Spring launcher lab | Mistake Master Studio

The situation

A spring stands in a vertical tube. Compress it by a distance x, seat a payload of mass m on top, and release: the spring flings the payload straight up. A peak marker on the rail beside the tube latches at the very top of the flight and reads the height of the latch above the launch point, in centimeters. Below you will get a working rig with three knobs: the compression x, the payload mass m, and how long you hold the spring compressed before you let go.

First, commit to a prediction. Then the apparatus unlocks.

Predict first

Commit before you touch the sliders

Which changes make the peak marker latch higher? Check all you expect to. Compressing the spring further before release Launching a heavier payload on the same compression Holding the spring compressed longer before releasing

Plot peak height versus compression. What shape do you expect? A straight line sloping up (each added centimeter of squeeze buys the same extra height) A curve that starts shallow and steepens as the compression grows (h is proportional to x²) A flat line (compression has no effect)

Explore

Test your prediction on the apparatus

Drag the sliders and latch the peak marker at different settings. Or pick a test chip to lock everything but one variable and watch its relationship with h draw itself. The x slider sets how far the spring is squeezed before release; the m slider swaps in a lighter or heavier payload; the hold slider sets how long the spring waits compressed before it fires. The cartridge is labeled k = 200 N/m, the tube is frictionless, air resistance is negligible, and the rig sits on Earth, g = 10 N/kg. Re-latching at identical settings repeats exactly, so any change you see is real.

Compression xx = 0.060 m

Payload mass mm = 0.10 kg

Hold timehold = 2.00 s

Mystery cartridge: k = ?

Peak height vs compression

Drag the unlocked slider. Every position you visit drops a measured point.

Which fit matches your points?

Measure and straighten

How stiff is the sealed cartridge?

The cartridge has been sealed and its stiffness is hidden. So the slope stays honest, the payload is fixed at m = 0.10 kg (stated on the launcher), the tube stays frictionless, and g = 10 N/kg. Choose at least 5 different compressions, latch the peak marker at each, convert each reading to a height in meters (the marker reads centimeters: divide by 100), and enter each (x, h) pair below. Then straighten the plot, and work through Read the slope: the walkthrough hands you the stiffness only once you can say why the slope carries it, and the stiffness opens the seal.

Collect your data, then work through the Read the slope steps: they walk you to the transform that straightens the plot and the slope that carries the spring stiffness k. Finish them and the Record button turns on and checks your k against the sealed cartridge.

Transfer

One changed variable

Back on the open rig, a friend compresses the spring to the same x but seats a 0.20 kg payload where the 0.10 kg one sat, and predicts the same peak: same spring, same squeeze, same stored energy, so the same rise. What actually happens?

The stored energy is the same, and that is exactly why the peak drops. The squeeze fixes the elastic energy (1/2) k x², and at the top all of it has become m g h. With twice the mass to lift, the same energy reaches half the height: h = (1/2) k x² / (m g) halves when m doubles. The friend was right that the energy did not change and wrong to expect the same rise, because the same energy spread over a heavier payload buys less height. Notice the hold time never entered the reasoning, exactly as your slider showed.