Unit 2 Overview
A force is a push or pull upon an object resulting from the object's interaction with another object.
Properties of Forces
Types of Forces
In this unit, we conducted the Unbalanced Forces Lab to explore the relationship between acceleration, net force, and total mass.
Properties of Forces
- Magnitude: size of the force, how strong the push/pull is
- measured in Newton (N)
- magnitude does not indicate direction
- Direction: where the force is traveling (up, down, left right, etc.)
Types of Forces
- Contact
- Normal Force = two surfaces in contact preventing them from passing through each other (perpendicular to the surface)
- Spring Force = force between compressed stressed string with object attached (opposite direction of stretch/ compression)
- Friction Force = resistive force when the surface of 2 objects when they rub together (opposite of desired direction the object wants to slide)
- Air Resistance = frictional force between object and air it travels through
- Drag = frictional force between object and the fluid it travels through
- Applied Force = direct push/pull on object (any direction)
- Tension Force = push/pull transmitted through a rope/ cable/ wire and the object attached (direction of the rope)
- Buoyancy = force exerted between a fluid and an object immersed in the fluid (push upward on object)
- Non-Contact
- Gravity = attractive force between two objects with mass
- object on Earth --> acts on object toward center of the Earth
- Gravity = attractive force between two objects with mass
In this unit, we conducted the Unbalanced Forces Lab to explore the relationship between acceleration, net force, and total mass.
Newton's First Law of Inertia
An object will continue to move at a constant velocity unless it feels an unbalanced push or pull
Inertia: an object's tendency to resist a change in motion (acceleration)
- constant velocity = no acceleration = balanced forces = no net force (ΣF = 0, a = 0 m/s^2)
- Reminder: 0 m/s (an object at rest) is still a constant velocity
- unbalanced push/ pull = net force is not 0 N (ΣF ≠ 0)
Inertia: an object's tendency to resist a change in motion (acceleration)
- Inertia is solely dependent on its mass (i.e. a more massive object is harder to stop)
- A given force accelerates a less massive object more than it accelerates a more massive object
Balanced Forces |
Unbalanced Forces |
Newton's Second Law of Acceleration, Net Force, and Mass
Acceleration is proportional to the net (total) force acting on a system, and inversely related to the total mass of a system
- Acceleration (m/s^2): rate at which an object changes its velocity (change in velocity/ change in time)
- constant acceleration = net force acting is constant in magnitude & direction
- Net Force (N): all forces acting upon an object
- Mass (kg): amount of matter (stuff) in an object
- quantitative measure of inertia (inertia wholly depends on mass)
- scalar quantity
Acceleration & Net ForceThe graph shown above passes through the point (0,0), indicating that when the net force is 0 N, the acceleration is 0 m/s^2.
As net force increases, the acceleration also increases. |
Acceleration & Total MassThe graph shown above has no x-intercept or y-intercept. This is because as total mass decreases, acceleration increases. As total mass increases, acceleration decreases. However, when the total mass is 0, acceleration is also 0.
As total mass increases, the acceleration decreases at a decreasing rate. |
Equation
Newton's Third Law
When there is an interaction between two objects, there is a force upon each of the objects that is of the same magnitude, but in the opposite direction from that of the other.
Reminder: These forces are exerted on different objects and cannot be added to find the sum of forces exerted on one object
Reminder: These forces are exerted on different objects and cannot be added to find the sum of forces exerted on one object
Example:
The diagram on the left depicts the Earth exerting a force on the moon, and the moon exerting a force on the Earth. Once again, these two gravitational forces have the same magnitude force but are in the opposite direction from each other. Image Credits: https://msuperl.org/wikis/pcubed/doku.php?id=183_notes:examples:calcgravforce |
Identifying Interactions: System Schemas and Force Diagrams
How to Create a Force Table
In Example: The horse and the wagon are moving at a constant velocity of 10 m/s. The wagon is 55 kg, and the horse is pulling with a 100 N force. |
Force Equations |
Force Calculations |
To Calculate Net Force (2 methods)
To Calculate Force of Gravity (Gravitational Force Law)
|
Solving Force Problems
General Steps
- identify all known variables
- determine if velocity is constant or not constant
- draw a force diagram
- use the force diagram to create a force table
- solve for unknown variables
Example:
A person pushes a cart with a force of 30 N to the left. A frictional force of 10 N opposes the motion. The cart and its contents have a mass of 40 kg. What is the net force?
A person pushes a cart with a force of 30 N to the left. A frictional force of 10 N opposes the motion. The cart and its contents have a mass of 40 kg. What is the net force?
Relating Representations of Motion & Force Models
- constant velocity = no acceleration = balanced forces = no net force (ΣF = 0, a = 0 m/s^2)
- changing velocity = acceleration! = unbalanced push/ pull = net force is not 0 N (ΣF ≠ 0)
- An object's velocity change, and its acceleration always points in the direction of the sum of forces that other objects exert on it
- if net force points in same direction as object's velocity --> object speeds up
- if net force points in opposite direction as object's velocity --> object slows down
- if net force = 0 --> object's velocity does not change
Force Model = force diagram with object of interest, arrows in the direction of the force, and force labels
Motion Diagram= velocity arrows and change in velocity
- increasingly longer v--> arrows indicate object of interest's speed changes from 0 to nonzero
- increasingly shorter v--> arrows indicate object of interest's speed changes from nonzero to 0
Example:
A ball is on a moving train. |
Motion Diagram |
Force Diagram |
Solving Problems with Forces and Motion
General Steps
- identify all known variables
- use force calculations and kinematic equations to substitute in known variables into equation
- draw a force diagram
- use the force diagram to create a force table
- solve for unknown variables
Example:
A person drops a 1 kg cup that accelerates at a rate of 9 m/s^2 as it falls down
A person drops a 1 kg cup that accelerates at a rate of 9 m/s^2 as it falls down