Two-horses-pull-horizontally-on-ropes-attached-to-a-stump-The-two-forces-F-and-T-that-they-applied-to-the-stump-are-such-that-the-resultant-R-has-a-magnitude-equal-to-F-and-makes-an-angle-of-90-with-

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Question Number 16015 by chux last updated on 16/Jun/17

$$\mathrm{Two}\mathrm{horses}\mathrm{pull}\mathrm{horizontally}\mathrm{on}$$$$\mathrm{ropes}\mathrm{attached}\mathrm{to}\mathrm{a}\mathrm{stump}.\mathrm{The}$$$$\mathrm{two}\mathrm{forces}\mathrm{F}\mathrm{and}\mathrm{T}\mathrm{that}\mathrm{they}$$$$\mathrm{applied}\mathrm{to}\mathrm{the}\mathrm{stump}\mathrm{are}\mathrm{such}\mathrm{that}$$$$\mathrm{the}\mathrm{resultant}\mathrm{R}\mathrm{has}\mathrm{a}\mathrm{magnitude}$$$$\mathrm{equal}\mathrm{to}\mathrm{F}\mathrm{and}\mathrm{makes}\mathrm{an}\mathrm{angle}\mathrm{of}$$$$90°\mathrm{with}\mathrm{F}.\mathrm{Let}\mathrm{F}=1300\mathrm{N}\mathrm{and}$$$$\mathrm{R}=1300\mathrm{N}.\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{T}.$$

Commented by chux last updated on 17/Jun/17

$$\mathrm{please}\mathrm{help}\dots \mathrm{its}\mathrm{urgent}.$$

Answered by mrW1 last updated on 17/Jun/17

$$\mathrm{T}=1300\times \sqrt{2}$$$$$$$$\mathrm{as}\mathrm{vector}$$$$\text{boldsymbol}\mathrm{R}=\text{boldsymbol}\mathrm{F}+\text{boldsymbol}\mathrm{T}$$$$1300\mathrm{j}=1300\mathrm{i}+\text{boldsymbol}\mathrm{T}$$$$\Rightarrow \text{boldsymbol}\mathrm{T}=-1300\mathrm{i}+1300\mathrm{j}$$$$\mathrm{T}=1300\sqrt{2}$$

Commented by chux last updated on 18/Jun/17

$$\mathrm{thanks}\mathrm{so}\mathrm{much}\dots$$$$\mathrm{thanks}\mathrm{so}\mathrm{much}\dots$$

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