Physics Lab 4 - Projectile Motion Virtual Lab - Physics Aviary (1) NG PDF

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PHYS 1101

– 001

Date:

Names: Nancy Gonzales

Projectile Motion Virtual Lab

Objective: 

In this activity, you will be investigating the relationships between some of the different variables involved in projectile motion.

Helpful Hints: 

Estimate the ball’s landing location by looking at the landing spot for the center of the bottom of the ball. See example in the picture below:



Three speedometers will show you the total speed of the ball, the horizontal speed of the ball, and the vertical speed of the ball

Procedure Part 1: Learning to use the simulation & reviewing concepts in projectile motion 1. Open the virtual projectile lab in by clicking or entering in on the following

URL link: https://www.thephysicsaviary.com/Physics/Programs/Labs/Projecti leLab/ 2. Discover the purpose of each of the controls (shown below) until you understand or at least have an idea of what they do. Feel free to play with the simulation until you are comfortable enough to go on to the next step.

3. With the speed set to 20 m/s, adjust the launch angle to 0° and the height to 30 meters. When all the settings are ready, then press the button. 

Keep your eye on the three speedometers during the time of flight of the projectile. Describe in what happens to following quantities during the course of its flight in at least one complete sentence:



the total speed of the projectile – The total speed of the projectile moved fairly slowly while the ball was thrown. It started at 20 and moved to around 30.



the horizontal speed of the projectile – The horizontal speed did not move at all it remained the same from start to finish.



the vertical speed of the projectile –The vertical speed started at around 0 and moved to about 25 as the ball moved.

4. Next, put the launch angle at 90° and the height at zero. Then fire the projectile with a speed of 30 m/s. 

Describe in your lab book what happens to the speed of the projectile when it reaches its maximum height in at least one complete sentence.

When the ball reached its max height it stayed for a split second and then slowly went back down to where it started. It was simply like throwing a ball straight up into the air. 

Also describe what you notice about the speed of the projectile when it returns to the ground in at least one complete sentence.

It came down at about the same rate. It looked like it was going faster, but in reality, if paying attention to the seconds it looks as if it takes the same amount of time to come back down. 5. Now put your launch angle at 60°, your height at 15 m and your speed at 20 m/s. 

Does the speed of the ball hit zero when the ball reach its highest height? If not, why not? Please explain your answer in at least two complete sentences.

No, the ball does not hit zero when it reached its highest height. This is because the ball was constantly moving or accelerating until it starting moving in a downward motion. The ball never stopped moving so the speed could never be at zero. 

Does the speed of the ball when it reaches the ground equal the speed of the ball at launch? If not, why not? Please explain your answer in at least two complete sentences.

No, it does not. This is because the ball had a faster rate of speed as it went down from where it was launched. It was launched at an angle into the air so it went down faster.

6. Now put your launch angle at 53°, your height at 0 m and your speed at 25 m/s. Record the horizontal speed, the vertical speed and the total speed.  How can the total speed number be obtained from the numbers you have for horizontal speed and vertical speed? o Please explain how you know this in at least two complete sentences or using mathematical equations. The total speed was 25 m/s the horizontal speed is 15 m/s and the vertical speed is 20 m/s. Horizontal speed= cos53= 0.60 then 25x0.60=15 m/s Vertical Speed= sin53=0.80 then 25x.80= 20 m/s For total speed its

√ 152+ 202=25 m/s

Part 2: Horizontal Projectiles Fired from a Fixed Height 1. Set your height to 30 meters and your angle to 0°. These variables will not be altered for the rest of this part of the experiment. 2. Fire the projectile at 8 different speeds including a speed of 0 m/s. For each speed record in a data table the speed you fired the projectile with, the horizontal distance it travelled, and the time of flight. Table 2. Projectile Speed, vi (m/s)

Horizontal distance, Δx (m)

Time of flight (ToF), Δt (sec)

1

0

0

0

2

10

24.74

1.0632

3

15

37.1

4

20

49.5

5

25

61.8

6

30

74.2

7

35

86.6

8

40

99

1.5846 2.094 2.5875 3.0612 3.5117 3.9354

3. Using a graphing utility such as MS Excel or similar, create two graphs of time of flight vs. speed and horizontal distance vs. speed. Transfer both graphs to your lab submission and make sure they have all the following criteria: a. Proper chart title b. X-axis label c. Y-axis label d. Trendline e. Trendline equation

4. Based on your graphs, explain how the horizontal distance traveled and time of flight change with increasing speed in at least two complete sentences. Be sure to explain each of your graphs. You can also describe the shapes of your graphs as well. The time of flight continually increased as the speed increased. For the first graph it looked as if they were going to keep going up at a constant speed. The second graph look like it dipped into the negative then went back up and remained constant. 5. What is the physical significance of the slope of your horizontal distance vs. speed graph? Please explain how you know your answer in at least two complete sentences.

Part 3: Horizontal Projectiles Fired with a Fixed Speed 1. Set your initial projectile speed to 25 m/s and your angle to 0°. These variables will not be altered for the rest of this part of the experiment. 2. Fire the projectile at 8 different heights including a height of 0 m. For each height record in a data table the height from which you fired the projectile, the horizontal distance it travelled, and the time of flight. Table 3.

Launch height, Δy (m)

Horizontal distance, Δx (m)

Time of flight, Δt (sec)

√ Δy ( √ m)

1

0

0

0

0

2

5

11.067

0.4447

2.2360680

3

10

21.798

0.886

3.1622776 6

4

15

31.866

1.3205

3.8729833

5

20

40.966

1.745

4.4721359 6

6

25

48.822

2.1562

5

7

30

55.194

2.551

8

40

62.764

3.2795

5.4772255 75 6.3245553 2

3. Using a graphing utility such as MS Excel or similar, create a graph of time of flight vs. height and horizontal distance vs. height. Transfer both graphs to your lab submission and make sure they have all the following criteria:

6. Are these graphs linear or non-linear? Be sure to explain each of your graphs. You can also describe the shapes of your graphs as well. What equation should be used to describe them?

These graphs are linear. Both of the graphs start at the bottom and increase as the distance increases. 7. Make another graph of time of flight vs. √ Δy with all the required information on it, including the trendline equation. This graph should be linear now. Attach this to your lab submission.

Time √ of Flight vs √� (� √√) Time of Flight (sec)

7 6

6.32

f(x) = 0.77 x − 1.2 R² = 0.96

5

4.47

4

5

5.48

3.87 3.16

3 2.24

2 1 0

0

0

2

0

0

4

6

8

10

12

T√√� � (√√)

8. Take the slope of this graph and solve for the acceleration due to gravity, g = 9.8 m/s2, using the following equation and please show your calculations below: M=

√

slope , m=

√

2 g

2 2 =7.23 m / s2 =0.526 g= ( 0.526 )2 g

9. Was your calculated g value close to the accepted value? How much was your percent error? Please explain your results in at least two complete sentences. No, it was not it was higher. The percent error was 26.2%. Part 4: Fired at an Angle from the Ground 1. Set your initial projectile speed to 28 m/s and your height to 0 m. These variables will not be altered for the rest of this part of the experiment. 2. Fire your projectile at angles ranging from 0° to 90° using 15° increments. For each angle record in a data table the angle from which you fired the projectile, the horizontal distance it travelled, and the time of flight. Table 4. Initial angle,

cos (θi)

sin (θi)

Horizontal

Time of

θi (degrees) 0

distance, Δx (m)

flight, Δt (sec)

0

0

39.977

1.478

69.204

2.854

1

0

1

2

15

0.966

3

30

0.866

4

45

0.707

0.707

79.897

4.036

5

60

0.5

0.866

69.216

4.944

6

75

0.259

39.988

5.514

7

90

0

0

5.708

0.259 0.5

0.966 1

3. Using a graphing utility such as MS Excel or similar, create graphs of time of flight vs. initial angle and horizontal distance vs. initial angle. Transfer both of these graphs to your lab submission and make sure they have all the following criteria:

4. Are these graphs linear or non-linear? Try to explain the shape of each of your graphs in at least two complete sentences. They are non-linear. The shape of the first graph starts off straight then goes at an angle as it is curving hen it looks like it would stay constant before falling. The second graph is a curve and almost like throwing a basketball in a shooting position. It reaches it max while still moving forward and then falling. The dotted lines show what it should be if they were linear. 5. What [trigonometric] function should be used to describe each of these graphs? Please explain your guess in at least two complete sentences. I would guess sin could be used for these graphs, but I am not entirely sure if that is correct just a hunch. 6. Now make another two graphs of horizontal distance Δx vs. (Δt*cos θi) and time of flight Δt vs. (vi* sin θi). These graphs should be linear now.

7. For the horizontal distance Δx vs. (Δt*cos θi ) graph, compare the slope to your initial projectile speed. Is it close or not? No, the slope is not the same. It is about half off. 8. For the time of flight Δt vs. (vi*sin θi) graph, take the slope of the graph and solve for the acceleration due to gravity g using the following equation and please show your calculations below:

slope , m=

2 g

Slope is 5 m=

2 g

= 2/5= 0.4

Part 5: Projectile Motion vs. Air Resistance [PhET HTML5 simulation] 1.

Now we’re going to explore what air resistance does to the trajectory of a projectile. Please click on the following link https://phet.colorado.edu/sims/html/projectilemotion/latest/projectile-motion_en.html then click on the ‘Vectors’ section, as shown below.

2.

Then click on the ‘Components’, ‘Velocity Vectors’, and ‘Acceleration Vectors’ in the simulation as shown below:

3.

Be sure to uncheck ‘Air Resistance’ for this first trial

4.

Also slow down the simulation speed by clicking on ‘slow’, as shown on the right.

5.

Set the angle to 45°, which should give the projectile its maximum range.

6.

Launch the projectile by clicking the button and observe the components of the velocity and acceleration on the projectile. Which one changes? Which one stays the same? Please explain your answer in at least two complete sentences.

The acceleration vector changed the most to where it disappeared completely when the cannon ball landed. The green one also changed a lot because it started at the top and then went down when the ball was going in a downward motion. 7.

Where is the acceleration pointing? Does the acceleration change or stay the same? Please explain your answer in at least two complete sentences.

It is pointing downward as the ball moves. At 45 degrees the ball remains in the air for a longer time, but then it would be launched at a lower horizontal speed at the start. It would then slow down more because of the longer flight time.

8.

Now check ‘Air Resistance’ but keep the angle at 45°.

9.

Launch the projectile again by pressing the button and observe the components. Is the trajectory the same or different by including air resistance? Please explain your answer in at least two complete sentences. As the projectile moves through the air and it is slowed down by air resistance. Air resistance decreases the horizontal component of a projectile. The effect of air resistance is small but must be considered to increase the horizontal component of a projectile.

10. Are the velocity components changing or staying the same? Please explain your answer in at least two complete sentences. They are increasing. Having a higher initial horizontal velocity means there will be an increase of the length of the flight time and the distance covered. With a higher initial vertical velocity this will increase the height of the trajectory, resulting in a longer flight path.

11. With air resistance, is the acceleration vector changing or stay the same? How many components does it have with air resistance? Please explain your answer in at least two complete sentences. Air resistance the acceleration is changing. The faster the speed the greater the air resistance force and the direction of the air resistance force is in the opposite direction as the velocity of the object. Kind of like throwing a basketball. 12. Take a screenshot of same angle, same speed with/without air resistance and attach it to your lab submission.

13. How is the maximum height and range [maximum horizontal distance] affected by air resistance? Please explain the differences in the two trajectories with and without air resistance. When there is an object moving through air, they are slowed down due to air resistance. Air resistance affects the maximum height by reducing the range and the velocity of the projectile. Just think of being in space if we throw a ball up it will continue to go up because of the zero gravity where if we throw a ball up here it will come back down because the gravity and air resitance brings it down....