4. In order to unscrew the tapped faucet A, a plumber uses two pipe wrenches as

Question

4. In order to unscrew the tapped faucet A, a plumber uses two pipe wrenches as shown. By exerting a 40-lb force on each wrench, at a distance of 10 inches from the axis of the pipe and in a direction perpendicular to the pipe and to the wrench, he prevents the pipe from rotating and thus avoids loosening or tightening the joint between the pipe and the tapped elbow C. Determine (a) the angle that the wrench at A should form with the vertical if elbow C is not to rotate about the vertical, and (b) the force- couple system at Cequivalent to the two 40-lb forces when this condition is -satisfied. 40 lb y 10 in. 40 1b 10 in 7.5 in 7.5 in 25 in. 18 in

Explanation / Answer

a)

for the elbow C to not rotate about the vertical the moments due to the two 40lb forces should be = 0.

now the moment due to the 40lb force at B is = 40*7.5 = 300 lb.in (CCW moment abot y-axis)

now resolving the 40lb force at A into horizontal and vertical components we have

Fa(horizontal) = 40 cos along the -ve x- axis.

Fa(vertical) = 40 sin along the -ve z-axis.

now the moment due to this force at C about vertical is = Fa(horizontal) * 15 = 40cos*15 .( CW moment abou the vertical at C)

balancing the moments we have 40 cos*15 = 300 => = 60 degrees.

b)

the force couple system is therefore

given by Fequivalent = (40- 40 cos ) i - 40 sin j = 20 i - 34.64 j

the couple is therefore M = 15*Fv i = 519.615 lb.in

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