To reduce the mass of a titanium bulkhead for a spacecraft, a machinist drills an array of holes in the bulkhead. The bulkhead is a triangular-shaped plate with a base and height of 13.0 ft and 8.00 ft, respectively, and a thickness of 2.0x101 mm. For the density of titanium, use p = 4.43g/cm³.
How many 2.5 cm diameter holes must be drilled clear through the bulkhead to reduce its mass by 20.0 kg? Consider the best and worst cases, i.e. what is the smallest and largest number of holes that will need to be drilled, given the uncertainties?
Show your conversion factors. Use the correct number of significant figures in your final answer.
Problem # 2 (20 pts)
A new experimental pump was tested to determine the power required to produce a range of fluid discharges. Various rates of discharge were measured and the corresponding power required for each discharge was recorded.
The discharge values Q, in units of liters per second, are 5, 10, 15, 20, 25, 30, 35.
The corresponding power P, in units of kilowatts, are 31, 39, 45, 53, 60, 67, and 75.
a) Construct a table showing the power versus the discharge rate.
b) Construct a rectilinear graph of the data (to be done by hand, not using MATLAB or another tool)
c) Using the technique of linear regression, write the equation of the relationship in terms of P and Q. You do not need to take significant figures into account for this part. Express the equation's parameter values to two decimal places.
d) Using the results from Part (c), extrapolate the power required to produce a
discharge of 40 L/s.
Problem #3 (10 pts)
Find two examples of "badly" designed graphs from outside sources. They can be from a magazine article, a book, a research paper, or a website. If the source is printed material, you can cut out the actual page, or photocopy it, or scan it.
a) For each graph, list what is wrong with the graph.
b) Choose just one of your "bad" graphs and re-do it by hand either on graph paper or via a graphing program. Fix all of the things that are wrong with the original graph. You are allowed to change the type of graph if that enhances understanding of the data.
Here are additional requirements:
Each graph should be from a different source, e.g., one from a book and another from a website.
In addition to submitting a copy of the original graph, include enough of the text around the graph to show its context.
Only submit graphs that are substantially bad! Each graph should have at least two major things wrong with it. The worse, the better!
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