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A 400-N force P is applied at point A of the bell crank shown. (a) Compute the moment of t...

A 400-N force P is applied at point A of the bell crank shown. (a) Compute the moment of the force P about O by resolving it into components along line OA and in a direction perpendicular to that line. (b) Determine the magnitude and direction of the smallest force Q applied at B that has the same moment as P about O.

Fig. P3.4

Step-by-Step Solution

Solution 1
Step #1 of 6

Figure shows the force P components along line OA and in a direction perpendicular to that line.

3-6P

Step #2 of 6

(a)

Resolve the force P into components along line OA and in a direction perpendicular to that line

Let &are components along line OA and in a direction perpendicular to that line

Find the component of the force P along the line OA.

Find the component of the force P in a direction perpendicular to line OA.

Step #3 of 6

Find the moment of the force P about O using the equation.

Therefore, the moment of the force about O is .

Step #4 of 6

(b)

Figure shows equivalent loading with force Q applied at B:

3-6P1

Step #5 of 6

Find the direction of the smallest force.

For the smallest force Q applied at B, the force should be perpendicular to the line OB

Hence,

Therefore, the direction of the smallest force is .

Step #6 of 6

Find the magnitude of the smallest force Q applied at B.

Moment about point O is same on both cases

Therefore, the magnitude of the smallest force Q applied at B is .

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