Instead of being shocked or worried about the health of his ace, Cooper smiled and assessed the incident from Peavy's point of view.
"You know what? It probably got him [mad]," said Cooper with a laugh, knowing Peavy emerged from the incident without any harm done.
Aside from this near-miss on his glove shoulder, Peavy's Cactus League debut for the White Sox was virtually flawless. The right-hander hurled three scoreless innings, fanning three, giving up two hits and not issuing a walk.
After leaving the mound, Peavy provided an assessment concerning the team's 2010 outlook that just might have fans of the South Siders smiling through late October.
Peavy believes the White Sox can be something special during his first full season in Chicago.
"I'm as excited as I've ever been about any season I've ever been a part of," Peavy told reporters in Arizona. "I believe this team can win a World Series if healthy.
"We can be the favorites, or we can finish last, but I can promise you, the 25 guys we break camp with believe we're the favorites. We don't ever take the field feeling like an underdog. Whether that's right or wrong, I don't know. But I believe when John Danks pitches, he's believes he's going to win.
"I don't care if he's facing CC Sabathia or a callup, that's just the way he is. That's what I love about this team -- the attitude of this team."
Cooper pointed out how the driven Peavy has pretty much done everything in his career but win that World Series title.
"His hunger really ignites everybody," said Cooper. "But he's passionate about life, it seems like, not only baseball. You see him pitching and doing what he was doing [on Thursday] night [hosting the Woodjock charity concert in Scottsdale].
"He has a Cy Young, a few All-Star appearances. Now we have our hearts set on the ring, and a guy like Peavy is a big addition."
Staying healthy would be the only major concern for Peavy, who was limited to 16 starts last year because of a strained tendon in his right ankle. He also lost a couple of 2010 starts after taking a line drive off his pitching elbow during a Minor League rehab start.
So Friday's first inning, against the Angels, was a little too close for comfort, especially for such an integral figure in what the White Sox hope will be a title drive.
"It was scary," said Peavy of the line drive that grazed his left shoulder. "My reaction ... I almost ducked my head into it. It could have got ugly. It's part of the game -- balls are going to be hit back at you. You've got to react. We were fortunate there.
"Today's results were nice, but sometimes you don't always have those desired results. If I go out there and give up 10 runs, I'm trying to accomplish something, I'm trying to get stronger and work on certain stuff. Today I was able to do that."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.