We know from item 10 that:
So, the equation becomes:
The yield strength of CP titanium welds was measured for welds cooled at rates of \(10^{\circ}C/s,15^{\circ}C/s\ \text{and}\ 28^{\circ}C/s\). The results are presented in the following table. (Based on the article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds,” D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s.)
\(\begin{array}{}
\hline
\text{Cooling Rate}&\text{Yield Strenghts}\\
\hline
10&71.00&75.00&79.67&81.00&75.50&72.50&73.50&78.50\\
15&63.00&68.00&73.00&76.00&79.67&81.00\\
28&68.65&73.70&78.40&84.40&91.20&87.15&77.20&80.70&84.85&88\\
\hline
\end{array}\)
a. Construct an ANOVA table. You may give a range for the P-value. b. Can you conclude that the yield strength of CP titanium welds varies with the cooling rate?
At t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by 𝜃(𝑡) = (250 𝑟𝑎𝑑/𝑠 )𝑡 − (20.0 𝑟𝑎𝑑/𝑠 2 )𝑡 2 − (1.50 𝑟𝑎𝑑/𝑠 3 ) 𝑡 3 . (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity. (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t=0 when the current was reversed? (e) Calculate the average angular velocity for the time period from t=0 to the time calculated in part (a). A