Question

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+10R

Answer 1

`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`