Modified Atwood lab | Mistake Master Studio

The situation

A cart sits on a low-friction track. A string runs from the cart, over a pulley at the table's edge, down to a hanging mass. Let go, the hanger falls, the string pulls, and the cart speeds up the whole way along the track. Below you will get a working rig with three knobs: the total mass of everything that moves m_tot (cart, ballast, string, and hanger together, read off a built-in balance), the hanging mass m_h, and the release position x₀ along the track. A speed gate beeps exactly 1.00 s after release and reads the cart's speed at that instant, in centimeters per second.

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

Predict first

Commit before you touch the sliders

Which changes make the gate read a bigger speed at the beep? Check all you expect to. Hanging a heavier mass from the string Loading more ballast onto the cart (a bigger balance reading) Releasing the cart from farther along the track

Plot acceleration versus total mass. What shape do you expect? A straight line sloping down (each added kilogram removes the same amount of acceleration) A curve that falls steeply at first and flattens as the mass grows (a is proportional to 1 over m_tot) A flat line (total mass has no effect)

Explore

Test your prediction on the apparatus

Drag the sliders and read the gate at different settings. Or pick a test chip to lock everything but one variable and watch its relationship with a draw itself. The m_tot slider loads ballast onto the cart (the hanging mass stays put); the m_h slider slides ballast between the cart and the hanger, so the balance reading stays put while the hanging share changes. The track is low-friction and the rig sits on Earth, g = 10 N/kg. Re-reading at identical settings repeats exactly, so any change you see is real.

Total mass m_tot (balance)m_tot = 2.0 kg

Hanging mass m_hm_h = 0.20 kg

Release position x₀x_0 = 20 cm

Mystery hanging mass: m_h = ?

Acceleration vs total mass

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

Which fit matches your points?

Measure and straighten

How heavy is the sealed hanger?

The hanging mass has been sealed inside a box, and the rig stays on Earth (g = 10 N/kg). The balance still reads the total moving mass, the release still works, and the gate still beeps at 1.00 s. Choose at least 5 different total masses by loading and unloading the cart's ballast, read the gate at each, convert each reading to an acceleration in m/s² (the cart starts from rest and the gate reads exactly 1.00 s in, so divide the cm/s reading by 100), and enter each (m_tot, a) pair below. Then straighten the plot, and work through Read the slope: the walkthrough hands you the hanging mass only once you can say why the slope carries it, and the hanging mass opens the box.

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 hanging mass m_h. Finish them and the Record button turns on and checks your m_h against the sealed box.

Transfer

One changed variable

Back on the open track, suppose you double the total mass of the system while keeping the same hanging mass. Using the same relationship, by what factor does the acceleration change?

a is proportional to 1/m_tot. Twice the total mass divides the acceleration by 2: the pull m_hg has not changed, but it now has twice as much stuff to move, so the gate reads half the speed at the beep. Notice the release position never entered the reasoning, exactly as your slider showed.