Question

A torque wrench grips a bolt at the origin of coordinates, with the free end of the torque wrench located at the point (r0, 0, 0). The force on this end of the torque wrench points in the direction of V = 10, 0, 16 . Note that r = r0, 0, 0 in this problem. Compute the length of the lever arm L needed to produce a torque with magnitude 360 ft-lb if the magnitude of the force is 120 pounds.

Answer 1

Answer:

L = 3.54 ft

Step-by-step explanation:

Given:

vector r = < r0 , 0 , 0 >

V = < 10 , 0 , 16 >

F = 120 lb

T = 360 lb -ft

Step 1: Compute unit vector of V

V_unit = < 10 / sqrt (10^2 + 16^2) , 0 ,  16 / sqrt (10^2 + 16^2) >

V_unit = < 10 / 18.86796 , 0 ,  16 / 18.86796 >

V_unit = < 0.53 , 0 ,  0.848 >

Step 2 : Torque

Torque = r x F

<0 ,360, 0 > = < r0 , 0 , 0 > x < 0.53*120 , 0 ,  0.848*120 >

<0 ,360, 0 >  = < r0 , 0 , 0 > x < 63.6 , 0 ,  101.76 >

<0 ,360, 0 > = <0 ,101.76*ro, 0 >

Comparing coefficient:

ro = 3.54 ft