Unit 2 Summary - Free Bodies and Trigonometry
In this unit, our efforts were pushed forward by force! We learned about different kind of forces, how they react upon certain objects, and how to predict the force's measurement using trigonometry.
Force: An interaction between two objects
A push or pull (Represented as Fpush/Fpull)
Forces speed up, slow down, stop, and change direction but only when forces are unbalanced.
If you are pushing or pulling on an object and it does not move, the push and friction will be equal.
Normal forces are the forces perpendicular to the surface of the object in analysis. Frictional forces are the forces parallel to the surface of the object in analysis. Gravitational forces pull the object in analysis down towards the Earth.
Some forces include: Fg - Gravity: Pull between an object and the center of the Earth (weight)
Fn - Normal: Crunching/Scrunching, a perpendicular force
Ff - Friction: Parallel force, sharing force between two surfaces
Ft - Tension: Force along a rope/chain/etc when taut/tight
Fs - Spring: Returns to it's normal state when being compressed/stretched
To express these forces, we learned how to create a force of free body diagram. They display the forces acting upon an object at any given time.
To create a force diagram, you must:
1) Sketch the system and its surroundings
2) Enclose the system within a system boundary
3) Shrink the system to a point at the center of coordinate axes with one axis parallel to the direction of motion
4) Represent all relative forces (across the system boundary) with a labeled vertex
5) Indicate which forces (if any) are equal in magnitude to other forces
Using the example of a ball being propelled into the air out of a cart, we can observe several unusual rules of force.
The ball an cart move forward at a constant velocity. When the ball is thrown into the air, there is no other force acting upon it so the ball will continue moving forward at a constant velocity.
This is proved in Newton's Third Law: An object in motion stays in motion unless acted upon by an outside force.
The motion map of the ball will remain the same no matter how it is thrown because, once the ball has left the thrower's hand, gravity is the only force acting upon it.
We also learned how to calculate net force from both the horizontal and vertical directions. For the ball, the net forces will be set up in an equation.
fVertical = fgravity > 0N
fHorizontal = 0N
Elaborating on this information, we learned how to create Free Body Diagrams at an angle. If an object is being pulled up by a force at an angle to it's surface, than the vectors representing the angled forces are also going to be angled on the diagram.
Since the tension force is angled upwards, component forces have to be added to balance the diagram. Tension gets divided into ftx and fty.
If the object is getting pulled with a force of 38N at an angle of 55o, we could find the force of friction using trigonometry.
The cos formula will give the length of ftx, which is equal to ff.
Cos = adjacent/hypotenuse. We are trying to find the adjacent side, since ft is the hypotenuse.
Cos 55 = adj/38N
38(cos 55) = .8408167379
This can be rounded to a friction force of .84N
All together, in unit 2, we learned about forces and how they affect various objects. We learned how to display actions of forces with Free Body Diagrams. We learned how to calculate the net force of an object and we learned how to find the amount of force projected on an object using trigonometry.
