Assignment 3

Assignment 3 ENGG 349 – Dynamics, Fall 2023 Instructor: Dr. Ahmad Ghasemloonia Page 1 of 3 Problem 1 : The motor M reels in the cable at a constant rate of 100 ௠௠ ௦ . Determine the velocity of the load 𝐿 , and the velocity of pulley 𝐵 with respect to load 𝐿 . Dynamics, Beer, Problem 11.54 Answer: 𝑣 ⃗ ௅ ൌ 16.67 ௠௠ ௦ ↑; 𝑣 ⃗ ஻/௅ ൌ 16.67 ௠௠ ௦ ↑ Problem 2 : Determine the constant speed at which the cable at 𝐴 must be drawn in by the motor in order to hoist the load 6 𝑚 in 1.5 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 . Dynamics, Hibbeler, Problem 12.200 Answer: 𝑣 ⃗ ஺ ൌ 32 ௠ ௦ ↓ Problem 3 : A secret agent is running toward the back of a moving bus, his intent being to jump off the back before the explosive he planted at the front goes off. At the illustrated instant, the bus has a constant velocity of 10 𝑚𝑝ℎ to the right. Currently, the agent is 30 𝑓𝑒𝑒𝑡 from the rear of the bus and moving at zero mph with respect to the bus.

Assignment 3 ENGG 349 – Dynamics, Fall 2023 Instructor: Dr. Ahmad Ghasemloonia Page 2 of 3 a) What constant acceleration will he need with respect to the bus so that he will leave the rear of the bus with zero velocity relative to the ground? b) Where will he land with respect to point 𝐴 ? Answer: 𝑎ሻ 𝑎 ⃗ ௔௚௘௡௧/௕௨௦ ൌ 3.6 ௙௧ ௦ మ ←; 𝑏ሻ 𝑎𝑡 60 𝑓𝑡 𝑓𝑟𝑜𝑚 𝑝𝑜𝑖𝑛𝑡 𝐴 Problem 4 : At the instant shown, airplane 𝐴 is flying horizontally in a straight line. It has a horizontal speed of 450 ௞௠ ௛௥ and this speed is increasing at a constant rate of 8 ௠ ௦ మ . At the instant shown, airplane 𝐵 is flying at the same altitude as airplane 𝐴 but is following a circular path of 300 𝑚 radius to take a 180 ° turn. At this instant, the airplane 𝐵 is travelling at a speed of 540 ௞௠ ௛௥ . This speed of 𝐵 is decreasing at a rate of 𝑎 ൌ െ0.034𝑣 , where 𝑣 is in ௠ ௦ and 𝑎 is in ௠ ௦ మ . After two seconds has elapsed from the position shown, determine the velocity of 𝐵 relative to 𝐴 and the acceleration of 𝐵 relative to 𝐴 . Figure adapted from Dynamics, Beer, Problem 11.142 Answer: 𝑣 ⃗ ஻/஺ ൌ െ201𝚤̂ െ 127𝚥̂ ௠ ௦ ; 𝑎 ⃗ ஻/஺ ൌ െ65𝚤̂ ൅ 32𝚥̂ ௠ ௦ మ