1-D Montion Lab: Part 1

Modeling 1-D Equations of Motion with the PhET Projectile Motion simulation (Links to an external site.)

https://phet.colorado.edu/sims/html/projectile-motion/latest/projectile-motion_en.html

Your goal in this lab is to verify the 1-D equations of motion with constant acceleration using the PhET Projectile Motion simulation.

Introduction:

If you fire a projectile straight up it will reach a maximum height and fall back to the ground.

Approximation: If you remain close to the surface of Earth, the acceleration due to gravity is constant: g = 9.81 m/s2

Choose y as the vertical direction in space.
y = 0 = ground level
Choose up as the y direction.
Ignore air resistance

The resulting equations of motion for the vertical direction are:

y = yo voyt – ½ gt2
vy = voy – gt
vy2 = voy2 – 2g(y-yo)

yo = the initial height
voy = the initial velocity in the y direction.
ay = -g, with g = 9.81 m/s2 = the acceleration due to gravity near the surface of Earth.
Why is ay negative?

Check the PhET Projectile Motion simulation (Links to an external site.)

Select INTRO

Set yo = 2.00m
Point the cannon straight up (90 degrees)
Choose voy = 10.0 m/s and g = 9.81 m/s2 (default value).

Part I: Check the Equations of Motion

Fire the cannon and select any two points at random along the trajectory.
Use the “blue” measuring tool to determine the values of the height y and the time t for both of your two points.
Verify that both of your points satisfies Equation 1: y = yo voyt – ½ gt2 (show your work).

Part II: When does it hit the ground?

The object will hit the ground when y = 0. Use Equation 1 given above to solve for the time when the projectile hits the ground (yes, it is a quadratic equation), and use the measuring tool to check your answer.

Part III: When does it reach maximum height?

The object reaches its maximum height when vy = 0. Use equation 2 given above to solve for the time when the object reaches maximum height and use the measuring tool to check your answer.
Part IV: How close are your predictions?

The best way to compare two values is to use the Relative Difference.

Relative Difference = ∣∣(Measured−Predicted)Predicted∣∣

x100%

Note that the units will cancel out, and the Relative Difference is a positive percentage.

How close were your predictions for parts II and III?

Part V: Lab Report

Each group turns in one report. I prefer WORD or PDF documents, but you can also take pictures of your hand-written results.
Use Submit Lab 1 on the next page.
Make sure everyone’s full name is on the first page of the report.
Turn in your results for parts I-IV. You do not need to create a formal lab report this week.