Mr. Rogers' Honors Physics

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
2D Force(5)
2D Motion(6)

Forces in 2 Dimensions-- Chapter 5
SC Standards :


P-2.1 Represent vector quantities (including displacement, velocity, acceleration, and force) and use vector addition.

P-2.7 Use a free-body diagram to determine the net force and component forces acting upon an object


Practice Test Study Guide


Essential Question: Does 1 + 1 = 2?

Graphical Vector Addition and Components

  1. Recognize the relationship between vectors that are directly proportional to each other. The direction of each is always the same.
  2. Examples:

    Force and acceleration F = ma
    Velocity and Displacement V = (Displacement) / (time increments
  3. Sketch 2 ways to graphically add vectors. Vectors are represented as arrows. The length of the arrow represents the magnitude and the way the arrow points represents the direction. For addition purposes, arrows can be moved around as long as the angle they make with respect to the vertical and horizontal dimensions is not changed. The sum of 2 or more vectors is called the resultant.
  • head-to-tail or heal to toe
  • parallelogram method
    Vector addition: head to toe Vector addition: parallelogram method




Essential Question: What are the parts of a vector?

Vector Components

  1. Define vector components. A vector's components are the x and y coordinates of a vector, assuming that the vector's tail is at the origin. Components can also be considered the or x and y parts of a vector that added together will equal the original vector.

    1. Given vector components find the resultant vector (A) and its angle (theta).
    2. A = (Ax2 + Ay2)1/2

      q = arctan Ay / Ax

    3. Given a vector (A) find its components Ax and Ay.

      Ax = A cos q

      Ay = A sin q

    Vector addition

The Engineering Connection: One of the first steps in designing complex structures such a bridges and buildings consists of analyzing the components of the various complex forces in the structure. From this, it is possible to correctly size the parts of the structure that use standardized items such as i-beams. This process is called statics and is one of the first courses almost all college engineering majors take. It is particularly of interest to civil or structural engineers


Homefun (formative/summative assessment): Read sections 5.1


Formative Assessment: Physics Investigation

Research Question  
Data, Calculations  

Follow up Questions




Essential Question: What is the fastest way to swim across a swiftly flowing river?

Mathematical Vector Addition

  1. State the relationship between the magnitudes of vector components that exist in different dimensions (such as the x and y dimensions). They are totally independent of each other. Different dimensions are like separate worlds.

  2. State the relationship between the direction of vector components in different dimensions. They are at a 90 degree angle with each other.

  3. Add vectors together using the component method.

    1. Make a vector diagram showing all the vectors with their tails at the origin of an x and y axis.

    2. Break all the vectors into components.

    3. Sum the x-components and sum the y-components.

    4. Vectorially add the x-components and sum the y-components.

  4. Solve problems involving adding or subtracting 2 vector components.

    Formative assessments:

  • Swimmer problems -- Running Bear (1960, Johnny Preston. The song was #1 for three weeks in January 1960 on the Billboard Hot 100 in the United States. The song also reached #1 in the UK in 1960.)

  • Airplane problems -- Meet me in St. Louis (Judy Garland, 1944 movie)

  • Displacement problems

Homefun (formative/summative assessment):

Read sections 4.2,

do Practice Problems 5, 7, and 9 on page 125.

Write a paragraph discussing the following question: Before the advent of modern navigation techniques such as GPS, why would having a compass not be enough to successfully navigate the oceans and actually arrive at a given destination?


Essential Question: Is friction helpful or harmful?

The 3 Models for Friction

  1. Describe static friction.

    • Prevents sliding between surfaces
    • Variable - adjusts to match the force which would otherwise cause sliding (the parallel force).

      Friction Graph

  2. Correctly use the model for calculating static friction.

Fs = Fp

static friction = parallel force

  1. Correctly use the model for calculating the transition point between static and dynamic friction.

Fsmax = msFn

ms= static COF or static coefficient of friction, an experimentally determined or measured constant for given surfaces
  1. Describe the relationship of normal force to transition point between static and dynamic friction and describe how this knowledge is used with fasteners. Fasteners, such as screws, are a form of inclined plane and have very high mechanical advantages that can produce extremely high normal forces resulting in extremely high friction forces that resist "unscrewing".

  2. Describe dynamic or sliding  friction.

    • Resists sliding between surfaces

    • Constant for a give normal force

  3. Correctly use the model for calculating the dynamic friction.
Fd = mdFn
  1. State which form of friction tends to be lower, the maximum static friction or sliding friction. Dynamic is generally lower but never higher than the maximum static friction.

  2. Be aware that there are actually 3 different mathematical models for friction. (see above)

  3. State the relationship between contact area and friction. (Hint: contact area is not in any of the 3 equations)

  4. Calculate friction forces. Note COF = coefficient of friction. Static COF = ms, dynamic COF = md

  5. Solve friction problems

    Formative assessments:

    Jake's dog

    Push vs. pull


The Engineering Connection: Friction is a huge issue in many aspects of machine and vehicle design. The drive belts on pulleys cannot slip, but on the other hand, for chutes designed for unloading materials such as coal, the materials must slide easily. Both acceleration in speeding up and slowing down depends on tire friction. Even simple components like nuts and bolts depend on friction to keep from coming undone. Mechanical and materials engineers would be especially concerned with friction.

Homefun (formative/summative assessment): problems 17, 19, 21, page 128


Essential Question: What makes an object slide or roll down a slope?

Weight Force Components on a Slope

  1. Find the normal (Fwn) and parallel (Fwp) components of the weight force (Fw) for objects on a slope that makes an angle of with the horizon β.

    Note: Fw= mg

Fwn = Fw cosβ, this is the component of the weight force that acts perpendicular to the slope.

Fwp = Fw sinβ, this is the component of the weight force that can make an object slide down a slope.


  1. Find the angle of the slope where the normal component of weight exceeds the parallel component.

  2. Solve for acceleration of objects on a slope with zero friction.

    Formative assessments

    An ice road truck sliding down an icy slope


The Engineering Connection: Forces on slopes are a major issue to traffic and civil engineers. If the the slope is two steep in either the upward or downward directions, the result can be serious safety or traffic flow problems.

Homefun (formative/summative assessment): problems 33, 35, 37 page 133


Essential Question: How can you best prepare for the test?

Review of Objectives 1- 13 (1-3 days)

Formative Assessments:

  1. Work review problems at the board

  2. Work practice problems.

Metacognition Problem Solving Question: Can I still work the problems done in class, several hours or days later? Some amount of repetition on the exact same problems is necessary to lock in learning. It is often better to thoroughly understand a single example of a problem type than to work example after example understanding none of them completely.

Relevance: Good test preparation is essential to performance in physics class.

Homefun (formative/summative assessment): problems 67, 75, 77, 89 (add the vectors mathematically), 85, and 99 , page 141-143; problems turn in on the day stapled to the back of the test.

Summative Assessment: Unit exam objectives 1-16


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