Fill in the blanks. Red arrow:   Green arrow: Yellow arrow: The measurement in the image is normal if it is less than cm.  

The shaft shown below is made from 1040 steel with properties of Sy = 71 ksi and Sut = 85 ksi with dimensions given, and the journal bearings at A & B prevent motion of the shaft but do not create reaction moments. Forces F1 = [F1]0 lbf and F2 = [F2]0 lbf are applied in the vertical direction to the shaft as it rotates. Determine the minimum diameter needed for the shaft so that it will last an estimated N = [N],000 cycles before fatigue failure. Use an endurance limit of Se = 40 ksi.Hint: The critical location will be at bearing B.Enter your answer in units of inches and rounded to 3 decimal places. Write down all your work to scan and submit. L1 = [L1] inch, L2 = [L2] inch, L3 = [L3] inch  

The top crossbar for a gantry crane is to be constructed out of 6 × 2.034 channel (see table below for geometric properties) and with a length L = 7 feet. The channel is implemented as shown in the close-up so that it can be considered as a simply-supported beam that bends about the 1-1 axis. It is desired that the crane be used to repeatedly lift a weight at the midpoint of the crossbar. Consider the weight as a point force acting through the centroid of the channel that varies between 0 lbf and 8,000 lbf. The channel material is hot-rolled AISI 1045 (Sut = 82 ksi, Sy = 45 ksi), and you don’t need to consider any stress concentrations or the weight of the channel crossbar. Determine the following: The maximum bending stress (σmax) in the crossbar (the shear stress can be ignored in the analysis) The modified endurance limit (Se) for this application with 90% reliability The factor of safety with respect to infinite life (nf) using the Modified Goodman criteria The number of cycles (N) it is expected to last before fatigue failure Write down all your work to scan and submit, including a free-body diagram and bending moment diagram for the crossbar. σmax = [stress] ksi (round answer to 1 decimal place)Se = [Se] ksi (round answer to 1 decimal place)nf = [nf] (round answer to 2 decimal places)N = [N] (round answer to nearest thousand; enter “infinite” if infinite life is predicted)      

The top crossbar for a gantry crane is to be constructed out of 6 × 2.157 channel (see table below for geometric properties) and with a length L = 8 feet. The channel is implemented as shown in the close-up so that it can be considered as a simply-supported beam that bends about the 1-1 axis. It is desired that the crane be used to repeatedly lift a weight at the midpoint of the crossbar. Consider the weight as a point force acting through the centroid of the channel that varies between 0 lbf and 9,000 lbf. The channel material is hot-rolled AISI 1040 (Sut = 76 ksi, Sy = 42 ksi), and you don’t need to consider any stress concentrations or the weight of the channel crossbar. Determine the following: The maximum bending stress (σmax) in the crossbar (the shear stress can be ignored in the analysis) The modified endurance limit (Se) for this application with 95% reliability The factor of safety with respect to infinite life (nf) using the Modified Goodman criteria The number of cycles (N) it is expected to last before fatigue failure Write down all your work to scan and submit, including a free-body diagram and bending moment diagram for the crossbar. σmax = [stress] ksi (round answer to 1 decimal place)Se = [Se] ksi (round answer to 1 decimal place)nf = [nf] (round answer to 2 decimal places)N = [N] (round answer to nearest thousand; enter “infinite” if infinite life is predicted)    

Create the sample space where one coin is flipped and then one die is rolled.

Given: ,  , and  

A card is drawn from a well-shuffled standard deck of 52 cards. Find the probability of drawing a face card.

Two cards are drawn from a well-shuffled standard deck of 52 cards. The first card is drawn, then replaced, and a card is drawn again. What is the probability that a black card is drawn, and then a black seven is drawn?

A fair die is rolled. Find the probability that the number is greater than 3.

Thoroughly explain why for arbitrary sets  and ,