Force Summary

Types of Forces

Listing All Forces On An Object: Long-Range Forces

• Weight:

  • Consider weight unless it's negligible.

  • It is negligible if the object is very light compared to other large forces.

  • Weight is relevant if the object is not rolling down, sliding down, sagging, or falling.

• Electric or Magnetic Forces:

  • Not typically covered in this class.

  • Look for:

    • Electric Forces: Charged objects

    • Magnetic Forces: Charges, electric currents, bar magnets, iron, nickel, or cobalt.

• Gravitational Force: Represented as $\vec{F}_g$

Listing All Forces On An Object: Contact Forces

• Identify Contact:

  • List every object the object of interest is touching.

• Determine Force Types for Each Object in Contact:

  • Pulling: If a string, chain, or similar object is pulling, consider tension.

  • Touching Surfaces: Consider normal forces.

  • Sliding: Consider kinetic friction.

  • Rolling: Consider rolling friction and if it has traction

  • Touching a Fluid:

    • Buoyant force should be considered.

    • Buoyant force is negligible if the fluid has low density and the object is not very light.

  • Moving Through a Fluid:

    • Consider drag force.

    • Drag force is negligible if the object is moving slowly, is very heavy, or very small

• Important Note:

  • No other forces exist besides those listed.

  • Objects must pass a "kick test" to ensure the forces are real.

• Common Contact Forces:

  • Normal Force: $\vec{F}_N$

  • Tension: $\vec{F}_T$

  • Kinetic Friction: $\vec{F}_k$

  • Static Friction: $\vec{F}_S$

  • Rolling Friction: $\vec{F}_R$

  • Buoyant Force: $\vec{F}_B$

  • Drag Force: $\vec{F}_D$

Clicker Questions Breakdown

The following sections break down the clicker questions included in the transcript.

Clicker Question 14

• Scenario: Boxes being pulled up a ramp.

• Question: Which free body diagram best represents the forces on box A?

• Correct Answer: C)

• Forces Illustrated:

  • $\vec{F}_g$ (Gravitational Force)

  • $\vec{F}_N$ (Normal Force)

  • $\vec{F}_T$ (Tension)

Clicker Question 15

• Scenario: Boxes being pulled up a ramp.

• Question: Which free body diagram best represents the forces on box B?

• Correct Answer: D)

• Forces Illustrated:

  • $\vec{F}_N$ (Normal Force)

  • $\vec{F}_g$ (Gravitational Force)

  • $\vec{F}_T$ (Tension)

  • $\vec{F}_k$ (Kinetic Friction)

• Additional Notes from the slide:

  • $\vec{F}_{T, rope \text{ on } B}$ represents the tension force by the rope on box B.

  • $\vec{F}_{N, floor \text{ on } B}$ represents the normal force by the ramp/floor on box B.

  • $\vec{F}_{k, floor \text{ on } B}$ represents the kinetic friction force by the ramp/floor on box B.

Clicker Question 16

• Scenario: Forces on a weight on a string as it swings back and forth.

• Question: Which free body diagram best represents the forces on the weight?

• Correct Answer: B)

• Forces Illustrated:

  • $\vec{F}_g$ (Gravitational Force)

  • $\vec{F}_T$ (Tension)

Clicker Question 17

• Scenario: Forces acting on a person.

• Question: Which free body diagram best matches the situation of the person?

• Correct Answer: B)

• Forces Illustrated:

  • $\vec{F}_N$ (Normal Force)

  • $\vec{F}_g$ (Gravitational Force)

Newton's Laws of Motion

Slides Overview

• Newton’s Third Law: Forces between Objects

• Newton’s First Law:

  • Forces without acceleration

  • Lab 5: Net Force

• Newton’s Second Law:

  • Forces with acceleration

  • Lab 6: Unbalanced Forces

Forces Between Objects: Newton’s Third Law

• Basic Idea: When you push on something, it pushes back.

• Common Phrasing: “Every action has an equal and opposite reaction.”

• Better Phrasing: “For every force by A on B, B exerts a force back on A equally hard in the opposite direction.”

• Newton’s Third Law (Equation): $\vec{F}<em>{by \, A \, on \, B} = -\vec{F}</em>{by \, B \, on \, A}$

Newton’s Third Law on Free Body Diagrams

• Labeling Convention: Each force in a free body diagram should end with “on [object]”.

• Third Law Pairs: Pairs of forces are on different free body diagrams.

• Examples discussed:

  • Box B:

    • $\vec{F}_{g, Earth \, on \, B}$

    • $\vec{F}_{N, ramp \, on \, B}$

    • $\vec{F}_{T, rope \, on \, B}$

    • $\vec{F}_{N, A \, on \, B}$

    • $\vec{F}_{k, ramp \, on \, B}$

    • $\vec{F}_{S, A \, on \, B}$

  • Box A:

    • $\vec{F}_{g, Earth \, on \, A}$

    • $\vec{F}_{N, B \, on \, A}$

    • $\vec{F}_{S, B \, on \, A}$

Clicker Question 1 (Newton's Third Law Pairs)

• Scenario: Books stacked on a table.

• Question: Which of the following forces are Newton’s 3rd Law pairs?

• Correct Answer: C) $\vec{F}<em>{N, by \, A \, on \, B}$ & $\vec{F}</em>{N, by \, B \, on \, A}$

Clicker Question 2 (Number of Newton's Third Law Pairs)

• Scenario: Three books stacked on a table.

• Question: How many Newton’s 3rd Law pairs of normal forces would appear on the 3 FBD, one for each book?

• Correct Answer: D) 3

Class Problem: Books on a Table (Part 1)

• Problem: Three books (A, B, C with masses 0.5 kg, 1 kg, and 2 kg respectively) are stacked on a table.

• Tasks:

  • Draw a properly labeled free body diagram for each book.

  • Identify Newton’s 3rd Law force pairs.

• Key Insight: Newton’s Third Law force pairs are the same force, just flipped in direction.

• Forces Identified:

  • $\vec{F}_{g,E \, on \, A}$

  • $\vec{F}_{g,E \, on \, B}$

  • $\vec{F}_{g,E \, on \, C}$

  • $\vec{F}_{N,B \, on \, A}$

  • $\vec{F}_{N,A \, on \, B}$

  • $\vec{F}_{N,C \, on \, B}$

  • $\vec{F}_{N,B \, on \, C}$

  • $\vec{F}_{N,T \, on \, C}$

Clicker Question 3 (Semi Truck vs. Small Car Collision)

• Scenario: A semi truck collides with a small car.

• Question: Which force is greater?

• Correct Answer: C) The two are equal.

• Explanation: According to Newton's Third Law, the forces will always be equal, although the acceleration experienced by each vehicle will differ due to their different masses.

Net Force with Constant Velocity: Newton's 1st Law

Lab 5: Net Force (Part 1)

Newton’s First Law

• Basic Idea: Objects don’t change velocity without a net force on them.

• Common Phrasing: “An object in motion stays in motion unless acted upon by an external force.”

• Better Phrasing: “If and only if there is no net force on an object, it has no acceleration.”

• Equation: $\sum \vec{F}<em>{on \, A} = 0 \text{ if and only if } \vec{a}</em>A = 0$

  • $\sum \vec{F}_{on \, A}$ is the net force on a generic object “A”.

  • $\vec{a}_A$ is the acceleration of “A”.

Clicker Question 4 (Puck Sliding on Ice)

• Scenario: A puck slides across a slick ice rink at a constant speed, in a straight line.

• Question: What direction is the net force?

• Correct Answer: C) There is no net force.

Clicker Question 5 (Tension in a Pulley System)

• Question: What is the tension in the string for this system of pulleys?

• Answer: The correct answer is C) $\frac{1}{2}mg$

Class Problem: Books on a Table (Part 2)

• Problem: Three books are stacked on a table (A, B, and C with masses 0.5 kg, 1 kg, and 2 kg respectively).

• Task: Find the magnitude of all forces.

• Solution:

  • $\vec{F}_{g, E \, on \, A} = 4.9 \, N$

  • $\vec{F}_{g, E \, on \, B} = 9.8 \, N$

  • $\vec{F}_{g, E \, on \, C} = 19.6 \, N$

  • $\vec{F}_{N, B \, on \, A} = 4.9 \, N$

  • $\vec{F}_{N, A \, on \, B} = 4.9 \, N$

  • $\vec{F}_{N, C \, on \, B} = 14.7 \, N$

  • $\vec{F}_{N, B \, on \, C} = 14.7 \, N$

  • $\vec{F}_{N, T \, on \, C} = 34.3 \, N$

• Labels: Book A, Book B, and Book C.

Newton’s 1st Law in Two Dimensions

• Key Principle: Newton’s 1st Law works separately along each axis.

• Example: Projectile Motion

  • No horizontal forces, so $\sum F_x = 0$

  • No horizontal acceleration, so $\, a_x = 0$

• Equations:

  • $\sum F<em>{x, on \, A} = 0 \text{ if and only if } a</em>{A, x} = 0$

  • $\sum F<em>{y, on \, A} = 0 \text{ if and only if } a</em>{A, y} = 0$

Clicker Question 6 (Sling Throws a Stone)

*Scenario: A sling throws a stone by releasing it as it swings in a circle.
*Question: What path would the stone take after release?
*Answer: A)

Lab 5: Net Force (Parts 2 and 3)

Newton’s 1st Law: Problem Solving Steps

1. Diagram Situation

2. Identify Objects of Interest

   • Know or want to know forces or acceleration.

3. Identify Forces on Objects of Interest

4. Freebody Diagram of Objects of Interest

   • Label objects.

   • Label type of force, “by” object and “on” object.

   • Ensure all “on” objects match diagram object.

   • Example: Person

     • $\, \vec{F}_{g, by \, E \, on \, P}$ (Gravitational force)

     • $\, \vec{F}_{N, by \, G \, on \, P}$ (Normal force)

Newton’s 1st Law: Problem Solving Steps (Continued)

5. Set up Newton’s 1st Law equation for each object of interest

   • General form: $\, \sum \vec{F}_{on \, P} = 0$

   • Expand sum: $\, \vec{F}<em>{g, by \, E \, on \, P} + \vec{F}</em>{N, by \, ground \, on \, P} = 0$

   • Write component equations:

     • $\, F<em>{g,x} + F</em>{N,x} = 0$

     • $\, F<em>{g,y} + F</em>{N,y} = 0$

   • Find components of each force:

     • $\, F<em>{g,x} = 0, F</em>{g,y} = -m_Pg$

     • $\, F<em>{N,x} = 0, F</em>{N,y} = F_N$

   • Plug in each component:

     • $\,-m<em>Pg + F</em>N = 0$

     • $\, 0 + 0 = 0$

6. Solve for variables of interest

   • $\, F<em>N = m</em>Pg$

Problem Solving Suggestions

1. Acceleration is often implied ($\vec{a} = 0$ for constant velocity)

2. Tension points in the direction of ropes/string/etc.

   • Same angles on forces as angles in situation.

   • Find angle of rope means find direction of tension force.

3. Negligible mass (“very light”, “massless”, …)

   • Ignore weight: $\, \vec{F}_g \sim 0$

   • Tension constant magnitude throughout “string”.

4. Rotate axes to align with the majority of forces (especially on tilted surface)

General Physics I Fall 2023 Quiz 2 (Version B): Question 1 Walkthrough

• Problem: A 20 kg block is dragged up the ramp at a constant speed with a rope. The coefficient of kinetic friction between the ramp and block is 0.5. What is the tension in the rope?

• Solution Steps:

  • Draw a Free Body Diagram (FBD).

  • List knowns: Mass $\, m = 20 \, kg$, coefficient of friction $\, \mu_k = 0.5$, and acceleration $\, a = 0$.

  • Identify forces:

    • Tension force $\, F_T$

    • Normal force $\, F_N$

    • Weight $\, W = mg$

    • Kinetic Friction $\, F<em>k = \mu</em>k F_N$

  • Establish coordinate system where x is parallel to the ramp and y is perpendicular.

  • Express components of Weight $\, W$:

    • Parallel: $\, mg\sin(\theta)$

    • Perpendicular: $\, mg\cos(\theta)$

  • Since $\, a=0$, $\, \sum F = 0$

  • $\, \sum F_x = 0$

  • $\, \sum F_y = 0$

  • $\, \sum \vec{F}<em>{Tx} + \vec{F}</em>{kx} + \vec{W_x} = 0$

  • $\, \sum \vec{F}<em>{Ty} + \vec{F}</em>{Ny} + \vec{W_y} = 0$

  • Find Tension, $\, F_T = (0.5 \dot mg \cos(\theta)) + mg \sin(\theta)$

  • $\, = mg(\mu_k \dot \cos(\theta) + \sin(\theta))$

General Physics I Fall 2023 Quiz 2 (Version B): Question 2 Walkthrough

• Problem: A spring hangs vertically with no weight on it and no tension in it. In this state, it has a length of 10 cm. Then a 200 g weight is attached to the bottom, which stretches it until it is 25 cm long. Find the spring constant of the spring.

• Solution Steps:

  • Apply equilibrium of forces.

  • $\sum F = 0$

  • Free body force diagram. There is a gravitational force going down and Tension going up.

  • $\sum F<em>{igy} + F</em>{ty}=0$

  • $-mg + k(\Delta x) = 0$

  • Rearrange to solve for k

  • \k = \frac{mg}{(\Delta x)}

General Physics I Fall 2023 Quiz 2 (Version B): 3 Conceptual Multiple-Choice Questions.

• 1. A stationary block rests on a ramp as a rope pulls it to the right. Which free body diagram matches the situation?

• 2. A pendulum is swinging back and forth, as shown in the figure to the right. At which point is the tension the smallest?

• 3. Which of the following pairs of forces are always equally large but in opposite directions, regardless of the motion of the objects?

Extra Credit Essay (Worth up to 10pts)

• A) State one of Newton’s Laws in words, using the “better phrasing” discussed in class or equivalently accurate wording.

• B) State another of Newton's Laws in words, using the “better phrasing” discussed in class or equivalently accurate wording.

• C) State the last Newton’s Laws in words, using the “better phrasing” discussed in class or equivalently accurate wording.

• D) Identify which of the three answers above are Newton’s 1st Law, Newton’s 2nd Law, and Newton’s 3rd Law.

Example Problem: Slippery Slope

• Problem Statement: A woman walks up a slick slope at a steady pace, trying not to slip down. If the coefficient of static friction between her shoes and the ground is 0.5, what is the steepest slope she can climb?

• Answer: 26.6 degrees off the horizontal.

• Key Concepts:

  • Static Friction: The force that prevents an object from starting to move.

  • Equilibrium: The state where the net force on an object is zero.

  • Free Body Diagram: A diagram showing all forces acting on an object.

  • Components of Forces: Breaking forces into horizontal and vertical components for easier analysis.

• Solution Approach:

  • Draw a Free Body Diagram (FBD).

    • Forces on the person:

      • Gravitational force $\, F_g$

      • Normal force $\, F_N$

      • Static friction force $\, F_s$

  • Set up coordinate system where y is parallel to the ramp and x is perpendicular.

  • Relate the angle to the coefficient of static friction.

Clicker Question 7 (Stationary Box)

• Which FBD best illustrates forces on Stationary Box?

• Correct Answer: D

Clicker Question 8 (Angles in Box FBD)

• Question: Which angle(s) in the box FBD are equal to $\, \theta$ in the figure?

• Correct Answer: (A)

Clicker Question 9 (Stationary Ramp)

• Question: Which FBD best illustrates the forces on the stationary ramp?

• Correct Answer: A

Clicker Question 10 (Angles in Ramp FBD)

*Question: Which angle(s) in the ramp FBD are equal to $\, \theta$ in the figure?
*Correct Answer: B

Clicker Question 11 (Newton's 3rd Law Pairs)

*Question: Which pairs of forces are Newton's 3rd Law pairs?
*Correct Answer: D)

Class Problem: Box & Ramp Forces

• Problem Statement: Find the magnitude of each forces on both the box and ramp, both of which remain stationary.

• Provided Information:

  • Box stationary

  • Ramp stationary

  • Angle $\, \theta = 30$

• Break Down:

  • A $=$ Adjacent.

  • O $=$ Opposite

• Therefore Pythagorean theory is required

• $F_{S,,y}=-\,m<em>g</em>cos(0)$

Net Force & Acceleration: Newton's 2nd Law

Causing Motion Discussion

• Discussion Points:

  • What causes motion?

    • Net force causes acceleration.

    • Acceleration leads to speeding up, slowing down, or turning.

Mistaken Intuition on Forces

• Intuition: Forces cause velocity.

  • Velocity is in direction of force.

  • Without net force, objects stop.

  • $\, \vec{v} \propto \vec{F}$

• Reality: Forces cause acceleration.

  • Acceleration is in the direction of force.

  • Without net force, velocity doesn’t change.

  • $\, \vec{a} \propto \vec{F}$

• Apparent vs Actual Situations

  • Apparent situation: Net force at constant velocity.

  • Actual situation: No net force at constant velocity.

• Friction: Friction is the reason that most objects require an applied force to move along the ground.

Newton's Second Law

• Basic Idea: Net force produces acceleration.

• Generalizes Newton’s First Law

• Equation: $\, \sum \vec{F}<em>{on \, A} = m</em>A \vec{a}_A$

• Where:

  • $\, \sum \vec{F}_{on \, A}$ is the net force on generic object “A.”

  • $\, m_A$ is the mass of “A.”

  • $\, \vec{a}_A$ is the acceleration of “A.”

• $\, \sum \vec{F}$ & $\, \vec{a}$ point in same direction!

Clicker Question 12 Braking Car

*Question: A car brakes to a stop. While braking, which direction is the net force on the car?
*Correct Answer: A
*The net force direction is toward the rear of the car.

Clicker Question 13 Braking Car Passenger

*Question: A car brakes to a stop. While braking, which direction is the net force on the passenger?
*Correct Answer: A
*The New Force Direction: Towards The rear of car

Clicker Question 14 Braking Car Forces

*Question: A car brakes to a stop. While braking, which experiences the largest net force?
*Correct Answer: B
*The car experiences the largest net force

Newton’s 2nd Law: Problem Solving Steps

1. Diagram situation

2. Identify objects of interest

   • Know or want to know forces or acceleration

3. Identify forces on objects of interest

4. Freebody diagram objects of interest

   • Label objects

   • Label type of force, “by” object and “on” object

   • Make sure all “on” objects match diagram object

   • [Person (jumping)]

     • Gravitational force, $\, \vec{F}_{g,by \, E \, on \, P}$

     • Normal force, $\, \vec{F}_{N,by \, G \, on \, P}$

Newton’s 2nd Law: Problem Solving Steps

1. Set up Newton’s 2nd Law equation for each object of interest

   • General form: $\, \sum \vec{F}<em>{on \, P} = m</em>Pa_P$

   • Expand sum: $\, \vec{F}<em>{g,by \, E \, on \, P} + \vec{F}</em>{N,by \, ground \, on \, P} = m<em>Pa</em>P$

   • Write component equations: $\, F<em>{g,x} + F</em>{N,x} = m<em>Pa</em>{P,y}, F<em>{g,y} + F</em>{N,y} = m<em>Pa</em>{P,x}$

   • Find components of each force and acceleration:

     • $\, F<em>{g,x} = 0, F</em>{g,y} = -m<em>Pg, F</em>{N,x} = 0, F<em>{N,y} = F</em>N, a<em>{P,x} = 0, a</em>{P,y} = a$

   • Plug in each component:$\,-m<em>Pg + F</em>N = m_Pa, 0 + 0 = 0$

2. Solve for variables of interest $\, (F<em>N = m</em>P(g + a))$

Problem Solving Suggestions

1. Acceleration is often implied ($\vec{a} = 0$ for constant velocity)

2. Tension points in the direction of ropes/string/etc.

   • Same angles on forces as angles in situation.

   • Find angle of rope means find direction of tension force.

3. Negligible mass (“very light”, “massless”, …)

   • Ignore weight $\, \vec{F}_g \sim 0$, approximately zero net force $\, ma \sim 0$

   • Tension constant magnitude throughout “string”

4. Rotate axes to align with majority of forces (esp. on tilted surface)

New steps in bold

Freefall Revisited

• Revised definition

  • An object is in freefall if only gravitational forces act on it

• Why does $\, a = g$ in freefall?

  • Newton’s 2nd Law explanation

    • Step 1: $\, \sum \vec{F}<em>{on \, A} = m</em>A\vec{a}_A$

    • Step 2: $\, \vec{F}<em>{g,Earth \, on \, A} = m</em>A\vec{a}_A$

    • Step 3: $\, m<em>Ag</em>{Earth} = m<em>A\vec{a}</em>A$

    • Step 4: $\, g<em>{Earth} = \vec{a}</em>A$

Finer Point: Which Acceleration to Use?

• Basic issue

  • Newton’s Laws describes motion with one acceleration per object

  • …but which acceleration?

• Currently limited to objects that only have one acceleration

  • Point particles

    • Negligible dimensions so only one position

  • Rigid, non-rotating objects

    • All pieces share the same acceleration

• Later we will define which acceleration it describes for any object

Class Problem: Books in an Elevator

The table from the previous problem is placed in an elevator accelerating at 1 m/s^2 upward. What are all the forces now?

• $\, F_{g,E} = 4.9N$

• $\, F_{g,E} = 9.8N$

• $\, F_{g,E} = 19.6N$

Lab 6: Unbalanced Forces

Newton's Laws Recap

Forces & Motion:

• 1st:

  $\, \sum \vec{F}<em>{on A} = 0 iff \vec{a}</em>A = 0$

• 2nd:

  $\, \sum \vec{F}<em>{on A} = m</em>A*\vec{a}_A$

Forces as interaction:

• 3rd:

  $\,\vec{F}<em>{by A on B} = - \vec{F}</em>{by B on A}$

Class Problem: Slipping Down

A box of unknown mass is set on a board, as shown. The board is tilted up until the box begins to slip. If the coefficient of friction is 0.6 (static) and 0.4 (kinetic) between the board and box, find:

• The angle at which the box begins to slip. 31.0°

• The speed it reaches right before hitting the floor. 0.71 m/s

Example Problem:

Atwood Machine

What's the acceleration of the masses?

Class Problem: A Balanced Design

al blocks remain stationary, if the weight of the rope and frictional forces are both negligible?
an the blocks remain stationary: Answer = 𝟏𝟗. 𝟓°