20180308 - Dynamics Questions

Thursday, 8 March 2018

11:07 AM

𝐴𝑠 𝑡ℎ𝑒 𝑏𝑢𝑠 𝑡𝑎𝑘𝑒𝑠 𝑎 𝑠𝑡𝑒𝑎𝑑𝑦 𝑡𝑢𝑟𝑛 𝑤𝑖𝑡ℎ 𝑟𝑎𝑑𝑖𝑢𝑠 8𝑚 𝑎𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑦 𝑠𝑝𝑒𝑒𝑑, 𝑛𝑜𝑡𝑖𝑐𝑒 𝑡ℎ𝑎𝑡 𝑎 𝑚𝑎𝑠𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟𝑖𝑛𝑔 ℎ𝑎𝑛𝑔𝑠 𝑎𝑡 30° 𝑡𝑜 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙. 𝐻𝑜𝑤 𝑓𝑎𝑠𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑏𝑢𝑠 𝑔𝑜𝑖𝑛𝑔?

N2 Vertical: 𝑇𝑐𝑜𝑠𝜃−𝑚𝑔=0 (1)
N2 Horizontal: 𝑇𝑠𝑖𝑛𝜃=𝑚𝑎=﷐𝑚﷐𝑣﷮2﷯﷮𝑟﷯ (2)

(1):
𝑇𝑐𝑜𝑠𝜃−𝑚𝑔=0
𝑇𝑐𝑜𝑠𝜃=𝑚𝑔

(2) ÷ (1):
﷐𝑇𝑠𝑖𝑛θ﷮𝑇𝑐𝑜𝑠θ﷯=﷐﷐𝑚﷐𝑣﷮2﷯﷮𝑟﷯﷮𝑚𝑔﷯
𝑡𝑎𝑛𝜃=﷐﷐𝑣﷮2﷯﷮𝑟𝑔﷯

𝐴 𝑡𝑜𝑦 𝑡𝑟𝑢𝑐𝑘, 𝑚𝑎𝑠𝑠 𝑚, ℎ𝑎𝑠 𝑤ℎ𝑒𝑒𝑙 𝑡ℎ𝑎𝑡 𝑟𝑜𝑙𝑙 𝑓𝑟𝑒𝑒𝑙𝑦. 𝑊𝑖𝑡ℎ 𝑚𝑦 𝑓𝑖𝑛𝑔𝑒𝑟, 𝐼 𝑎𝑝𝑝𝑙𝑦 𝑎 𝑓𝑜𝑟𝑐𝑒 𝐹 𝑎𝑡 𝑎𝑛𝑔𝑙𝑒 =30° 𝑡𝑜 𝑡ℎ𝑒 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑡𝑜 ℎ𝑜𝑙𝑑 𝑖𝑡 𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦 𝑎𝑔𝑎𝑖𝑛𝑠𝑡 𝑎 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑤𝑎𝑙𝑙. 𝐷𝑟𝑎𝑤 𝑎 𝐹𝐵𝐷 𝑑𝑖𝑎𝑔𝑟𝑎𝑚, 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 𝑓𝑜𝑟 𝑁𝑒𝑤𝑡𝑜﷐𝑛﷮′﷯𝑠 𝐿𝑎𝑤𝑠

∑﷐𝐹﷮𝑣﷯=𝐹𝑐𝑜𝑠𝜃−𝑚𝑔=0
∑﷐𝐹﷮ℎ﷯=𝐹𝑠𝑖𝑛𝜃−𝑁=0
𝐹=﷐𝑚𝑔﷮𝑐𝑜𝑠𝜃﷯
𝑁=﷐𝑚𝑔﷮𝑐𝑜𝑠𝜃﷯𝑠𝑖𝑛𝜃

Created with Microsoft OneNote 2016.