- #1
knyaz
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Hi all,
I recently came upon the following problem in Giancoli's Physics Principles With Applications, 6th ed. textbook that I am having some issues understanding. I am new here, so I do apologize if I have made any mistakes in formatting or anything else.
A 0.140-kg baseball traveling 35.0 m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove?
1.) favg = m*aavg
This is where I am struggling—the solutions manual to this book states that the following equation is also to be used:
2.) aavg = (v2 - v0 2) / 2(x - x0)
I am familiar with that second equation up there when used to find constant acceleration, but I do not see how it can be used to find average acceleration. The derivation of this equation from the basic definitions of average velocity and acceleration involves using the following:
vavg = (v + v0)/2
As far as I can tell, this wouldn't work for average acceleration—at non-constant acceleration, the average velocity would not necessarily be halfway between the initial and final velocities. Thus, it seems to me that the equation the solutions manual uses, no.2 above, cannot be used in solving the problem.
Is the solutions manual wrong, then, and is the problem unsolvable (to anyone this far in the textbook, at any rate) as it is stated? Please do tell me if I am missing something in my reasoning on this, or if I am otherwise incorrect.
I also do want to mention that I saw a similar post on here, involving this exact conceptual issue with a very similar problem. However, there the problem had asked for an estimate, which meant that eq (2) above was alright to use as an estimate of average acceleration. Here, the problem seems to ask for an exact answer—I do not know if it was meant to ask for an estimate, instead.
Thanks for hearing me out on this, and thanks in advance to anyone who replies!
-Alex
I recently came upon the following problem in Giancoli's Physics Principles With Applications, 6th ed. textbook that I am having some issues understanding. I am new here, so I do apologize if I have made any mistakes in formatting or anything else.
Homework Statement
A 0.140-kg baseball traveling 35.0 m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove?
Homework Equations
1.) favg = m*aavg
This is where I am struggling—the solutions manual to this book states that the following equation is also to be used:
2.) aavg = (v2 - v0 2) / 2(x - x0)
The Attempt at a Solution
I am familiar with that second equation up there when used to find constant acceleration, but I do not see how it can be used to find average acceleration. The derivation of this equation from the basic definitions of average velocity and acceleration involves using the following:
vavg = (v + v0)/2
As far as I can tell, this wouldn't work for average acceleration—at non-constant acceleration, the average velocity would not necessarily be halfway between the initial and final velocities. Thus, it seems to me that the equation the solutions manual uses, no.2 above, cannot be used in solving the problem.
Is the solutions manual wrong, then, and is the problem unsolvable (to anyone this far in the textbook, at any rate) as it is stated? Please do tell me if I am missing something in my reasoning on this, or if I am otherwise incorrect.
I also do want to mention that I saw a similar post on here, involving this exact conceptual issue with a very similar problem. However, there the problem had asked for an estimate, which meant that eq (2) above was alright to use as an estimate of average acceleration. Here, the problem seems to ask for an exact answer—I do not know if it was meant to ask for an estimate, instead.
Thanks for hearing me out on this, and thanks in advance to anyone who replies!
-Alex