Impulse lab | Mistake Master Studio

The situation

A cart sits at rest on a low-friction track. A pusher gives it a steady force F for a short time, then lets go, and the cart coasts through a speed gate that reports how fast it is moving. Below you get a working track with three knobs: the push time t you allow, the force F the pusher delivers, and the cart's mass m. The longer or harder the push, the faster the cart leaves; the heavier the cart, the slower. The gate reads the final 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 cart cross the gate faster? Check all you expect to. Pushing for a longer time before letting go Pushing with a larger force Making the cart heavier

Plot final speed versus push time. What shape do you expect? A straight line through the origin (v is directly proportional to t) A curve that starts shallow and steepens as t grows (v is proportional to the square of t) A flat line (push time has no effect)

Explore

Test your prediction on the apparatus

Drag the sliders and release the cart at different settings. Or pick a test chip to lock everything but one variable and watch its relationship with the final speed draw itself. The track is low-friction, so once the pusher lets go the cart holds its speed to the gate. Re-running at identical settings repeats exactly, so any change you see is real.

Push time tt = 0.50 s

Push force FF = 6.0 N

Cart mass mm = 1.0 kg

Sealed cart: mass = ?

Final speed vs push time

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

Which fit matches your points?

Measure and read the slope

How heavy is this cart?

The cart has been sealed inside a box, so you cannot weigh it and you cannot tell its mass from its size. The pusher is now fixed at a known force of F = 6.0 N, and the release, the push timer, and the gate still work. Choose at least 5 different push times, release the cart at each, and enter each (t, v) pair below. Then work through Read the slope. Your points come out on a straight line right away, so there is no transform to hunt for here; the slope carries the mass, and the walkthrough hands it to you once you can say why.

Fill the table with at least 5 push times, then work through the Read the slope steps. They lead you from the impulse equation to the slope F / m and on to the mass. Finish them and the Record button turns on and checks your mass against the sealed cart.

Transfer

One changed variable

Back on the open track, suppose you push the same cart for twice as long with the same force. Using the same relationship, by what factor does the final speed change?

v is directly proportional to t, so twice the push time gives twice the speed, not four times. The impulse F t doubles, the mass is unchanged, so the change in momentum doubles and the speed doubles with it. That is the straight-line, through-the-origin shape your data drew. Double the force instead and the speed also doubles; double the mass and the speed halves. All of that is the single relation v = F t / m.