Forces & Newton's Laws

2024-25 Regents Physics

A casual model for motion

What is a Force?

  • An interaction between two objects
  • Forces are the cause for differing motion

Motion is a result of all forces acting on an object.

Pivot - Balanced vs. Unbalanced Forces

How does motion differ when forces are balances vs. unbalanced?

Newton's First Law

graph TD A[Forces are Balanced] --> B[Objects at Rest
v = 0 m/s] A --> C[Objects in Motion
v ā‰  0 m/s] B --> D[a = 0 m/sĀ²] C --> E[a = 0 m/sĀ²] D --> F[Stay at Rest] E --> G[Stay in Motion
same speed and direction]

Balanced Forces

  • Net force = 0
  • Object either:
    • Stays at rest
    • Continues at constant speed

Unbalanced Forces

  • Net force ā‰  0
  • Object:
    • Speeds up
    • Slows down
    • Changes direction

Newton's First Law (Inertia)

  • Inertia is an object's resistance to changes in its state of motion

  • The amount of inertia is based solely on its mass

Mass and Inertia

  • Mass = amount of matter
  • More mass = more inertia
  • Example:
    • Harder to start/stop heavy cart
    • Easier to start/stop light cart

šŸ“ Worksheet: Inertia & Mass

Complete Independently

Pre-Conceptions

Students typically have many pre-conceived notions regarding concepts in Physics. It has always proven useful to bring these ideas to the forefront of your mind and to make an effort to evaluate their correctness. The following statements pertain in one way or another to common notions regarding central concepts of this unit. Identify each statement as being either true (T) or false (F).

  1. Fill out on sheet and then click answers into Google Form (linked in daily slides) and here.

āš–ļø Mini Experiment: Mass vs. Weight

Objective:

Determine the mathematical relationship between mass and weight using a spring scale.

Notes:

  • Don't forget a diagram of your setup
  • Include units in your measurements
  • Will need graph and equation for line of best fit

šŸŒŽ Gravity

Notes:

  • Weight == == Force of Gravity...so
  • Weight is a FORCE, mass is scalar quantity
  • is the gravitational field strength
    • Measured in N/kg
    • changes based on planet and location on that planet
    • near the surface of the Earth

āš–ļø Reminder Mass vs. Weight

Mass:

  • related to how much stuff there is
  • the same regardless of location in universe
  • measured in kilograms (kg)

Weight:

  • How much Earth is pulling on that stuff
  • depends on the gravitational field strength ()
  • measured in Newtons (N)

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The diagram to the right shows a 3 kg mass attached to spring scales on Earth, Mars, and Earth's Moon. Use the information in the diagram to calculate the gravitational field strength () for each Celestial Body.

Reminder:

āš–ļø Balanced Forces

Book at Rest

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  • Forces are equal in magnitude and opposite in direction, they balanced each other

šŸ“ Unbalanced Forces

Book Sliding across table

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  • Sometime in the prior history of the book, it may have been given a shove and set in motion from a rest position.
  • Friction now accelerates (slows) the book down

Balanced Forces

Book at Rest

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  • Constant velocity
  • (not necessarily v = 0)

Unbalanced Forces

Book Sliding across table

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  • Acceleration

A force is a push or pull upon an object resulting from the object's interaction with another object.

Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.

Force Categories

Contact Forces

  • Objects are physically in contact with each other
  • Examples: tension, friction, normal force, air resistance, applied forces

Action at a distance

  • Interaction when objects are not in contact with each other.
  • Examples: gravitational, electrical , magnetic

What is a Newton?

  • The unit of force
  • 1 N is the amount of net force required to accelerate a 1 kg mass 1 m/s/s.

Force is a vector

  • it has magnitude and direction

Types of Forces

Force & Symbol Description
Gravity The force of gravity is the force with which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth.
Applied Force An applied force is a force that is applied to an object by a person or another object. If a person is pushing a desk across the room, then there is an applied force acting upon the object. The applied force is the force exerted on the desk by the person.
Force & Symbol Description
Normal The normal force is the support force exerted upon an object that is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasions, a normal force is exerted horizontally between two objects that are in contact with each other. For instance, if a person leans against a wall, the wall pushes horizontally on the person.
Tension The tension force is the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. The tension force is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire.
Force & Symbol Description
Friction The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. There are at least two types of friction force - sliding and static friction. Though it is not always the case, the friction force often opposes the motion of an object. Friction results from the two surfaces being pressed together closely, causing intermolecular attractive forces between molecules of different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together.
Force & Symbol Description
Spring The spring force is the force exerted by a compressed or stretched spring upon any object that is attached to it. An object that compresses or stretches a spring is always acted upon by a force that restores the object to its rest or equilibrium position.
Air Resistance (Drag) The air resistance is a special type of frictional force that acts upon objects as they travel through the air. The force of air resistance is often observed to oppose the motion of an object. This force will frequently be neglected due to its negligible magnitude (and due to the fact that it is mathematically difficult to predict its value).

Net Force or

If forces are unbalanaced there is there is a total amount of unbalanced force. This is the net force on an object.

Note: Net force is not an individual force. It is a result of adding all of the force vectors acting on an object.

Net Force

Adding Vectors

Net Force with Force Diagrams

  • 1200 N + -800 N = 400 N
  • 600 N + -800 N = -200 N
  • 50 N + -50 N = 0 N
  • 20 N + 0 N = 20 N

Drawing Free Body Diagrams

A special type of force diagram that represents all the forces acting upon an object. Arrows represent the forces. The force arrows ā€¦

  • ā€¦ are labeled according to type,
  • ā€¦ are pointing in the direction of the force,
  • ā€¦ and have a length that is in proportion to their relative strength (longer arrows are stronger forces).

alt text

Drawing FBDs

  1. Identify forces that are present:
    • Is the object near a planet (charge or magnet)?
    • Is the object in contact with another object?
  2. Determine the direction of each force
  3. Draw an arrow to represent the force starting at the center of the dot or box representing the object and pointing in the direction of the force?
  4. Draw the force to scale to represent magnitude
  5. Label the arrow with the force type

FBD Demo āœļø

Newton's First Law

When forces are balanced our objects maintain their constant velocity

How do we handle unbalanced forces?

Newton's Second Law

Newton's Second Law

also written as...

On a whiteboard...

āœļø Sketch:

1. A graph of acceleration (y axis) vs. net force (x axis) for constant mass

2. A graph of acceleration (y-axis) vs. mass (x-axis) for constant net force

Newton's 2nd Law Lab: Fan Carts

Objective:

Using your fan cart, collect data to verify Newton's Second Law. Use acceleration as your dependent variable. Design two experiments.

Materials:

  • wireless dynamics cart
  • fan
  • track
  • assorted masses

Must Include:

  1. Two procedures.
  2. Free body diagrams for your fan cart to reference your net force, and how you will measure that fan force.
  3. Diagram of your experimental setup.
  4. Just one discussion & conclusion to write about both experiments.

N2L Lab: Measuring Cart Force

Experiment 2: vs.

  • Change the Fan force (can use 8 values) āž”ļø two fans
  • Measure acceleration
  • Be sure to record your control value (mass)

Measuring

  1. Zero force sensor (bottom right corner)
  2. Turn fan on
  3. Have fan at rest against a wall or mass
  4. Record force for a set period of time.
  5. Record average force value

N2L Results

vs. Acceleration

  • graph is linear
  • slope should be ()

Mass vs. Acceleration

  • graph is inverse relationship
  • constant in equation should be

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N2L Summary:

  • acceleration is directly proportional to Net Force
  • acceleration is inversely proportional to mass

šŸ’ŖšŸ§  Forces Packet page 12 & 13

Putting it all together

Using N2L and to find acceleration

  1. page 14 in packet together
  2. complete page 16 on your own

Assuming Friction...

Rank the boxes from easiest to acceleration to most difficult to accelerate. Explain your reasoning...

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Boxes are held at rest against rough, vertical walls by forces pushing horizontally on the boxes as shown.

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Rank the magnitude of the normal force exerted on the walls by the boxes.

Boxes are held at rest against rough, vertical walls by forces pushing horizontally on the boxes as shown.

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Rank the magnitude of the normal force on each box from greatest to least.

Ignoring the normal force...which box(es) do you think is the most difficult to hold up? Why?

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In both cases below, Grace pulls the same large crate across a floor at a constant speed of .

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Is the magnitude of the force exerted by Grace on the rope (i) greater in Case A, (ii) greater in Case B, or (iii) the same in both cases?
Explain your reasoning.

Friction

Notes:

  • is only for static friction
    • Why? Only need friction to balance so you don't need the maximum amount of static friction
  • (greek letter mu, pronouced "mew") - coefficient of friction
    • how likely surface pairs are to interlock
    • always less than 1

Common Values

** From NYS Regents Physics Reference Tables

How do Kinetic compare to Static values?

Friction Practice

Consider the free-body diagram for an object accelerating across a surface. The object has a mass of 2.12-kg. There is a forward thrust force of 50.0 N. The coefficient of friction between the object and the surface is 0.365. Determine the ā€¦

  1. experienced by the object
  2. experiened by the object
  3. experienced by the object
  4. Acceleration experienced by the object

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Dexter Eius is running through the cafeteria when he slips on some mashed potatoes and falls to the floor. (Let that be a lesson for Dexter.) Dexter lands in a puddle of milk and skids to a stop with an acceleration of . Dexter weighs .

Determine the coefficient of friction between Dexter and the milky floor.

Amaya is driving his car home after soccer practice. He is traveling down Lake Avenue with a speed of . A deer runs onto the road and Amaya skids to a stop in .

Determine the coefficient of friction between the car tires and the roadway.





Static Friction Lab Example

Friction Lab

Objective

Determine the coefficient of static friction between your block and a two flat surfaces in the classroom.

Materials

  • Wooden block
  • Electronic Force Sensor

Hypothesis

Which surface will have a greater coefficient of friction?

Newton's 3rd Law: Force Pairs

"For every action, there is an equal and opposite action."

šŸ˜‘

Forces are a result of two objects interacting. The force that each object applies on the other is equal in magnitude and opposite in direction.

While driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The firefly hit the bus and the bus hits the firefly. Which of the two forces is greater: the force on the firefly or the force on the bus?

In the top picture (below), Kent Budgett is pulling upon a rope that is attached to a wall. In the bottom picture, Kent is pulling upon a rope that is attached to an elephant. In each case, the force scale reads 500 Newton. Kent is pulling ...

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a. with more force when the rope is attached to the wall.
b. with more force when the rope is attached to the elephant.
c. the same force in each case.

Packet Page 23

Two toy trucks traveling at different constant speeds are about to collide.

(a) The two identical trucks are traveling in the same direction, and truck B is carrying a heavy load.
(b) The two identical trucks are traveling in opposite directions, and truck B is carrying a heavy load.
(c) The two identical trucks are traveling in the same direction, and truck A is carrying a heavy load.
(d) The two identical trucks are traveling in opposite directions, and truck A is carrying a heavy load.

During the collision, will the magnitude of the force exerted on truck A by truck B be (i) greater than, (ii) less than, or (iii) equal to the magnitude of the force exerted on truck B by truck A?

Angled Forces

Identical treasure chests (shown from above) each have two forces acting on them. All chests start at rest.

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Rank the speed of the treasure chest after 2 seconds.

A block is moving to the right across a rough table at a constant speed of 2 m/s. The tables and the blocks are identical in the two cases. In Case A, the block is pushed with a stick and in Case B, the block is pulled with a string. The angle that the applied force makes with the horizontal is the same in both cases.

Will the magnitude of the force on the block by the stick in Case A be (i) greater than, (ii) less than, or (iii) equal to the tension on the block by the string in Case B?

Explain your reasoning.

Partner Work - Another F = ma

(New Forces Packet)

Vector Review

  • Depending on the angle...

Adding Vectors

Using Components

You can sum the components of the two vectors to find the components of the resultant vector

If ...

A pack of five Artic wolves are exerting five different forces upon the carcass of a 500-kg dead polar bear. A top view showing the magnitude and direction of each of the five individual forces is shown in the diagram at the right.



1. Name that vector

2. Vector Guessing Game

Helpful Simulation: Vector Addition Simulation

Solving Force Problems with Components

Equilibrium - when forces on an object are balanced.

alt text

Example

Process 1: Vector Addition

becomes

Process 2: Vector Components:

becomes

šŸ”— Balance It!

Example Together

Here's the clown who came to town to sign your yearbook upside down

Suppose the tension in both of the cables is measured to be 50 N and that the angle that each cable makes with the horizontal is known to be 30 degrees. What is the weight of the sign?

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Example Together

Here's the clown who came to town to sign your yearbook upside down

Suppose the tension in both of the cables is measured to be 50 N and that the angle that each cable makes with the horizontal is known to be 30 degrees. What is the weight of the sign?

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Fg = 50 N

Example 2

The sign below hangs outside the physics classroom, advertising the most important truth to be found inside. The sign is supported by a diagonal cable and a rigid horizontal bar. If the sign has a mass of 50 kg, then determine the tension in the diagonal cable that supports its weight.

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Packet Page 5 & 6

šŸ”— Physics Classroom - Equilibrium 1

šŸ”— Physics Classroom - Equilibrium 2

Inclined Planes

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Inclined Planes

  • Component of gravity perpendicular to incline

  • Component of gravity parallel to incline

**if you can't find these with ease using trig, you MUST memorize those equations

Lab partners Anna Litical and Noah Formula placed a 0.25-kg glider on their air track and inclined the track at 10.4Ā° above the horizontal. Use the structure provided at the right to determine the ā€¦

  1. Force of gravity
  2. Parallel component of gravity
  3. Perpendicular component of gravity
  4. Normal Force
  5. Net Force
  6. Acceleration