Ch4_KwarkR

Chapter 4 toc

Lesson 1 (a-d)
a) What is Newton's First Law and what are its applications? Newton's First Law is basically the law of inertia; that an objects tends to keep doing what its been doing. Official Law: "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force." For example, say there was water in a container. There are three instances where the water would spill; when you move it when its at rest, when you stop moving it, or when you change the direction you're moving it; these are all unbalanced forces, which causes changes in the object's motion. This can be applied to everything that moves. Some examples are when you suddenly push the brake in your car; you keep moving forward, but the car slows down. This also occurs when you hit the bottom of a ketchup bottle to dislodge some ketchup.

b)What is Inertia and Mass, and what does it have to do with Newton's First Law? What did Galileo contribute? Inertia is the resistance an object has to a change in its state of motion. Forces do not keep objects moving; actually, force is needed to stop the object from moving, or to start the object moving. Friction is a force, which is the reason why balls don't roll forever and slid textbooks stop sliding after a while. Mass is solely dependent on inertia. The greater the inertia, the greater its mass. This makes sense, because it would obviously take more force to change the state of motion of a massive object than a tiny object; for example, a heavy brick and a sponge. The sponge is easier to move and maneuver than the brick. Galileo noticed that when he rolled a ball down an incline, the ball would reach nearly the same height it began on on the other plane. He took this and projected it to the idea that if there was no incline, the ball would keep rolling forever.

c)What does state of motion mean, and how does velocity and inertia relate to it? A state of motion can be described by its velocity. Inertia can thus be rewritten as the tendency of an object to resist changes in its velocity, or taken even further, the tendency of an object to resist accelerations. For example, a rolling ball will not change velocity at all unless it is acted upon by an unbalanced force like friction or a cricket bat.

d)What's the difference between a balanced and unbalanced force? A good explanation of a balanced force can be found in an example of a textbook thats lying on a table. The force of gravity pulls it down, but the normal force of the table pushes up the book. Since the force of gravity and the normal force are equal, they are called BALANCED. Thus, the book does not change its velocity and maintains inertia. An unbalanced force is when there is no equalizing or balancing force to counteract one force. For example, imagine the textbook is being slid across the table. The force of gravity and the normal force balance each other, but the object is moving across the table. According to Newton's first law, it should keep going... but an unbalanced force is working against the textbook. Friction is causing the book to slow down, and since there is no balancing force to counteract it, the book slows down instead of maintaining its velocity.

Lesson 2 (a-d)
a)What is a force, and what kinds of forces are there? A force is a push or a pull upon an object that is a result of the object's interaction with another object. Forces can be placed into two categories; contact forces and forces resulting from action-at-a-distance. Contact forces are forces that result from two objects physically contacting each other, like friction, tension, normal force, air resistance, etc. Action-at-a-distance forces are forces that result even when two objects are not in physical contact yet exert a push or a pull. Some examples are gravity, electric and magnetic forces. Force is measured through Newtons, which is 1kg * m/s^2. Force is also a vector quality that can be shown using a free-body diagram.

b)What are the types of forces? Also, what's the difference between mass and weight? Applied Force: A force that is applied to an object by something or someone. Gravitational Force:The force with which a massive object attracts another object towards itself; or, the weight of the object. F=m*g Normal Force: The support force an object exerts on another; like a book resting on a table. Frictional Force: The force exerted by a surface as an object moves across it (or tries to move across it). It usually opposes the motion of the object. Sliding friction is when an object slides across a surface. Static friction is when two objects are at rest and a force exists on one of the objects to set it into motion relative to the other object. For example, pushing with 5N of force against a stationary box means the box has a static friction force of 5 N, but say you use 6 N of force and it budges; that means the upper limit of the static friction force is anything from 0N to 6N. Friction can be found using µ * F(normal). Air Resistance Force: A special type of frictional force that acts upon things as they travel through air. Tension Force: A force that is transmitted through a string/rope/wire that is being pulled tight by forces acting from opposite ends. Spring Force: The force exerted by a compressed or stretched spring to an object attached to it.The magnitude is directly proportional to the amount of stretch or compression. Weight is affected by gravity; mass is the amount of matter contained by the object. Mass will be the same anywhere, but weight will vary according to the force of gravity.

c)How do you draw Free-body diagrams? Free-body diagrams are used to show magnitude and direction of all forces acting upon an object. The size of the arrow shows the magnitude, and the direction of the arrow shows the direction of the force. These arrows are labeled with their respective force. If there are two or more arrows of the same force, label them with a subscript 1, 2, etc.

d)How do you determine a net force? If all forces are balanced, then there is no net force; if some are unbalanced, there is a net force. The net force is the vector sum of all forces acting upon the object (review chapter 3 for vector addition). Net forces cause acceleration.

Lesson 3 (a,b)
a)What is Newton's Second Law? Newton's second law provides the explanation for the behavior of objects upon which the forces do not balance. It states that acceleration of an object by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and that it is inversely proportional to the mass of the object. Basically it is this formula: This is a spin-off from the First law, which says that objects tend to keep doing what they've been doing unless there is an unbalanced force acting upon it, which the Second law explains.
 * a = Fnet / m **

b)What is this big Misconception about Newton's Laws? The common misconception is that objects in motion have to keep having force applied to it to keep it in motion. IT DOES NOT. For example, a sled that goes down a hill will go on forever if friction and air resistance are taken away; this is the same idea as Newton's First Law. Also, on a free-body diagram, the body may have balanced forces but may still be moving at constant speed. A force is acceleration; it may be needed to start motion and increase/decrease speed, but at constant speed there is no unbalanced force acting upon an object.

Vectors Lesson 3 (a-f)
a)How do you add forces? You can use the head-to-tail method to find the magnitude and direction of the forces. You can also use the trigonometric function learned in chapter 3 to add the components of each force. The resulting sum (or resultant) is the net force of all the forces. When the forces are balanced, then there is no acceleration, and the converse is also true.

b)How do you resolve forces? Diagonal forces can be broken up into x- and y-components. Using the trigonometry functions, you can find the influence of one force. This is very similar to how we found the velocity magnitude and direction of winds and tides in the vector chapter.

c)What are the states of being in equilibrium and being static? When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium; that means that the up and down forces cause no acceleration on the y-axis and the same for the left and right forces. However, all the forces do NOT have to be equal. If an object is at rest and is in a state of equilibrium, then it is static. When an object is static, that means that all forces added together as a resultant must equal 0 Newtons.

d)How do you solve net force problems? First, you should draw a FBD, then find out the x and y components of any forces that are directed in a non-cardinal direction (up,down,left,right). You do this by using the trig functions and calculations that we learned in unit 3, with vectors. However, normal force is not necessarily equal to the weight force; if there is no acceleration up or down, then the y forces must be balanced. But if there is a y-component to some other force, that y-component must be accounted for as well. For example, if there is a tension force at 30º, and there is no acceleration on the y axis, then the y-component of the tension AS WELL as the normal force is balanced with the weight force.

e)How do you solve problems on an incline? After drawing the FBD, we can set the x and y components of the FBD as orthogonal vectors of each other such that the y-axis is perpendicular to the incline and the x-axis is parallel to the incline. The weight force is straight down, which means that it now has an x and y component (since we tilted the x-y coordinate plane). Using trigonometry, we can figure out the angle between the weight force and the x (or y) axis, and use that in the trigonometry functions to find out the weight force components and ultimately the answer to a question dealing with inclines.

f)How do you solve problems dealing with two bodies? You can use the entire system as a whole instead of drawing FBD diagrams for both bodies. They will both accelerate at the same rate (since they are connected by a tension force which exerts an equal and opposite force on both bodies). You can also use the systematic approach, solving for each individual body as individual systems. The important thing is to be systematic in your FBD drawings and your equations.