or False The force of static friction is usually larger than the force of kinetic friction.

What force makes you move forward when you walk?

We will work this problem in class: A string is used to pull a 3 kg object across a horizontal surface which has a coefficient of kinetic friction of 0.5. The coefficient of static friction is 0.6. The acceleration of the object is 0.3 m/s2. What is the value of the tension in the string?

If the FNET is zero an object is said to be in equilibrium. If the object is also at rest the object is said to be in static equilibrium What are some examples of static equilibrium?

As you work static equilibrium problems remember to keep X quantities in one equation and Y quantities in a separate equation. Again, vector components may be necessary to find X and Y quantities.

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