TBR physics example 2.8B

[Rexhina]

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It is frustrating that they dont list all the answers in this book. But anyways can someone tell me which one is the right answer

I think is "c" but i want to be positive

What happens to the centripetal acceleration of a space shuttle, if it goes into a higher orbit but keeps its tangential speed fixed?

a. the acceleration increases, because the orbital radius increases
b. the acceleration increases, because the angular velocity decreases
c. the acceleration decreases, because the orbital radius increases
d. the acceleration decreases, because the angular velocity increases

 

[phltz]

It is frustrating that they dont list all the answers in this book. But anyways can someone tell me which one is the right answer

I think is "c" but i want to be positive

What happens to the centripetal acceleration of a space shuttle, if it goes into a higher orbit but keeps its tangential speed fixed?

a. the acceleration increases, because the orbital radius increases
b. the acceleration increases, because the angular velocity decreases
c. the acceleration decreases, because the orbital radius increases
d. the acceleration decreases, because the angular velocity increases

There are two main equations we use for centripetal acceleration. v^2/r and w^2r. Because we're told that the tangential speed (which is essentially v) is constant, let's use the first equation. A higher orbit means a higher r. Because r is on the bottom of the equation, a higher r means a lower centripetal acceleration. So c looks like the best answer.

 

[Rexhina]

There are two main equations we use for centripetal acceleration. v^2/r and w^2r. Because we're told that the tangential speed (which is essentially v) is constant, let's use the first equation. A higher orbit means a higher r. Because r is on the bottom of the equation, a higher r means a lower centripetal acceleration. So c looks like the best answer.

thank you

 

[BerkReviewTeach]

It is frustrating that they dont list all the answers in this book. But anyways can someone tell me which one is the right answer

I think is "c" but i want to be positive

What happens to the centripetal acceleration of a space shuttle, if it goes into a higher orbit but keeps its tangential speed fixed?

a. the acceleration increases, because the orbital radius increases
b. the acceleration increases, because the angular velocity decreases
c. the acceleration decreases, because the orbital radius increases
d. the acceleration decreases, because the angular velocity increases

The answer is choice C. Depending on how old your book is, there are answers for all of the B questions. Check page 278 (if it's really old), 282 (if it's a year or so), or 288 (if it's the latest).

The current version of the book lists the answer explanations to B-questions (like the A-questions), so I decided to transcribe that answer here.

Solution
In this question we are given information about the radius and the tangential velocity of an object in a circular orbit. We are asked about acceleration, so the equation we need is:

acentirpetal = vexp2/r

The tangential velocity is said to remain the same, so the question comes down to the inverse relationship between acentirpetal and r. If r increases, then according to the equation the centripetal acceleration should decrease. This eliminates choices A and B. The angular velocity, omega, actually decreases, because the tangential velocity is constant while the radius increases. This means the shuttle has the same linear speed, but has to cover a greater distance to complete a full revolution. As a result, the shuttle does not orbit a full revolution as quickly as before. This can be verified by considering equation (2.22) which shows that as radius increases while v remains constant, the value of omega decreases.

omega = v/r

The reason why we did not choose to use acentirpetal = omegaexp2r (equation (2.29)) is because both variables on the right side of the equation (omega and r) change. Again, though, the variable that is squared (omega in this case) has a greater impact on the centripetal acceleration than the term that is not squared (r in this case).

The best answer is choice C.