Question

Two construction workers pull on the control lever of a frozen valve (Figure P4.14). The lever connects to the valve’s stem through the key that fits into partial square grooves on the shaft and handle. Determine the net moment about the center of the shaft.

 

Figure P4.14

Answer 1

Draw the free body diagram of the lever:

 

Calculate the components of the force F1

Calculate the y component of the force F1

F1y = F1 cos 20°

 

Substitute 200 N for F1

F1y = 200 cos 20°

= 187.94 N

 

Calculate the x component of the force 300 N

F1x = F1 sin 20°

 

Substitute 200 N for F1

F1x = 200 sin 20°

= 68.40 N

 

Calculate the moment about the center of shaft:

M = (lAB × F1y) + (lAB × F2) + (0 × F1x)

     = (lAB × F1y) + (lAB × F2)

 

Substitute 250 mm = 0.25 m for lAB, 187.94 N for F1y and 300 N for F2

M = (0.25 × 187.94) + (0.25 × 300)

    = 46.985 + 75

   = 121.985 N ∙ m

 

Therefore, moment of the forces about the center of shaft is 121.958 N ∙ m.

Therefore, moment of the forces about the center of shaft is 121.958 N ∙ m.