Chapter 2 Problem 2076 The device shown is a part of an auto

Chapter 2, Problem 2/076 The device shown is a part of an automobile seat-back-release mechanism. The part is subjected to the 7.6-N force exerted at A and a 280-N-mm restoring moment exerted by a hidden torsional spring. Determine the y-intercept of the line of action of the single equivalent force. Your answer will be positive if the intercept is above o and negative if below O. F=7.6N 12mm 27 41 mm 280 N-mm Answer: y =

Solution

Horizontal component of force=7.6cos27=6.77 N(towards right)

Vertical component of force =7.6sin27 =3.45 N(vertically upwards)

Moment about O due to horizontal component of force=6.77*41=277.57 Nmm(clockwise)

Moment about O due to vertical componet of force=3.45*12=41.4 Nmm(anticlockwise)

Restoring moment at O due to hidden spring=280 Nmm(anticlockwise)

Total moment at O=277.57-41.4-280=-43.83Nmm=43.83 Nmm(anticlockwise)

The single equivalent force should be placed such that the moment due to that force about O =43.83 Nmm(anticlockwise)

The y intercept required =43.83/(7.6*cos27)=6.47 mm

Also, since the net moment is anticlockwise, the intercept will be negative because the force of 7.6N has to be placed below O.

Therefore, answer is -6.47 mm