G WHIZ LAB• Grades are curved: graded out of 28 points instead of 33

Does a more massive object fall faster than a less massive one?

Were you able to calculate acceleration due to gravity close to the accepted value?

• Materials and safety notes

• Make sure to list at least 2-3 safety notes for the lab

• Constants in this lab?

• Time interval, dot timer used, if person dropping/holding dot timer were the same, possibly length of tape was held constant

• Some people put gravity as constant – this is what we are trying to prove in this lab though

• Procedure should be stated in sufficient detail so that it could be reproduced

• What side of the dot timer were the washers?

• How was the dot timer held when paper was dropped through?

• Draw pictures of procedures if necessary

• Problem statement: What are we trying to do in this lab?

• Prove the accepted value of gravity: 9.81 m/s2

• See if mass affects acceleration due to gravity

• Hypothesis should address the problem statement(s)

LAB REPORT COMMENTSProblem Definition Section

Experimental Design

LAB REPORT COMMENTS

• Include a “data presentation” section in report. Tell reader to see attached tables & graphs if they are attached at the back of the lab report

• Tables

• Add a border and center text for tables done on excel

• Title tables

• Calculations & Equations used

• Include this information here instead of in discussion & conclusion section

• First show equations, then sample calculations using those equations

• Show one sample calc for all calculations done

• Graphs

• Make sure to give a descriptive title to graphs (not just the default title given by excel)

• Data Presentation Section

• Be explicit about how IV affected DV…”The IV, which was the # of washers, had an affect on the DV, the distance between dots…”

• Refer back to your hypothesis: were your right?

• Refer to specific data collected: a specific table or data point in graph; use this information to support your conclusion

• Validity: Can someone reproduce this lab and get the same results? Were there major errors that invalidate your data?

• Were the # of trials appropriate for this lab?

• Were the procedures followed through consistently ? Were things held constant that should have been? Or should other things have been held constant that were not?

• What errors may have occurred? How can you prevent them?

• What improvements would you make in the lab in the future to make the lab more valid/repeatable? How would you extend this lab?

• Wrap up lab, and connect this lab to an everyday situation.

• Some people did not even tell what their calculated gravity values were at all in the report! Must calculate it and discuss your results!

• Make sure to answer questions so that reader knows question without looking at question.

• Use data to support your answers

• Do not show calculations in this section, just refer to data to support your answer.

• #4: Must divide the time by 60. What should the area under the velocity vs. time graph give you?

• Many people did not even calculate acceleration due to gravity – must calculate it in order to do #1 and 5.

LAB REPORT COMMENTSDiscussion Questions

Conclusion

UNIT 3: VECTORS & PROJECTILE MOTION

• How would you describe to someone how to get from MHS to Catsup & Mustard?

SCALAR

A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.

Magnitude – A numerical value with units.

*a scalar item in your text is written in italics.

Scalar Example

Magnitude

Speed 20 m/s

Distance 10 m

Time 25 seconds

Heat 1000 calories

VECTOR

A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION.

* A vector quantity in your textbook are denoted in bold text

Vector Magnitude & Direction

Velocity 20 m/s, N

Acceleration 10 m/s/s, E

Force 5 N, West

We will use an an ARROW above the variable to show a variable is a vector. The arrow is used to convey direction and magnitude.

VECTOR• Drawing pictures of physical

situation is very helpful when solving vector problems

• Vectors represent by arrows

• Point in direction of vector

• Length of arrow = magnitude of vector

• Use a scale to do this – usually use a ruler

Example 1: Mike skipped towards the east at 25 meters/second.

Example 2: Taylor pranced north for 40 meters.

Scale: 1 block = 1 m/s

Scale: 1 block = 1 m

APPLICATIONS OF VECTORSVECTOR ADDITION – If 2 similar vectors point in the SAME direction,

add them.

• Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started?

54.5 m, E 30 m, E+

84.5 m, E

Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION.

This is the resultant displacement

APPLICATIONS OF VECTORSVECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT.

• Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?

54.5 m, E

30 m, W-

24.5 m, E

NON-COLLINEAR VECTORS• Vectors have both horizontal and vertical

components

• Horizontal is usually the east or west directions, right or left

• Vertically is usually the north or or down

• Use pythagorean theorem and trigonometry (SOHCAHTOA!) to solve

hypotenuse

opposite

adjacent

Θ

a2 + b2 = c2 OR

Opposite2 + adjacent2 = hypotenuse2

Sinθ = opposite hypotenuse

Cosθ = adjacent hypotenuse

tanθ = adjacent opposite

NON-COLLINEAR VECTORS: DRAW A DIAGRAMWhat do vectors look like graphically in physics?

95 km,E

55 km, N

Start

Finish

A man walks 95 km, East then 55 km, north.

The hypotenuse in Physics is called the RESULTANT.

The LEGS of the triangle are called the COMPONENTS

Horizontal Component

Vertical Component

NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components TAIL TO TIP.

NON-COLLINEAR VECTORS: SOLVING MATHEMATICALLY

When 2 vectors are perpendicular, you must use the Pythagorean theorem.

95 km,E

55 km, N

Start

Finish

Let’s solve this problem: A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.

RESULTANT.

Horizontal Component

Vertical Component

BUT……WHAT ABOUT THE DIRECTION?In the previous example, DISPLACEMENT was asked for and since it is a VECTOR we

should include a DIRECTION on our final answer.

N

S

EW

N of E

E of N

S of W

W of S

N of W

W of N

S of E

E of S

N of E

BUT…..WHAT ABOUT THE VALUE OF THE ANGLE???

opposite

adjacent

Sinθ = opposite hypotenuse

Cosθ = adjacent hypotenuse

tanθ = adjacent opposite

q

hypotenuse

Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle.

SOHCAHTOA!

BUT…..WHAT ABOUT THE VALUE OF THE ANGLE???

30)5789.0(

5789.095

55

1

Tan

sideadjacent

sideoppositeTan

N of E

55 km, N

95 km,E

To find the value of the angle we will use a Trig function called TANGENT.

q

109.8 km

So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

VECTORS: SOLVING PROBLEMS GRAPHICALLY

We have been solving vector problems mathematically, but they can also be solved graphically, using a ruler and protractor.

Steps:

1. Develop a scale to use to draw the problem.

2. Draw the vector graphically.

3. Solve for unknowns, using a protractor and ruler.

Example: A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT and angle.

HOMEWORK SOLUTIONS: SOLVING GRAPHICALLYPage 1: Using a ruler and protractor to find horizontal and vertical components of a vector:

• Vertical: 10.8 cm

• Horizontal: 10.0 cm

• 44.5 degrees

• Magnitude: 14.2 cm

• Page 2: Finding the resultant vectors given its components:

1. 6.4 cm at 51 degrees above Horizontal

2. 11.7 cm at 59 degrees below the horizontal

EXAMPLE: BREAKING A VECTOR INTO ITS COMPONENTS

Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components?

65 m25°

H.C. = ?

V.C = ?

The goal: ALWAYS MAKE A RIGHT TRIANGLE!

To solve for components, we often use the trig functions sine and cosine.

Rearranging these equations to solve for the horizontal and vertical components…

EXAMPLEA bear, searching for food wanders 35 meters east then 20 meters north.

Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.

35 m, E

20 m, N

12 m, W

6 m, S

- =

23 m, E

- =14 m, N

23 m, E

14 m, N

The Final Answer: 26.93 m, 31.3 degrees NORTH or EAST

R

q

Step 1: Draw a diagram of the bear’s displacement.Step 2: Find the resultant displacement in the north direction & east direction. Draw This triangle.Step 3: Solve for the bear’s magnitude and direction.

EXAMPLE 1: SOLVE FOR RESULTANT VECTORA boat moves with a velocity of 15 m/s, N in a river which flows

with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.

1.28)5333.0(

5333.015

8

/17158

1

22

Tan

Tan

smRv

15 m/s, N

8.0 m/s, W

Rv q

The Final Answer : 17 m/s, @ 28.1 degrees West of North

EXAMPLE: RESOLVE A VECTOR INTO ITS COMPONENTSA plane moves with a velocity of 63.5 m/s at 32 degrees South of East.

Calculate the plane's horizontal and vertical velocity components.

SsmCVopp

EsmCHadj

hypopphypadj

hypotenuse

sideopposite

hypotenuse

sideadjacent

,/64.3332sin5.63..

,/85.5332cos5.63..

sincos

sinecosine

63.5 m/s

32°

H.C. =?

V.C. = ?

EXAMPLE: ADDING TWO VECTORS AT DIFFERENT ANGLES.

A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement graphically, and mathematically.

NkmCVopp

EkmCHadj

hypopphypadj

hypotenuse

sideopposite

hypotenuse

sideadjacent

,2.96440sin1500..

,1.114940cos1500..

sincos

sinecosine

0.20)364.0(

364.01.2649

2.964

1.28192.9641.2649

1

22

Tan

Tan

kmR

5000 km, E

40

1500 km

H.C.

V.C.

1500 km + 1149.1 km = 2649.1 km

2649.1 km

964.2 kmR

q

The Final Answer: 2819.1 km @ 20 degrees, East of North

VECTOR ACTIVITY: MEASURING BEYOND THE METER STICK ACTIVITY

MEASURE YOUR REACTION TIME!Reaction time affects your performance in many things that you do in life…so…

Today you will determine your reaction time!

1. Have a friend hold a meter stick vertically between the thumb and index finger of your open hand. Meter stick should be held so that the zero mark is between your fingers with 1 mark above it. Do not touch meter stick, let it fall freely. Your catching hand should be resting on a table

2. Without warning, your friend will drop the meter stick so that it falls between your thumb and finger. Catch the meter stick as quickly as you can!

3. Record the distance the meter stick falls through your grasp. Do this five times.

4. Calculate your average reaction time from the free fall acceleration and the distance you measure.