Questions: Consider two pieces of tubing 1/2 in and 3/4 in, two washers 3/16 in each, and a nut 1/16 in thick. The smallest length of a bolt that will pass through all these is in. (Type a whole number, proper fraction, or mixed number.)

Solution Steps

To find the smallest length of a bolt that will pass through all the given pieces, we need to sum the thicknesses of all the components: two pieces of tubing, two washers, and one nut.

1. Sum the thicknesses of the two pieces of tubing.
2. Sum the thicknesses of the two washers.
3. Add the thickness of the nut.
4. Combine all these sums to get the total length required.

We have two pieces of tubing with thicknesses \( \frac{1}{2} \) in and \( \frac{3}{4} \) in. We sum these thicknesses: \[ \frac{1}{2} + \frac{3}{4} = 0.5 + 0.75 = 1.25 \text{ in} \]

We have two washers, each with a thickness of \( \frac{3}{16} \) in. We sum these thicknesses: \[ 2 \times \frac{3}{16} = 2 \times 0.1875 = 0.375 \text{ in} \]

The nut has a thickness of \( \frac{1}{16} \) in: \[ \frac{1}{16} = 0.0625 \text{ in} \]

We combine the sums from the previous steps to get the total length required: \[ 1.25 + 0.375 + 0.0625 = 1.6875 \text{ in} \]

Final Answer