DAY 57

Essential Question: What would require the most work and energy: driving a car up a gently-sloped hill or driving a car up a steep hill to the same summit?

#Goals: SWBAT...

1. use the cosine function to find components of a vector

2. Define Work

3. List the requirements for a movement to be considered "work"

4. Determine if a scenario represents work 

Warm-Up (5min) 

A. Copy the drawings  from the board, then answer the questions listed here. Keep in mind that some of these could be a *tie*

• 1. Displacement: Rank the displacement (distance the car travels) from shortest to longest

• 2. Force: Rank the force required to move the car at a constant velocity from lowest to highest

• 3. Energy: Rank the energy required to move the car from the bottom to the top of the mountain from least to highest

B. Find the cosine (cos) of the following five angles (* means degrees)

0*

45*

90*

135*

180*

C. What is "cosine"?

the trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse

http://mathworld.wolfram.com/Cosine.html

CLASSWORK

1. 057A: Pre-Assessment: Work and Energy (20min)

    On Schoology. 

    Individual assignment

    Meant to assess your current knowledge of the topics before we begin the unit, so no penalty for not knowing these concepts at this point

2. 057B: NOTES: Work Definition & Equation

    Background:  Newton's laws serve as a useful model for analyzing motion and making predictions about the final state of an object's motion. In this unit, an entirely different model will be used to analyze the motion of objects. Motion will be approached from the perspective of work and energy. The effect that work has upon the energy of an object (or system of objects) will be investigated; the resulting velocity and/or height of the object can then be predicted from energy information.

    With that, over the next few days we will learn about work, power, kinetic energy, and potential energy

    Definition: Work is done upon an object when a force acts upon the object to cause a displacement of the object. Work is the product of force and displacement. A force is said to do work if, when acting, there is a movement of the object in the direction of the force. Work transfers energy from one place to another, or one form to another.

For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). 

Scenarios: (are these work?)

1. A teacher applies a force to a wall and becomes exhausted.

2. A book falls off a table and free falls to the ground.

3. A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed. (Careful! This is a very difficult question that will be discussed in more detail later.)

4. Tires push on the road to accelerate a Tesla Model Y, Dual Motor, Black.

p1 end

EQUATION: Mathematically, work can be expressed by the following equation. When the force 

 is constant and the angle between the force and the displacement d is θ, then the work done is given by W = Fd cos θ.

W = F • d • cos Θ

where F is the force, d is the displacement, and the angle (theta) is defined as the angle between the force and the displacement vector. The angle measure is defined as the angle between the force and the displacement. Work is a SCALAR

UNIT: The SI unit of work is the joule (J).

• Scenario A: A force acts rightward upon an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are in the same direction. Thus, the angle between F and d is 0 degrees.

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• Scenario B: A force acts leftward upon an object that is displaced rightward. In such an instance, the force vector and the displacement vector are in the opposite direction. Thus, the angle between F and d is 180 degrees.

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• Scenario C: A force acts upward on an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are at right angles to each other. Thus, the angle between F and d is 90 degrees.