Unit 2: Forces
Overview
A Force is a push or pull of an object on another object. Forces have directions and magnitudes. The direction of a force tells us whether a force is moving to the right, left, up, or down. Upward force and rightward forces are usually designated as the positive direction, and downward force and leftward force are the negative directions. Magnitude is a measure of how strong a force is. Magnitude does not indicate direction, and it is usually measured in Newtons (N).
A Force is a push or pull of an object on another object. Forces have directions and magnitudes. The direction of a force tells us whether a force is moving to the right, left, up, or down. Upward force and rightward forces are usually designated as the positive direction, and downward force and leftward force are the negative directions. Magnitude is a measure of how strong a force is. Magnitude does not indicate direction, and it is usually measured in Newtons (N).
Terminology
Normal Force - two surfaces in contact that prevent the other surface from passing through it (counteracts gravitational force)
Gravitational Force - a non-contact force caused by the pull of two objects with mass, ex. objects being pulled towards the center of the Earth (counteracted by normal force)
Spring Force - the force created by a spring attempting to return to equilibrium (direction of equilibrium)
Tension Force - the force transmitted by a rope or cable or wire on the object that is attached (towards the rope)
Applied Force - the force created by a push or pull on an object (with the direction of the object of the push or pull)
Friction Force - the force caused by two surfaces that rub against each other (opposite of the direction the object wants to or is traveling)
Buoyancy - the force exerted on an object immersed in a fluid (upward push of the fluid)
Air Resistance - the frictional force between an object and the air when the object is moving (opposite direction that the object is traveling in)
Drag - the frictional force between an object and the fluid its on
Normal Force - two surfaces in contact that prevent the other surface from passing through it (counteracts gravitational force)
Gravitational Force - a non-contact force caused by the pull of two objects with mass, ex. objects being pulled towards the center of the Earth (counteracted by normal force)
Spring Force - the force created by a spring attempting to return to equilibrium (direction of equilibrium)
Tension Force - the force transmitted by a rope or cable or wire on the object that is attached (towards the rope)
Applied Force - the force created by a push or pull on an object (with the direction of the object of the push or pull)
Friction Force - the force caused by two surfaces that rub against each other (opposite of the direction the object wants to or is traveling)
Buoyancy - the force exerted on an object immersed in a fluid (upward push of the fluid)
Air Resistance - the frictional force between an object and the air when the object is moving (opposite direction that the object is traveling in)
Drag - the frictional force between an object and the fluid its on
Newton's First Law of Inertia
Inertia
- an object's tendency to remain unchanged
- an object's resistance to change
- Solely dependent on the mass of an object
- Greater Mass = More Inertia = Less Acceleration
- an object in motion will move at a constant velocity when the forces are balanced
- If ΣForce = 0, acceleration = 0, v is constant
Newton's Second Law of Acceleration, Net Force, and Mass
Acceleration is proportional to net (total) force acting on a system, and inversely related to the total mass of the system
- Acceleration (m/s^2) - the rate at which the velocity of an object is changing
- Net Force (N) - the sum of all the forces acting upon an object
- Total Mass (kg) - the total mass of the system
Proportional Model
y = mx When the Net Force is 0, the forces are balanced and the acceleration is 0. As the net force increases, the acceleration increases at a proportional rate. |
Inverse Model
y = A/x As mass increases, acceleration decreases. However, there is no proportional or linear relationship. |
Newton's Third Law
When there is an interaction between two objects, there is a force upon each of the objects, just in different directions. The objects may have the same magnitudes by they push on opposite directions.
Ex. Gravitational Force is balanced by Normal Force
Ex. Applied Force is balanced by Friction Force
Ex. Gravitational Force is balanced by Normal Force
Ex. Applied Force is balanced by Friction Force
Identifying interactions: System Schemas and Force Diagrams
System Schema - visual representation of objects in a system and how they interact
System Schema - visual representation of objects in a system and how they interact
- Forces are interactions between two objects
- Each object is a circle
- Each force is a line connecting two circles
- Dotted lines are used for gravity because its a non-contact force
Force Diagram / Free Body Diagram
- While system schemas don't care about direction, force diagram shows both magnitude and direction
- Draw a line from the object of interest to the direction that the force is acting towards
- Label
- Type of Force (ex. Fn, Fg, Ft, FA)
- By (Object that causes the force on the object of interest)
- On (Object of Interest)
Force Table
- Three columns: Type of Force, x-component of force, y-component force
- A row for each force in the system
- Add up all the forces together to determine the Net Force (both horizontal and vertical components)
- A dash is used when a force does have an affect on the horizontal or vertical component
- Positive Direction
- Right, Up
- Negative Direction
- Left, Down
Force Calculations
a = ΣF / m
Fs = -k * Δx
f = μ * Fn
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Relating Representations of Motion and Force Models
Solving Problems with Force and Motion
1. Determine the known variables
2. Draw a force diagram to figure out whether a force moves in the positive or negative, x or y direction
3. Draw a force table in order to figure out what forces you need to calculate in order to reach the correct net force (0 for constant velocity, > 0 for constant acceleration)
4. Use the formula a = ΣF / m to solve for certain variables
5. Use the kinematic equations to solve for certain variables as well (a, vi, vf, Δx)
1. Determine the known variables
2. Draw a force diagram to figure out whether a force moves in the positive or negative, x or y direction
3. Draw a force table in order to figure out what forces you need to calculate in order to reach the correct net force (0 for constant velocity, > 0 for constant acceleration)
4. Use the formula a = ΣF / m to solve for certain variables
5. Use the kinematic equations to solve for certain variables as well (a, vi, vf, Δx)
Ex. A hot air balloon uses hot air to create buoyancy, an upward force by air on the balloon. The hot air balloon has a mass of 450kg and is accelerating upward at 1.8 m/s^2.
1. Since we were given the mass of the balloon, we use the formula Fg = m * g to find the force of gravity (-4500N)
2. Since we know acceleration and mass, we use the formula ΣF = m * a to find the net force (810N)
3. Subtracting the gravitation force from the force of gravity we can find the force of buoyancy [ 810N - (-4500N) = 5310N ]
1. Since we were given the mass of the balloon, we use the formula Fg = m * g to find the force of gravity (-4500N)
2. Since we know acceleration and mass, we use the formula ΣF = m * a to find the net force (810N)
3. Subtracting the gravitation force from the force of gravity we can find the force of buoyancy [ 810N - (-4500N) = 5310N ]