Chapter 10, Problem 17A

Inside Biker Bob’s space station is a ladder that extends from the inner surface of the rim to the central axis. Bob climbs the ladder (toward the center). Point A is at the floor, point B is halfway to the center, and point C is at the central axis.

a. Rank the linear speeds of Bob relative to the center of the station, from highest to lowest. Or are the speeds the same at all parts of the ladder?

b. Rank the support forces Bob experiences on the ladder rungs, from greatest to least. Or are the support forces the same in all locations?

To determine

To rank: The linear speed of person B relative to the center of the station.

Answer to Problem 17A

A> B> C.

Explanation of Solution

Introduction:

Artificial gravity is activated inside the space station to have stability and no collisions due to free fall. The more the distance, the less gravitational force will be experienced.

Artificial gravity will be experienced maximum on the floor. Thus, B’s linear speed is maximum at the inner surface of the rim.

Now, at halfway to the central axis, acceleration due to gravity will be half value of the former. So, the linear speed is half.

Now, at the central axis, gravity will be null. Hence, B will have no linear speed here i.e. zero motion.

Conclusion:

Thus, the linear speed of the B relative to the center of the station would be highest at the floor then it would be intermediate at the halfway to the center, and then it would be lowest, as it is reaching towards the Central axis. The rank is A> B> C

To determine

To rank: The support forces person B experiences on the ladder rungs from greatest to least.

Answer to Problem 17A

A > B > C

Explanation of Solution

Introduction:

Artificial gravity is activated inside the space station to have stability and no collisions due to free fall. The more the distance, the less gravitational force will be experienced.

Support forces would vary from the central axis as per the value of acceleration due to gravity “g”. At the floor that is, at the inner surface of the rim, g will be maximum. Thus, support forces would be maximum at the inner surface of the rim.

Since B is at halfway to the central axis, the value of acceleration due to gravity would be half of it was at point “A” leads to half of the support forces at point “A”.

At last, at the central axis value of acceleration due to gravity reaches to zero. Thus, no support forces will be experienced at the central axis.

Conclusion:

Thus, Support forces vary from inner surface to the central axis as

A > B > C