How solve this vector´s problem ?

The graph shows the vectors F and R that represent a pair of forces applied to the wheel of a toy, where the origin of the coordinate system corresponds to the position of the wheel axis.
Calculate the total force with operation 5 F+10Renter image source here

1 Answer
Nov 29, 2017

T = 5absF+10absR

Explanation:

Assuming the question asks for the total torque due to the forces F and R we have

T = d_1 absF + d_2 absR

but

d_1 = sqrt(3^2+4^2)= 5
d_2 =sqrt(6^2+8^2)=10

then

T = 5absF+10absR

NOTE

If the forces are in a scale representation we have

absF = lambda sqrt(3^2+4^2) = 5 lambda
absR = lambda sqrt(3^2+4^2) = 5 lambda

and then

T = (5 xx 5 + 10 xx 5)lambda = 75 lambda

Here lambda is the scale factor for F,R