MODULE 07 · LAB 2 / LAB BENCH
g from a projectile
Fire a ball, film it, and find g from the video the way you would with real video-analysis software: you set up the launcher and the camera, calibrate the picture, mark the ball frame by frame, and choose the fits.
Your assignment
Determine g, and report it with an uncertainty. Make 2 or more launches with different angles or spring settings, track at least 10 frames of each, and fit x–t, y–t, vx–t and vy–t.
- Set up the launcher and camera, then fire and film a launch
- Calibrate the video: the metre stick’s two ends, then the origin
- Mark the ball on each frame
- Work out the first three vx and vy values by hand
- Choose a model for each graph and fit it
2 · Video analysis
No video yetFire a launch to get a video.
Arrow keys move the cross-hair one pixel (Shift: ten); Enter marks; , and . step frames. The circle shows a magnified view under the pointer.
3 · Data
0 pointsCalibrate the video, then mark the ball: each mark adds a row.
| frame | t (s) | x (m) | y (m) | fit |
|---|
4 · Velocities
04Mark the ball on at least 4 frames: each pair of neighbouring positions gives one velocity.
Work out the first three vx and vy values yourself. Each velocity belongs to an interval between two neighbouring positions: vx = Δx / Δt and vy = Δy / Δt, plotted at the middle time tmid. Type them in the velocity table, then check. As the columns fill in, compare them: what does each velocity do?
| interval | tmid (s) | Δt (s) | Δx (m) | Δy (m) | vx (m/s) | vy (m/s) |
|---|
5 · Graphs and fits
05For each graph, choose the model the data should follow and fit it. The fit gives the coefficients with their uncertainties; working out g from them is up to you.
How do the coefficients relate to g?
Without air, a projectile’s horizontal velocity is constant and its vertical acceleration is −g. Ask yourself which graphs should be straight lines, which a parabola, and which coefficient carries the acceleration. What should the slope of the vx–t line be, and what does that say about the horizontal force? If a graph is a parabola y = A + B t + C t², what is d²y/dt²? If a graph of vy against t is a straight line, what does its slope mean?
The ± on each coefficient comes from how far your points scatter about the fit. If you work out g from a coefficient by multiplying it by a number, multiply its ± by the same number.
Lab notebook
0 of 2 launches analysed| # | Angle | Spring | fps | Points | Calibrated | Fits | Your g from it (optional) | Actions |
|---|
No launches yet.
Your result
06Report the value and uncertainty you believe, from your launches, to sensible significant figures.
Your completion code. Copy it and paste it into the Canvas assignment.
You can submit again after more work: paste the newest code. Your instructor grades the last code you paste.