PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
Two blocks are connected by a light, inextensible string that passes over a frictionless pulley. Block A (mA=4.0kg) rests on a horizontal surface where kinetic friction is negligible, while block B (mB=2.0kg) hangs freely and is allowed to move vertically. Two different sets of free-body diagrams have been proposed for each block.
Set X (drawn by Student X):
• Block A: arrows labeled T (to the right from the dot), mg (down), and N (up).
• Block B: arrows labeled T (up) and mg (down).
Set Y (drawn by Student Y):
• Block A: arrows labeled Tright (to the right), Tleft (to the left), mg (down), and N (up).
• Block B: arrows labeled T (up), mg (down), and an arrow labeled “inertia” pointing upward.
Air resistance is negligible.
(a) For block A, decide which diagram (Set X or Set Y) is physically correct. For the incorrect diagram, identify every error and explain your reasoning.
(b) Repeat the analysis for block B.
(c) Draw any corrected free-body diagrams needed so that there is exactly one accurate diagram for each block. Follow accepted conventions.
(d) Using the correct diagrams, derive expressions for the magnitude of the system’s acceleration and the tension in the string in terms of mA, mB, and g. Then compute their numerical values for the given masses.
(e) Discuss how the incorrect forces identified in parts (a) and (b) would have affected the calculated acceleration had they been used in Newton’s second law.