A cable car across a river on a wire, car weighs 2500 pds, stopped about 2/3 of the way across, and deflects cable relative to horizontal. Left side deflection 15 deg downward from horizontal, right side 7 deg deflection downward from horizontal.... good picture???
I understand the picture, and that the objective is to find magnitudes of u and v..... or |u| and |v|.
It says to "write each force vector in terms of i and j."
They have: u= |u|(cos 7deg)i + |u|(sin 7deg)j
v= |v|(-cos 15deg)i + |v|(sin 15deg)j (by the way... why is this ai+bj instead of ai - bj...?)
w = -2500j
I understand that they have -2500j becuase its a straight vertical force downward, or negative, which doesn't give it an i (or horizontal) value to be added, or 0i, right??
But how do they get the equations for u and v?? I understood the rest of the chapter.... magnitude, standard vector movement, all the addition/ subtraction/ scalar multiplication, and i and j expression when given a vector like <-2,4>, but i don't see where they got those equations? I think it might have something to do with unit vector with the same direction, like u = (1/|v|)v, but i dont see how...
Also, continuing on, i see how the substitution and algebra is done to get two equations that need to be equal to zero, for equilibrium that is, and they are :
(cos 7deg)|u| + (-cos 15deg)|v| = 0 and
(sin 7deg)|u| + (sin 15deg)|v| - 2500 = 0
And now im supposed to solve using "standard methods" (i think its solve for one and then use substitution to solve for the other one, solve a system of 2 variables by substitution) but i cant figure out how to solve it....
The answers are |u|=6400 and |v|=6600
Any help would be appreciated...... thanks
I understand the picture, and that the objective is to find magnitudes of u and v..... or |u| and |v|.
It says to "write each force vector in terms of i and j."
They have: u= |u|(cos 7deg)i + |u|(sin 7deg)j
v= |v|(-cos 15deg)i + |v|(sin 15deg)j (by the way... why is this ai+bj instead of ai - bj...?)
w = -2500j
I understand that they have -2500j becuase its a straight vertical force downward, or negative, which doesn't give it an i (or horizontal) value to be added, or 0i, right??
But how do they get the equations for u and v?? I understood the rest of the chapter.... magnitude, standard vector movement, all the addition/ subtraction/ scalar multiplication, and i and j expression when given a vector like <-2,4>, but i don't see where they got those equations? I think it might have something to do with unit vector with the same direction, like u = (1/|v|)v, but i dont see how...
Also, continuing on, i see how the substitution and algebra is done to get two equations that need to be equal to zero, for equilibrium that is, and they are :
(cos 7deg)|u| + (-cos 15deg)|v| = 0 and
(sin 7deg)|u| + (sin 15deg)|v| - 2500 = 0
And now im supposed to solve using "standard methods" (i think its solve for one and then use substitution to solve for the other one, solve a system of 2 variables by substitution) but i cant figure out how to solve it....
The answers are |u|=6400 and |v|=6600
Any help would be appreciated...... thanks