# UTPA STEM/CBI Courses/Physics (Calculus Based)/Vectors and Free Body Diagrams

Course Title: Calculus Based Physics I

Lecture Topic: Vectors and Free Body Diagrams

Instructor: Dr. Liang Zeng

Institution: University of Texas-Pan American

## Backwards Design

Course Objectives

• Primary Objectives- By the next class period students will be able to:
• Introduce syllabus and learning modules
• Know, understand and apply Newton’s three laws
• Understand why and how to use vectors
• Know how to derive two-dimensional free-body diagrams for various physical systems (including normal forces)
• Sub Objectives- The objectives will require that students be able to:
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• Difficulties- Students may have difficulty:
• No physics background from high school
• Thinking you know those concepts, but not mastering them
• Trigonometry skills (Review B-3 Geometry and B-4 Trigonometry in Appendix); decompose vectors
• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
• Vectors
• Dipoles in some molecules (electrical fields)
• Beam analysis
• Newton’s first law (the law of inertia)
• Safety belts , when car comes to a sudden unexpected stop from a high speed, one can fly out the car
• It takes longer time for a train, a big cruise ship, 18 wheeler truck to come to a stop than a sedan
• Our experience with driving an automobile (accelerating, decelerating, turning in a curve)
• Adult versus child in a swing (easier to push the child to move than the adult)
• Air-cushion table
• Newton’s second law (F=ma)
• m and a are inversely proportional: In Gym, lift weights (muscle force counteracting weights) , 2.5 lbs (weight unit) versus 100 lbs; Given same F, harder to push a heavier object forward, heavier desk versus lighter one.
• F and a are proportional, given m constant: Our own weight due to gravity W=mg (on earth g=9.8 m/s2)): g on the Moon = 1/6 * 9.8 m/s2 Consequently, you can jump six times higher on the moon than on the earth
• a: constant acceleration does not mean zero velocity, or constant velocity; constant velocity means zero acceleration (cruise control v=60 mi/h)
• Newton’s third law (every action has a reaction, with equal magnitude, but opposite direction)
• Hanging Traffic Light (action: weight of the object, reaction: tension in the rope)
• Rocket launch (action: exhausting enormous gas downward, reaction: rocket lifts off); Jet Airplane (action: gas exhaustion, reaction: plane flights opposite direction)
• Walking on the ground (action: feet push backward against the ground, reaction: body moves forward); Skiing (action: rods push backward), Skating on ice (action: feet push backward against ice)
• Boat (action: paddle water, reaction: boat moves)

Model of Knowledge

• Concept Map
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• Content Priorities
• Enduring Understanding
• Newton’s first law
• Statement
• Application
• Newton’s second law
• Statement
• Application
• Newton’s third law
• Statement
• Application
• Vectors
• Mathematical representation of vectors
• Mathematical operations of vectors: Adding, subtract vectors
• Geometric interpretation of vector addition, subtraction, decomposition
• Apply and draw free-body diagrams using geometric shapes, center of mass, vectors representing forces
• Important to Do and Know
• Express the decomposed forces with trigonometry appropriately (sinθ, cosθ, tanθ)
• Choose a coordinate system appropriate to problem solving (sliding object on a incline)
• Worth Being Familiar with
• Apply and draw free-body diagrams for more complicated physical systems (one object stacked on another and move together, insert a diagram)
• Geometric representations of addition and subtraction of three or more vectors

Assessment of Learning

• Formative Assessment
• In Class (groups)
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• Homework (individual)
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• Summative Assessment
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## Legacy Cycle

OBJECTIVE

By the next class period, students will be able to:

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The objectives will require that students be able to:

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THE CHALLENGE

In order for astronauts to board a space station the space shuttle must first dock at a docking area of the station. A round cabin door located on the space shuttle must fit perfectly with a similar looking door on the space station. Outline a procedure that would allow the space shuttle to dock with the space station and relate these procedures with Newton’s laws. Explain why your procedure ensures the success of the docking process.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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GO PUBLIC

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## Homework

1.(Newton’s laws: First law: Wilson, Buffa, Lou 6th edition page 130 #3). If an object is moving at constant velocity:

a) there must be a force in the direction of the velocity

b) there must be no force in the direction of the velocity

c) there must be no net force

d) there must be a net force in the direction of the velocity

2.(Newton’s laws: First law: Wilson, Buffa, Lou 6th edition page 130 #5). The force required to keep a rocket ship moving at a constant velocity in deep space is

a) equal to the weight of the ship

b) dependent on how fast the ship is moving

c) equal to that generated by the rocket’s engines at half power

d) zero

3.(Newton’s laws: Second law: Wilson, Buffa, Lou 6th edition page 132 #24). The acceleration of an object is

a) inversely proportional to the acting net force

b) directly proportional to its mass

c) directly proportional to the net force and inversely proportional to its mass

d) none of these

4.(Newton’s laws: Second law: Wilson, Buffa, Lou 6th edition page 132 #25). The weight of an object is directly proportional to

a) its mass

b) its inertia

c) the acceleration due to gravity

d) all of the preceding

5.(Newton’s laws: Third law: Wilson, Buffa, Lou 6th edition page 134 #47). A brick hits a glass window. The brick breaks the glass, so

a) the magnitude of the force of the brick on the glass is greater than the magnitude of the force of the glass on the brick

b) the magnitude of the force of the brick on the glass is smaller than the magnitude of the force of the glass on the brick

c) the magnitude of the force of the brick on the glass is equal to the magnitude of the force of the glass on the brick

d) none of the preceding.

6.(Newton’s laws: Third law: Wilson, Buffa, Lou 7th edition page 133 #14). Is something wrong with the following statement? When a baseball is hit with a bat, there are equal and opposite forces on the bat and baseball. The forces then cancel, and there is no motion. Please explain your reasoning.

7.(F = m x a relationship: Wilson, Buffa, Lou 6th edition page 132 #34). What is the weight of a 150-lb person in Newtons? What is his mass in kilograms?