4:04 PM * 20%D Verizon This quiz deals with a practical problem of loosening or

Question

4:04 PM * 20%D Verizon This quiz deals with a practical problem of loosening or tightening a rusty nut by applying a force at the end of a wrench. To model this, we apply a force of 50 lbs with POA at the end of the wrench with an angle of 30 degrees with respect to the arm of the wrench. The length of the wrench is 100 cm. The radius of the nut is 2 cm, and the MO is at the center of the nut. If you do not know what POA or MO is, please read your lecture notes. There is a frictional force that produces a frictional torque that opposes the intended "rotational" motion from the wrench. Assuming that the applied torque is sufficient enough to just "balance" the frictional torque. Calculate (1) The applied torque in (Nm) and direction (in or out of the paper). You have to apply the right-hand-rule to find the applied torque. Be careful about the r and F directions .. remember the tail-to-tail and the requirements for cross-product. (2) The frictional torque in (Nm) and direction (in or out of the paper) with fr as an unknown (3) By making the total torque to be zero, determine fr (in Newtons first then convert it to lbs). (4) Should fr be smaller than 50lbs?? (5) Does the result make sense?? Refer to your lecture about the diagram of the wrench and the nut. A 1100 ce 30 0tbs

Explanation / Answer

given, F = 50 lbs with angle theta = 30 deg with the wrench

a. the applied torque, from the figure will be

T = F*1*sin(30) = 50*1*sin(30) = 25 l;b m

now 1 m = 39.3701 in

so T = 759.2525 lb in

b. the frictional torque is present to prevent the wrench from slipping hence it should be same as the applied torque in opposite direction

hence Tf = -759.2525 ln in

c. now fr*0.02 = 50*sin(30)*1

fr = 1250 lb

d. fr is larger than F, as distance between fr and the center of rotation is less than the distance between the point of application of force

e. the result makjes sense as due to newtons third law, tis fr will produce fr on the nut in opposite direction, which will provide a large amount of torqu to the nut to rotate ( which is the primary objective of using the wrench)

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