Monday, November 9, 2015
Wednesday, November 4, 2015
Balanced Force Particle Model
Introduction:
In Unit two of our physics class, titled "Balanced Force Particle Model", we learned about Newton's first and third law, free body diagrams, balanced free body diagrams, force vectors, weight and mass, friction, as well as different forces acting upon objects in motion, at rest, and accelerating.
Free Body Diagrams: Free body diagrams are a way of illustrating forces that are acting upon an object. It is important to remember that when drawing a diagram, we only include forces acting upon an object and not forces that the object is creating. Several important rules are used when creating a free body diagram.
Newton's 1st Law: Newton's first law states that 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. One real world example of this was when we rode the hovercraft. We continued to move without anyone pushing us.
Newton's 3rd Law: This law states that for every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. For example, when I push on the wall, the wall pushes back with the same amount of force. A real world example is when a car hits a bug on the road. Although it seems counterintuitive, the bug pushes back on the car as hard as the car pushes on the bug. This is a good example of an equal and opposite reaction.
Friction Force: Friction is the resistance that one surface or object encounters when moving over another. This means that it often slows an object or keeps it from moving in a certain direction. It is always parallel to the surface the object is on.
Gravity Force: Vector always goes straight down, no matter which way the axis is tilted.
Normal Force: Vector always goes perpendicular to the surface the object is resting upon.
Tension: Used when a rope is present, goes in the direction that the rope is pulling.
Tilting an Axis: When an object is on a surface that is at an angle, we can tilt the whole coordinate plane in order to make the free body diagram easier to draw. The x-axis can be tilted to be at the angle of the surface.
Vectors: Vectors are a special type of arrow used in physics. A vector's length determines how large it is in value. For example, if one vector is longer than another, it will have a larger force than the smaller one.
Splitting Vectors: Some vectors will not land on the x or y axis. This is a problem, because we can only balance a diagram when its components lie on an axis. To do this, we can break the vector into x and y components. The vectors on the x and y axis will represent this force in a way that we can use to balance an equation.
Balanced Diagrams: When vectors are equal length on opposite sides of the same axis, the diagram is balanced. This means that the object is either at rest or moving at a constant velocity. When vector lengths are not equal, an object is speeding up or slowing down.
In the example below, a box is resting on a slope. Because the surface that the box is on is tilted, we can tilt the axis in order to create an accurate free body diagram. Using our rules above, we can conclude that gravity pulls the object straight down, normal force goes perpendicular to the surface, and friction keeps the box from sliding down the hill. One thing that you will notice when looking at the diagram is that gravity does not lie on an axis. Because of this, we must split it into two vectors, Fgx and Fgy as seen below. Also, the FN and Fg vectors are much longer than the Ft and Fgx vectors. This tells us that the voce of gravity and normal force are larger than that of friction and gravity on the y-axis. We can also conclude that the object is either at rest or moving at a constant velocity because of the equal vector lengths.
In Unit two of our physics class, titled "Balanced Force Particle Model", we learned about Newton's first and third law, free body diagrams, balanced free body diagrams, force vectors, weight and mass, friction, as well as different forces acting upon objects in motion, at rest, and accelerating.
Free Body Diagrams: Free body diagrams are a way of illustrating forces that are acting upon an object. It is important to remember that when drawing a diagram, we only include forces acting upon an object and not forces that the object is creating. Several important rules are used when creating a free body diagram.
Newton's 1st Law: Newton's first law states that 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. One real world example of this was when we rode the hovercraft. We continued to move without anyone pushing us.
(A video of a hovercraft)
Newton's 3rd Law: This law states that for every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. For example, when I push on the wall, the wall pushes back with the same amount of force. A real world example is when a car hits a bug on the road. Although it seems counterintuitive, the bug pushes back on the car as hard as the car pushes on the bug. This is a good example of an equal and opposite reaction.
Both the push on the wall and the push back from the wall are equal.
Friction Force: Friction is the resistance that one surface or object encounters when moving over another. This means that it often slows an object or keeps it from moving in a certain direction. It is always parallel to the surface the object is on.
Gravity Force: Vector always goes straight down, no matter which way the axis is tilted.
Normal Force: Vector always goes perpendicular to the surface the object is resting upon.
Tension: Used when a rope is present, goes in the direction that the rope is pulling.
Tilting an Axis: When an object is on a surface that is at an angle, we can tilt the whole coordinate plane in order to make the free body diagram easier to draw. The x-axis can be tilted to be at the angle of the surface.
Vectors: Vectors are a special type of arrow used in physics. A vector's length determines how large it is in value. For example, if one vector is longer than another, it will have a larger force than the smaller one.
Splitting Vectors: Some vectors will not land on the x or y axis. This is a problem, because we can only balance a diagram when its components lie on an axis. To do this, we can break the vector into x and y components. The vectors on the x and y axis will represent this force in a way that we can use to balance an equation.
Balanced Diagrams: When vectors are equal length on opposite sides of the same axis, the diagram is balanced. This means that the object is either at rest or moving at a constant velocity. When vector lengths are not equal, an object is speeding up or slowing down.
In the example below, a box is resting on a slope. Because the surface that the box is on is tilted, we can tilt the axis in order to create an accurate free body diagram. Using our rules above, we can conclude that gravity pulls the object straight down, normal force goes perpendicular to the surface, and friction keeps the box from sliding down the hill. One thing that you will notice when looking at the diagram is that gravity does not lie on an axis. Because of this, we must split it into two vectors, Fgx and Fgy as seen below. Also, the FN and Fg vectors are much longer than the Ft and Fgx vectors. This tells us that the voce of gravity and normal force are larger than that of friction and gravity on the y-axis. We can also conclude that the object is either at rest or moving at a constant velocity because of the equal vector lengths.
Below is an example of a diagram for an object that is slowing down. This particular diagram is for a ball being thrown in the air. Notice how the only force is gravity, which means that this equation is unbalanced. This means that the object is either accelerating, changing direction, or slowing down.
Weight and Mass: Although commonly thought of as the same thing, weight and mass are actually very different. An equation to find the weight or mass of an object is Weight = (Mass)(Gravity). Gravity is always 10 (on Earth), weight is always measured in Newtons, and mass is always measured in Kilograms.
Example problem: A ball has a mass of 15kg on earth. What is its weight?
-W=(mass)(gravity)
-W=(15)(10)
-W=150 Newtons
Kinetic Friction: Friction can be determined with the equation f=(µk)(W) Where F is frictional force, µk is the coefficient of friction, and W is weight. Friction never changes with speed or surface area, but will change with different types of surfaces as well as with different weights.
Example problem: The coefficient of kinetic friction is .5 between an 80N book and sandpaper. What is the force of friction between the book and the sandpaper when it is sliding?
- f=(µk)(W)
- f=(.5)(80)
- f=40N
Solving for Unknown Values In FBD's: In a free body diagram, we often have information like angles and some vectors, but not the vector that we need in order to solve for a certain force value. To solve for a given side, we can use Sin, Cosine, and Tangent. By using the mnemonic "SohCahToa". In the diagram below, angle X has an opposite side, adjacent side, and hypotenuse. These can be used to determine the length of certain vectors.
Example:
By using our knowledge of sin, cosine, and tangent, we can determine that we must use sin, since we are using both the opposite and hypotenuse.
Work: Sinθ = Opposite/Hypotenuse
Sin (40) = 9/x
(X)(sin40) = 9
X = 9/(sin40)
x = 12.001
Real World Connection: We encounter forces every day. Although we may not notice it, we are constantly exerting forces in order to move and do everyday chores. For example, as you are reading this, gravity and normal force are acting upon you right now. Action reaction pairs, and Newton's laws are also constantly appearing when we drive, have tug of war contests, and when we are sleeping. In this unit, we used real world situations and explored the reasoning and math behind them.
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