Rolling race lab | Mistake Master Studio

The situation

An object is released from rest on a low-friction ramp and rolls down without slipping. As it drops, its gravitational potential energy turns into motion. But a rolling object does two things at once: its center moves forward, and it spins. Both take energy, so how the object shares that energy between moving and spinning sets how fast it reaches the bottom. Below you get a working ramp with three knobs: the release height h, the object's mass m, and the object's shape. The ramp tilt is fixed at 30 degrees, and a gate at the bottom reads the speed in meters per second.

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

Predict first

Commit before you touch the sliders

Which changes make the object reach the bottom faster? Check all you expect to. Releasing it from a greater height Making the object heavier Choosing a solid sphere instead of a ring

Plot the bottom speed versus release height. What shape do you expect? A curve that rises fast then flattens (v grows like the square root of h) A straight line through the origin (v is directly proportional to h) A curve that steepens as h grows (v is proportional to the square of h)

Explore

Test your prediction on the apparatus

Drag the sliders, switch shapes, and roll the object at different settings. Or pick a test chip to lock everything but one variable and watch its relationship with the bottom speed draw itself. The ramp stays at 30 degrees and rolls without slipping. Re-running at identical settings repeats exactly, so any change you see is real.

Release height hh = 0.50 m

Object mass mm = 1.0 kg

Object shape

Sealed roller: shape = ?

Bottom speed vs release height

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

Which fit matches your points?

Measure and straighten

What shape is sealed inside?

The object has been sealed inside an opaque roller, so you cannot see whether it is solid or hollow. The ramp is still 30 degrees and rolls without slipping, and the release, the height slider, and the gate still work. Choose at least 5 different release heights, roll the object at each, and enter each (h, v) pair below. Then work through Read the slope: your raw points come out on a curve, and the walkthrough leads you to the transform that straightens it, then to the slope, and finally to the shape number that names the roller.

Fill the table with at least 5 heights, then work through the Read the slope steps. They lead you from energy conservation to the transform that straightens the plot, the slope 2g / (1 + b), and the shape number b. Finish them and the Record button turns on and checks your b against the sealed roller.

Transfer

One changed variable

Back on the open ramp, suppose you release the same object from four times the height. Using the same relationship, by what factor does the bottom speed change?

v is proportional to the square root of h, so four times the height multiplies the speed by the square root of 4, which is 2. The speed only doubles. Two more things your sliders showed: swap the solid sphere for a ring from the same height and the ring arrives slower, because its larger shape number b sends more of the energy into spinning and less into moving forward. And the mass never entered the reasoning, so a heavy ring and a light ring of the same shape tie.