chapter4

__Chapter 4 Newton’s Laws__

In this chapter, we will deal with Newton’s three laws of motion, which help us solve problems in everyday life. The first law of **Inertia**, The second law dealing with net force, mass and acceleration, and finally the third law that states forces come in equal and opposite pairs. These are laws that we see in action around us everyday. In this chapter we also encounter: the force due to **Gravity**, forces in nature, and **Free-Body Diagrams**. Some of the questions that will be answered in this chapter are, “why do objects start to move?” (Textbook) Using these laws, we can start solving problems involving objects in motion and at rest. __Newton’s Three Laws__
 * Newton****’s First Law:** An object at rest stays at rest //unless// acted on by an external force. An object in motion continues to travel with constant velocity //unless// acted on by an external force.

Some key words to remember that are associated with Newton’s first law are **Inertia** and **Inertial reference frame. Inertia** is a property described first by Galileo, when he reasoned that if an object moved on a frictionless surface with no forces acting upon it, its velocity would be constant and never change. So, this means that once an object gets going and acted upon by an external force, it will never stop moving until it is acted on by another force. **Inertial reference frames** are reference frames with respect to which the acceleration of an object remains zero, and no forces act upon it. These reference frames are very important becauseNewton’s three laws are only valid in this type of reference frame. (Textbook)

∑F=//m//**a**
 * Newton****’s Second Law:** The direction of the acceleration of an object is in the direction of the net external force acting on it. The acceleration is proportional to the external net force** F ** net in accordance with ** F ** net = //m//**a**, where //m// is the mass of the object. The net force acting on an object, also called the resultant force, is the vector sum of all the forces acting on it: ** F ** net = ∑F. Thus,

Newton’s second law allows us to compare the masses of two objects that are acted upon by the same net force if we know the resulting acceleration of the two.


 * Newton****’s Third Law:** Forces always occur in equal and opposite pairs. If object A exerts a force on object B, an equal but opposite force is exerted by object B on object.

What this basically says is that when two objects interact, they exert forces on each other that are equal and opposite. This law is often called the action-reaction law, however one should not make the assumption that on force is in reaction to the other. Both forces occur simultaneously and either one can be called the acting or reacting force.

Example Problems forNewton’s Law: 1. An object is observed to be moving at a constant velocity in an inertial reference frame. It follows that (a) no forces act on the object, (b) a constant force acts on the object in the direction of motion, (c) the net force acting on the object is zero, (d) the net force acting on the object is equal and opposite to its weight. 2. A given force produces an acceleration of 5 m/s on the standard object of mass m1. When an equal force is applied to a carton of ice cream of mass m2, it produces an acceleration of 11 m/s2. (a) What is the mass of the carton of ice cream? (b) What is the magnitude of the force? 3. An 80kg man on ice skates pushes his 40kg son, also on skates, with a force of 100N. The force exerted by the boy on his father is (a) 200 N, (b) 100N, (c) 50N, (d) 40N. 4. A 1000-kg load is being moved by a crane. Find the tension in the cable that supports the load as (a) it moves upward with a speed increasing by 2m/s each second, (b) it is lifted at constant speed, and (c) it moves upward with speed decreasing by 2 m/s. 5. A man pushes a 24-kg box across a frictionless floor. The box begins moving from rest. He initially pushes on the box gently, but gradually increases his force so that the force he exerts on the box varies in time as F=(8N/s)t. After 3 s, he stops pushing the box. The force is always exerted in the same direction. (a) What is the velocity of the box after 3 s? (b) How far has the man pushed the box in 3 s? (c) What is the average velocity of the box between 0 s and 3 s? (d) What is the average force that the man exerts on the box while he is pushing it? **__Weight__** Weight is the force on an object due to gravity. Many people often make the mistake of using weight and mass interchangeably, when they are two different things. Mass is constant everywhere in the universe, whereas your weight changes because your weight depends on the acceleration due to gravity. So for instance on the moon you will weigh approximately six times less than here on earth because the acceleration due to gravity six times weaker. This also means that lifting an object on the moon requires one sixth of the force that is required on earth. The equation to calculate weight is **w=**//**m**//**g,** where //**m**// is the mass and **g** is the acceleration due to gravity. Since the value of gravity changes the further you are from the center of mass of the earth, you will weigh less at the lowest point on the earth than you will at the highest point.

__Units of Force and Mass:__ The SI unit of mass is the kilogram. TheNewton, the unit of force, is expressed by three SI units, the second, the meter, and the kilogram. 1 N= (1kg)(1m/s 2 )= 1kg∙m/ s 2 . This expression means that the Newtonis the force that produces an acceleration of 1 m/s 2 when it acts on an object whose mass is 1 kg. In atomic and nuclear physics, the unified mass unit (u) is often used because of its convenience. The unified mass unit is 1.660540x10-27 which is one twelfth of a neutral carbon-12 atom. The mass of a hydrogen atom is about 1u.

Although the SI system is the most commonly used system, in the United Statesthere also exists such a thing as the U.S. Customary System, which is based on the second, the foot and the pound. The obvious major difference is that this system uses the pound instead of the kilogram. The pound has been defined as 4.448222 N, which means 1 kg is approximately 2.20 lb. The slug is the unit of mass in the U.S.customary system. The slug is an object that weighs 32.2 lb. When working with this system, you substitute w/g for m in the net force equation, where g is in feet per second. The value for g in feet per second is 32.2 ft/s 2 **__Forces in Nature__**

There are four basic forces that we can observe in nature that occur between elementary particles.


 * 1) The gravitational force- the force of mutual attraction between objects
 * 2) The electromagnetic force- the force between electric charges
 * 3) The strong nuclear force- the force between subatomic particles
 * 4) The weak nuclear force- the force between subatomic particles during certain radioactive decay processes.

Contact Forces: Contact forces are exerted by objects that are touching. These forces are electromagnetic in origin, because they are exerted between the surface molecules of the objects that are touching.

-Solids: the forces that result when two solids interact are because of the molecules compressing pushing back on one another. This force is called the normal force, or perpendicular force. For example, when an object rest on a table, the object exerts a force down on the table of mg, and the table exerts the normal force on the object. The normal force will balance out the weight of the object as long as the table doesn't break, and if you press down more on the object, the normal force will increase. Another force is a force that is applied parallel to the force applied on the object, and this is called the frictional force. The frictional force is the force that slows objects down when they are moving, and is expressed by the coefficient of friction **μ.**

Problems with Two or More Objects: When dealing with problems that involve two or more objects, the first thing to do is draw two separate free body diagrams, and then using Newton's second law to solve for unknowns. If the objects are in direct contact, the forces exerted must be equal and opposite in accordance with Newton's third law. If the two bodies are connected by a string, the acceleration components parallel to the string are the same for both objects. This means that if two objects are connected by a rope, and that rope is then draped over a pulley, the rate at which one side descends or ascends is equal and opposite to the rate of the other side. In a string, the force exerted by one segment of the string on the segment adjacent to it is called the tension. Tension varies in strings that have a large enough mass. This means that if you hang a thick rope from the ceiling with an object on the end, the tension will be greater nearer the top because that point also has to support the weight of the rest of the rope below it. However, in the problems that we work with, the mass of the string is usually assumed to be so negligible that its own mass does not affect the tension. __Chapter 4 Review__ 1. **Newton’s Laws** - First Law: An object stays at rest unless acted on by an external force. An object in motion continues to travel with constant velocity unless acted on by an external force. (Reference frames in which this occurs are called inertial reference frames.) -Second Law: The magnitude of the acceleration is proportional to the magnitude of the net external force, in accordance with ** F ** net = //m//**a,** where m is the mass of the object. The net force acting on an object, also called the resultant force, is the vector sum of all the forces acting on it. -Third Law: Forces always occur in equal and opposite pairs. If object A exerts a force on object B, an equal but opposite force is exerted by object B on object A.

2. **Inertial Reference Frames**: This is a reference frame where an object remains at rest if no force acts upon it. Any reference frame that is moving with constant velocity relative to an inertial reference frame is an inertial reference frame also, and a reference frame that is accelerating relative to an inertial reference frame is not an inertial reference frame.

3. **Force, Mass and Weight** -Force: Force is defined as the acceleration is produces on an object. A force on 1N produces an acceleration of 1m/s2 on an object with a mass of 1kg. -Mass: Mass is the intrinsic property of an object that measures its inertial resistance to acceleration. Mass does not depend on the location of the object, unlike weight. Applying an equal force to two objects with two different masses allows us to also compare their resultant accelerations usingNewton’s first law. -Weight: The weight of an object is the force of gravitational attraction exerted by the earth on the object. It is proportional to the mass of the object and the gravitational field. Weight, unlike mass, is dependant on the objects location because of the changes in gravity.

4. **Fundamental Forces** - All the forces observed in nature can be explained in terms of four basic interactions: 1. The gravitational force 2. The electromagnetic force 3. The strong nuclear force or hadronic force 4. The weak nuclear force.

5. **Contact Forces:** Contact forces of support and friction and those exerted by springs and strings are due to molecular forces that arise from the basic electromagnetic force. - Hooke’s Law: When a relaxed spring is compressed or extended by a small amount ∆x, the force it exerts is proportional to ∆x.

Laboratory:


 * Purpose:** This laboratory will demonstrateNewton’s Laws of Motion.


 * Materials:**
 * Clay || Ruler || Baseball || Tennis Ball ||
 * || Pool Ball || Ping Pong Ball || Balance || Tape ||


 * Procedure:**


 * 1) Go to a location in the room next to a wall.
 * 2) Place a piece of tape 1 meter above the floor.
 * 3) Take the mass of each of the balls using a balance and place these masses in the observation table provided.
 * 4) Roll up the clay into a ball and place the ball of clay on the floor under the piece of tape. Place a piece of tape to mark the top of the clay. The set-up should be similar to the diagram below:


 * 1) Drop each of the balls from the 1–meter mark so that they land on the clay. Using the taped mark just above the clay, measure how much each ball dents the clay. Place that amount in the observation table provided.
 * 2) During this laboratory, think about how you are observing Newton’s Three Laws of Motion.


 * Observation Table:**


 * Type of Ball || Mass of Ball || Depth of Indent in Clay ||
 * Pool Ball || .16kg || 3.1 cm ||
 * PingPong Ball || .0027kg || .05 cm ||
 * Baseball || .145kg || 2.8 cm ||
 * Tennis Ball || .057kg || 1.1 cm ||


 * Conclusion Questions:**

The objects dropped kept moving and accelerating until they were all acted upon by the clay, which slowed them down to rest.
 * 1) Describe one way you observed Newton’s First Law of Motion during this laboratory.

2. Newton’s Second Law of Motion explains the relationship between mass, force and acceleration. In this experiment acceleration due to gravity was the same for each ball. What was the relationship between FORCE and MASS when acceleration was held constant? The greater the mass of the object, the greater the force of the impact on the clay, resulting in a larger indent.

3. Describe one way you observed Newton’s Third Law of Motion during this laboratory. The force exerted by the object on the clay produced the indent, and in turn the clay produced a force on the object to slow it down to rest. ([|Mrs. Downs' Science Classes])


 * CATEGORY ||  SCORE (1-4)  ||  POINTS (0-20)  ||
 * Content || 3.5 || 17.5 ||
 * Organization || 4 || 20 ||
 * Accuracy || 4 || 20 ||
 * Appearance || 3 || 15 ||
 * Participation || 4 || 20 ||
 * TOTAL || 92.5 ||