“Projectile Motion” Physics

Motion in One Dimension

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Goals: Understand motion and the relationship between displacement (distance with direction), velocity (speed with direction), and acceleration. Understand reading a graph and how graphs can be used as a tool to interpret physical phenomena.

Requirements: Please read the section(s) in your text concerning motion in one dimension –

distance, velocity, and acceleration. Questions: Total of 8 questions and analysis/conclusion in this Lab. Background: In this activity we will learn rules of motion that involve three concepts: displacement,

velocity, and acceleration. Mastering these concepts in one dimension is fundamental to understanding motion in two and three dimensions. This lab will consider only the simplest form of motion along a straight-line vertical path. The concepts will be investigated in terms of vectors, which have a magnitude (the length of the vector) and a direction. Vectors are different than scalars, which have magnitude only – for example, temperature and height. Speed is a scalar because it tells you how fast something is going (e.g., 40 mph) but nothing about the direction or where you’re going. Velocity, on the other hand, is speed with direction. It is a velocity. Velocity must be stated with speed and direction, as in 40 mph east. Do note, when direction is not important, speed and velocity are used interchangeably.

This lab considers objects in a gravitational field. That is, the objects will always be under the influence of gravity (g = 9.8 m/s2). Because gravity is acceleration and acceleration is a vector, gravity is a vector with a magnitude of 9.8 m/s2 with a direction towards the center of the earth. Just consider the gravity vector pointing down normal to the ground. As studied in class, the relevant formulas for motion in a gravitational field are

𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕 s = 𝒗𝒊𝒕 + 𝟏

𝟐 𝒂𝒕𝟐 𝒔 =

𝟏

𝟐 (𝒗𝒇 + 𝒗𝒊)𝒕 𝟐𝒂𝒔 = 𝒗𝒇

𝟐 − 𝒗𝒊 𝟐

Click here to bring up the laboratory Activity in another window

If the above link does not work, please copy the following URL into a browser: https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_en.html

You should see this:

Motion in One Dimension

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Double click on Intro to see

Setup: a. Setup the lab as follows:

i. Adjust the grey cylindrical platform height (far left) to be 0 meters. ii. Angle the cannon to be vertical (90º). iii. Set the initial speed to be 20 m/s. iv. On the right, ensure the Pumpkin is selected and the ‘Total’ under Acceleration

Vectors is checked.

v. Move the tape measure next to the cannon so its zero measure (ground level)

aligns with the ground level of the cannon (if the tape measure will not go to zero, just align the red cross with the dashed line):

Motion in One Dimension

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vi. You lab should look like something similar to this:

vii. The red button fires the cannon and the yellow button (with the eraser) erases the trajectory path. Use the magnifiers (-)(+) in the upper left to adjust the viewing area in the event the projectile is outside the browser window area.

Exercises: Click on the red button to fire the cannon (pumpkin) and observe the yellow acceleration vector (g). (Click the yellow button to erase the path to do it again.)

Motion in One Dimension

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a. Question # 1: Why does the yellow acceleration vector always point down?

b. Question # 2: Why does the acceleration vector have the same length going up and down?

c. Question # 3: How high (maximum height) did the Pumpkin go (use the tape measure)?

d. Question # 4: How long did it take for the pumpkin to reach its maximum height (refer to the formulas discussed under Background). Unclick ‘Total’ under Acceleration Vectors and click on ‘Total’ under Velocity Vectors. Click on the yellow button to erase the trajectory. Click on the red button to fire the cannon (pumpkin) and observe the green velocity vector.

e. Question # 5: What happens to the velocity vector at the maximum height?

f. Question # 6: What is the magnitude of the velocity vector at the maximum height?

g. Question # 7: What behavior(s)/change(s) does the velocity vector undergo that the acceleration vector does not?

h. Question # 8: What is the speed of the vector once it reaches ground level after falling from its maximum height? Click on the yellow button to clear the trajectory path and then select the Cannonball from the choice of projectiles. Note the cannonball has more mass (heavier) than the pumpkin.

Click on the red button to fire the cannonball.

i. Question # 9: What is the maximum height of the cannonball?

Click on the yellow button to clear the trajectory path and then select the Car from the choice of projectiles. Note the car has more mass (heavier) than the cannonball. Click on the red button to fire the car.

j. Question # 10: What is the maximum height of the car?

Motion in One Dimension

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k. Question # 11: From questions 3, 9, and 10, what conclusion can you make regarding motion of mass in a constant gravitational field? (Hint: refer to the equations under Background.)

Feel free to further explore this lab by observing how the velocity and acceleration vectors change according to initial speed and projectile.