Mechanical Engineering Dynamics Problem

[Tribean]

Homework Statement

A plastic film moves over two drums. During a 4s interval the speed of the tape is increased uniformly from v0= 2ft/s to v1= 4ft/s. Knowing that the tape does not slip on the drums, determine (a) the angular acceleration of drum B, (b) the number of revolutions executed by drum B during the 4s interval.

diagram of problemhttp://www.chegg.com/homework-help/questions-and-answers/plastic-film-moves-drums-4s-interval-speed-tape-increased-uniformly-v0-2ft-s-v1-4ft-s-know-q3878687

Homework Equations

[itex]v^{2}_{f}[/itex]=v[itex]^{2}_{0}[/itex]+at
v=r[itex]\omega[/itex]
a[itex]_{t}[/itex]=r[itex]\alpha[/itex]

The Attempt at a Solution

I used the first equation to find that the linear acceleration of the tape is 3 ft/s^2. Since it's translating to drum B I would assume that the point that it touches the top of drum B would also have a linear acceleration of 3 ft/s^2 I then used my 2nd equation to figure out the angular acceleration of B by taking its radius of 15 in or 1.25 ft and dividing it from the linear acceleration coming up with 2.4 rad/s^2 but the back of the book states .400 rad/s^2

Where am I going wrong?

 

[mark726]

Hello,

Thank you for posting your problem and your attempted solution. Based on your equations and calculations, it seems like you are on the right track. However, there are a few things that may have caused you to get a different answer than the one given in the back of the book.

First, it is important to note that the angular acceleration of drum B will be different from the linear acceleration of the tape. This is because the tape is moving linearly, while the drum is rotating. Therefore, the equations you have used may not be directly applicable to finding the angular acceleration of the drum.

Secondly, it is not clear what units you used for your calculations. In your equations, you have used both ft/s and ft/s^2, which may cause confusion. It is important to use consistent units throughout your calculations to avoid errors.

Finally, it is possible that the back of the book has made a mistake in their calculation. Sometimes, textbooks and answer keys may contain errors. If you are confident in your approach and calculations, it may be worth double-checking with your professor or other reliable sources to confirm the correct answer.

I hope this helps clarify your understanding of the problem. Keep up the good work!