Question 4 — Lab data: the missing force (20 points) Student…
Question 4 — Lab data: the missing force (20 points) Students connect a cart on a level track to a hanging mass using a light string over a pulley. They release both from rest, record the cart’s velocity, and use the slope of each velocity–time graph to find the acceleration. Their first calculation assumes no friction and an ideal string and pulley. For a control test, they disconnect the string and hanging mass, give the 1.20 kg cart a push to the right, and record how it slows on the same track. The other cart mass is 1.80 kg. Use g = 9.80 m/s². Take right for the cart and down for the hanging mass as positive. Main trials Trial Cart mass (kg) Hanging mass (kg) Measured acceleration (m/s²) A 1.20 0.240 0.63 B 1.20 0.360 1.34 C 1.20 0.480 1.94 D 1.80 0.240 0.09 E 1.80 0.480 1.12 Selected sensor readings Time (s) Trial A velocity (m/s) Coast-down velocity (m/s) 0.00 0.000 1.80 0.50 0.315 1.20 1.00 0.630 0.60 1.50 0.945 0.00 Show your work: Draw free-body diagrams for the connected cart and hanging mass, including a force the initial calculation may have overlooked. Also draw a force diagram for the cart during the disconnected coast-down test. (3 pts) Use the raw velocity readings to determine the acceleration in Trial A and in the coast-down test. Explain the sign of each slope. (2 pts) Write Newton’s second law for both connected masses and derive the frictionless acceleration equation. Calculate predictions for Trials A and D; compare with measured acceleration. (3 pts) Use the coast-down result to estimate the resistive force on the 1.20 kg cart and its kinetic friction coefficient. State the assumption needed to apply that coefficient to the 1.80 kg cart. (3 pts) Include friction in the system equation. Recalculate the expected acceleration for Trials A and D, and compare with the measurements. (3 pts) What did the original model leave out? Support your explanation with three numerical observations, including one from the coast-down test. Give another possible explanation that the data do not fully eliminate. (4 pts) Describe a follow-up experiment that would distinguish your explanation from the alternative. State what you would change, control, measure, and expect to observe. (2 pts) Upload ONE PDF at the end of the exam containing all of your written solutions. Do not upload a separate file for this question.
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