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標題:
發問:
f sin x + mg = R cos x f cos x + R sin x = F From the equations, f = F cos x - mg sin x, then R = ?, tan x = ? Please briefly tell how to work out the answers. 更新: f, R and x are variables, but I just want to express R and tan x in terms of the others... Just like the example given above, we can find that f = F cos x - mg sin x from the two equations. Likewise, I want to know how to express R and tan x in similar form.
最佳解答:
Are f, R and x variables? There is no unique solution for 2 equations with 3 variables. Or you simply wants to express R and tan x in terms of the others? 2012-07-29 21:20:46 補充： (a) f sin x - R cos x = - mg .............(1) R sin x + f cos x = F ...........(2) f x (1) + R x (2) we get f^2 sin x + R^2 sin x = - mgf + RF so sin x = (RF - mgf)/(f^2 + R^2)......(3) Similarly, f x (2) - R x (1) we get f^2 cos x + R^2 cos x = fF + Rmg so cos x = (fF + Rmg)/(f^2 + R^2).....(4) tan x = (3)/(4) = (RF - mgf)/(fF + Rmg). (b) R^2 cos^2 x = (f sin x + mg)^2 R^2 sin^2 x = (F - f cos x)^2 Adding together and take square root, R = sqrt [ (f sin x + mg)^2 + (F - f cos x)^2] = sqrt [ m^2g^2 + 2fmg sin x + f^2 + F^2 - 2Ff cos x]
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Equations with sin cos tan發問:
f sin x + mg = R cos x f cos x + R sin x = F From the equations, f = F cos x - mg sin x, then R = ?, tan x = ? Please briefly tell how to work out the answers. 更新: f, R and x are variables, but I just want to express R and tan x in terms of the others... Just like the example given above, we can find that f = F cos x - mg sin x from the two equations. Likewise, I want to know how to express R and tan x in similar form.
最佳解答:
Are f, R and x variables? There is no unique solution for 2 equations with 3 variables. Or you simply wants to express R and tan x in terms of the others? 2012-07-29 21:20:46 補充： (a) f sin x - R cos x = - mg .............(1) R sin x + f cos x = F ...........(2) f x (1) + R x (2) we get f^2 sin x + R^2 sin x = - mgf + RF so sin x = (RF - mgf)/(f^2 + R^2)......(3) Similarly, f x (2) - R x (1) we get f^2 cos x + R^2 cos x = fF + Rmg so cos x = (fF + Rmg)/(f^2 + R^2).....(4) tan x = (3)/(4) = (RF - mgf)/(fF + Rmg). (b) R^2 cos^2 x = (f sin x + mg)^2 R^2 sin^2 x = (F - f cos x)^2 Adding together and take square root, R = sqrt [ (f sin x + mg)^2 + (F - f cos x)^2] = sqrt [ m^2g^2 + 2fmg sin x + f^2 + F^2 - 2Ff cos x]
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