Lab 4 Practice

Collisions, from the OnRamps Lab 4 worksheet. Crash two carts, then use statistics to decide whether momentum and kinetic energy were conserved. Every run gives new, realistic data.

Goal: collide two carts and decide whether the results show conservation of momentum and conservation of energy. You choose the collision type and the setup. At least five trials of one configuration.

Key formulas

p = mv (sign shows direction) p_tot = m₁v₁ + m₂v₂ Δp = p_f − p_i KE = ½m₁v₁² + ½m₂v₂² ΔKE = KE_f − KE_i mean = Σxᵢ / N s = √[Σ(xᵢ − mean)² / (N − 1)] Δx = s / √N 95% CI = mean ± 2Δx

Conserved means the change is zero. If 0 is inside the 95% CI of the change, the data are consistent with conservation. If 0 is outside, the quantity really changed.

Q1Experimental setup

Part 1 of the lab is 15 minutes of free exploration. For Part 2, pick one configuration. On the real worksheet you describe the setup and procedure in words and a sketch, and explain why each detail matters (for example, why you measure the cart masses).

Collision type

Initial motion

Rubric check (each worth 10 points)

My design gives data on momentum and energy both before and after the collision. My sketch shows both carts, their masses, the bumpers, both motion detectors, the + direction and labels. My steps are clear enough for another group to repeat without me. I listed every measured quantity with units: m₁, m₂, and all four velocities. I repeat the same configuration at least 5 times. I present my findings clearly, with averages and confidence intervals.

Show a sample setup and procedure

Q2Data table

Cart 1 mass

Cart 2 mass

Changing a mass starts a new data set, since every trial must use the same configuration.

Velocities are from the two motion detectors. Right is +. Detector 2 faces left, so its readings have already been flipped to match the + direction.

Trial	v₁ᵢ (m/s)	v₂ᵢ (m/s)	v₁f (m/s)	v₂f (m/s)

Q3Findings

A box turns green when you're within 2% (values near zero get a small allowance, about 0.5% of the starting total). Keep signs: a cart moving left has negative momentum.

a. Change in momentum for each trial, and the average

Trial	p_i (kg·m/s)	p_f (kg·m/s)	Δp (kg·m/s)

b. Change in kinetic energy for each trial, and the average

Trial	KE_i (J)	KE_f (J)	ΔKE (J)

Q4Uncertainty

The worksheet asks for the standard uncertainty and 95% confidence interval of Δp (a, b) and of ΔKE (c, d), with the general equation for each. Find s first; it's the step in between.

Quantity	Δp (kg·m/s)	ΔKE (J)

Statistics checks allow 3%, since rounding adds up. Use your Δ values from Q3.

Show the worked solution for this data

Q5Interpretation of findings

If momentum is conserved, Δp should be 0. If kinetic energy is conserved, ΔKE should be 0. Check whether 0 is inside each 95% CI.

a. Is 0 inside the 95% CI of Δp?

So, is momentum conserved?

b. Is 0 inside the 95% CI of ΔKE?

So, is kinetic energy conserved?

Show a sample written answer for Q5

Q6Did you expect this?

For this type of collision, what did you expect?

If the data don't match, the most likely reason a small momentum loss shows up is:

Show a sample written answer for Q6

More practice: the Momentum Quiz.