DAY 59
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Encuesta de Estudiantes - Español
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#Goals: SWBAT...
1. Determine if mass can be cancelled from all terms in the equation
2. Determine if a scenario represents work
3. Solve work problems
Warm-Up (4min): Did Everyone Bring Mass to the Party?
You have to be able to identify when mass cancels out of an equation.
Recall: The “equation” is the party and the individuals are the terms delineated by a subtraction, addition or equal sign.
Stuck? Confused? Check this LINK for help
Copy the equations below, then answer the question, which is: "Can mass be cancelled in the equation?" If it can, cancel it (show your work). If it can't, write why you can't cancel mass.
0 = max - Ff (assume FN=Fg)
mgh + 1/2mv2 = 4kx2
1/2mvi2 = 1/2mvf2 + mgL(1− cosθ)
Ftension - Fg = may
CLASSWORK
1. #059A: Building Your Problem Solving Skills
Recall: 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.
Solve the following. Draw FBD's. Show all work. Include units and correct sigfigs.
If you get stuck, or want to check your answers, there's a link to help in the Homework section below
Instructions: For each case, indicate which force(s) are doing work upon the object. Then calculate the work done by these forces.
A) A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m to the right.
B) A 10-N force is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m to the right.
C) An approximately 2-kg object is sliding at constant speed across a friction free surface for a displacement of 5 m to the right.
D) An approximately 2-kg object is pulled upward at constant speed by a 20-N force for a vertical displacement of 5 m.
3. Before beginning its initial descent, a roller coaster car is always pulled up the first hill to a high initial height. Work is done on the car (usually by a chain) to achieve this initial height. A coaster designer is considering three different incline angles at which to drag the 2000-kg car train to the top of the 60-meter high hill. In each case, the force applied to the car will be applied parallel to the hill. Her critical question is: which angle would require the most work? Analyze the data, determine the work done in each case, and answer this critical question.
a.
b.
c.
Angle
35 deg
45 deg
55 deg
Force
11,200N
13,900N
16,100N
Distance
105 m
84.9 m
73.2 m
Work (J)
4. Ben Travlun carries a 200-N suitcase up three flights of stairs (a height of 10.0 m) and then pushes it with a horizontal force of 50.0 N at a constant speed of 0.5 m/s for a horizontal distance of 35.0 meters. How much work does Ben do on his suitcase during this entire motion?
5. A force of 50 N acts on the block at the angle shown in the diagram. The block moves a horizontal distance of 3.0 m. How much work is done by the applied force?
6. How much work is done by an applied force to lift a 15-Newton block 3.0 meters vertically at a constant speed?
7. A student with a mass of 80.0 kg runs up three flights of stairs in 12.0 sec. The student has gone a vertical distance of 8.0 m. Determine the amount of work done by the student to elevate his body to this height. Assume that his speed is constant.
8. Calculate the work done by a 2.0-N force (directed at a 30° angle to the vertical) to move a 500 gram box a horizontal distance of 400 cm across a rough floor at a constant speed of 0.5 m/s. (HINT: Be cautious with the units.)
9. A tired squirrel (mass of 1 kg) does push-ups by applying a force to elevate its center-of-mass by 5 cm. Estimate the number of push-ups that a tired squirrel must do in order to do a approximately 5.0 Joules of work.
At Home Learning (HW)
1. Complete all problems from #059A
If you got stuck, answers and more help are here at this link: LINK
2. #059B: Monday we will cover Kinetic and Potential Energy: Watch/take notes/complete edPuzzles on the following:
(5:25) Introduction to Kinetic Energy with Example Problem - EDpuzzle
(5:48) Introduction to Gravitational Potential Energy with Zero Line Examples - EDpuzzle
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. Define Work
2. List the requirements for a movement to be considered "work"
3. Determine if a scenario represents work
4. Solve work problems
Warm-Up (5min)
A. Copy the drawing 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
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. #059A: 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.
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. A rocket accelerates through space.
Mathematically, work can be expressed by the following equation.
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.
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.
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.
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.
Three key parts to work:
force
displacement
cause
To Do Work, Forces Must Cause Displacements
Let's consider Scenario C above in more detail. Scenario C involves a situation similar to the waiter who carried a tray full of meals above his head by one arm straight across the room at constant speed. It was mentioned earlier that the waiter does not do work upon the tray as he carries it across the room. The force supplied by the waiter on the tray is an upward force and the displacement of the tray is a horizontal displacement. As such, the angle between the force and the displacement is 90 degrees. If the work done by the waiter on the tray were to be calculated, then the results would be 0. Regardless of the magnitude of the force and displacement, F*d*cosine 90 degrees is 0 (since the cosine of 90 degrees is 0). A vertical force can never cause a horizontal displacement; thus, a vertical force does not do work on a horizontally displaced object!!
It can be accurately noted that the waiter's hand did push forward on the tray for a brief period of time to accelerate it from rest to a final walking speed. But once up to speed, the tray will stay in its straight-line motion at a constant speed without a forward force.
Let's consider the force of a chain pulling upwards and rightwards upon Fido in order to drag Fido to the right. It is only the horizontal component of the tension force in the chain that causes Fido to be displaced to the right. The horizontal component is found by multiplying the force F by the cosine of the angle between F and d. In this sense, the cosine theta in the work equation relates to the cause factor - it selects the portion of the force that actually causes a displacement.
2. 059B: HW Review
(7:10) Notes Introduction to Work with Examples - Video: EDpuzzle
3. 059C: Work Interactive
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? Find out the answer with the It's All Uphill Interactive.
Complete the chart with 2kg mass, then do it a second time with 4kg
Learning at Home (HW)
1. Complete 059C for two masses: 2kg and 4kg
Need help with the second page of the handout? http://www.youtube.com/watch?v=_4XHk8FM8Kw
Check Your Understanding
Express your understanding of the concept and mathematics of work by answering the following questions. When done, click the button to view the answers.
1. Apply the work equation to determine the amount of work done by the applied force in each of the three situations described below.
A: 500N B: 433N C: 735N
2. On many occasions, there is more than one force acting upon an object. A free-body diagram is a diagram that depicts the type and the direction of all the forces acting upon an object. The following descriptions and their accompanying free-body diagrams show the forces acting upon an object. For each case, indicate which force(s) are doing work upon the object. Then calculate the work done by these forces.
Free-Body
Diagram
A 10-N force is applied to push a block across a friction free surface for a displacement of 5.0 m to the right.
Forces Doing Work
on the Object
Fa is the only one. Think about why....
Amount of Work Done
by Each Force
Fa=50N. Show your work to prove it
Unit Goals:What is a wave? How do they act? How are do waves differ?
Goals: SWBAT...
1. Discuss waves’ properties using common vocabulary and they will be able to predict the behavior of waves through varying medium and at reflective endpoints
Warm-Up (5min):
1. When you increase the amplitude of a wave, what happens to each of the following characteristics?
a. Height
b. Closeness of the waves (frequency)
c. Pattern (does the wave stay constant, or is it changing?)
d. Wavelength
CLASSWORK
1. #059A: Waves on a String
Directions:
1. Open Waves on a String: https://phet.colorado.edu/en/simulation/wave-on-a-string
2. With the Oscillate button on and with No End checked, investigate waves more carefully using the Amplitude slider.
Write answers to the following after your group has talked about each and agreed.
a) Define Amplitude in everyday language.
b) Explain how the wave behaves as the Amplitude changes using the characteristics you described in the warm-up
c) Use a rope/string/ on the floor for some investigations and explain how you could change the Amplitude of a wave.
3. Repeat step number 2, for Frequency, Tension and Damping.
4. Set Amplitude on high, Frequency to .25Hz, Damping on none, and Tension on low. Also, have on Oscillate, Timer and No End. Use the Pause button to freeze the wave.
a) Place a blank piece of paper on your monitor and trace the wave and the wave generator. Mark the green balls. This is a vertical position- horizontal position graph, label your axes.
b) Quickly press Play, and then Pause again. Use the same piece of paper, put it on the monitor and make sure to get the generator in the same spot. Trace the new wave.
c) Write about the differences and similarities in the characteristics. You may have to do some more tests by pressing Play, then Pause and tracing to test your ideas.
5. Same settings as above in #4. Set Amplitude on high, Frequency to .25Hz, Damping on none, and Tension on low. Also, have on Oscillate, Timer and No End. Use the Pause button to freeze the wave.
a) Measure the vertical location of a green ball with a ruler. B) Record the vertical position and time.
b) Quickly press Play, then Pause repeatedly to make a data table the vertical position of the green ball versus time.
c) Make a graph of vertical position versus time.
d) Write about the differences and similarities between vertical position- horizontal position graphs and vertical
position-time graphs.
6. Investigate how waves behave when the string end is Fixed and Loose with Manual settings. Discuss the behavior with your partners, or think about it on your own. Test your ideas and the write a summary.
7. Read to find out what a standing wave is, investigate how to produce one with the simulation and write a procedure that another student could follow to produce a standing wave. Links on standing waves are immediately below:
http://www.physicsclassroom.com/class/waves/Lesson-4/Traveling-Waves-vs-Standing-Waves
http://www.physicsclassroom.com/class/waves/Lesson-4/Formation-of-Standing-Waves
At Home Learning (HW)
1. Complete #059A. If you were on point in class today, you'll only have part 6 and 7 to complete at home.