Assignment 4

Assignment 4 ENGG 349 – Dynamics, Fall 2023 Instructor: Dr. Ahmad Ghasemloonia Page 2 of 2 Problem 4: The system shown below is released from rest with no slack in the cable. A constant force of 20 𝑁 is applied to block 𝐴 and acts through the entire motion. Determine the acceleration of each block and the tension developed in the cable. The coefficient of static and kinetic friction between block 𝐴 and the incline are 𝜇 ௦ ൌ 0.15 and 𝜇 ௞ ൌ 0.1 , respectively. Assume massless-frictionless pulleys and cables. Figure adapted and modified from Dynamics, Gray, 2 nd ed., Problem 3-159 Answer: 𝑎 ⃗ ஺ ൌ 0.438 ௠ ௦ మ 𝑢𝑝 𝑡ℎ𝑒 𝑖𝑛𝑐𝑙𝑖𝑛𝑒, 𝑎 ⃗ ஻ ൌ 0.219 ௠ ௦ మ ↓ , 𝑇 ൌ 71.93 𝑁 Problem 5 : A 20 𝑘𝑔 block 𝐴 is at rest on a rough surface when at time 𝑡 ൌ 0 , a force of 𝑃 ൌ 60𝑡 is applied, where 𝑡 is time in second and 𝑃 is in Newtons. Block 𝐵 has a mass of 10 𝑘𝑔 . Assume massless and frictionless pully and cables, but consider friction between block 𝐴 and the rough surface. a) Knowing that it takes 2 seconds before block 𝐴 starts moving, determine the static friction coefficient between block 𝐴 snd the rough surface. b) At 𝑡 ൌ 4 seconds, block 𝐴 is moving at 8 ௠ ௦ to the left. Dtermien the kinetic friction between block 𝐴 and the rough surface. Figure adapted and modified from Dynamics, Meriam, Figure 2/19 Answer: 𝜇 ௦ ൌ 0.362; 𝜇 ௞ ൌ 0.206