Question for those who can do mathematics/engineering problems

[m_c]

I'm working through an engineering maths module just now, and this example has me questioning my abilities.
Am I correct in thinking that the following example question is missing the radius?

The radius magically appears as 0.3 in the worked answer, and I want to make sure I'm not missing something blatantly obvious...

 

[Misterg]

Am I correct in thinking that the following example question is missing the radius?

I think you are. AFAICT you either need the radius or the length of the 'cord'.

 

[Munkul]

You are correct. The radius or the cord length needs to be provided, in order to use equation 1 divided by 2, it doesn't cancel out.

 

[daedalusminos]

It could be that the question has been taken out of context. If you assume the pendulum revolves once a second then the circumference would be 2m and the radius (2/PI) * 0.5 = 0.32 or 0.3 to 1DP

 

[malcolm]

True enough there is some information missing. If the length of the string is very small you could imagine a huge force in the string as the thing goes around at high speed. If the string is very long the speed is nothing and there would be very little force.

 

[Pigeon_Droppings2]

If this happens is an exam or assignment it's usually acceptable to write the answer in terms of "r" and arctan and just leave it at that.

I've had situations in exams where there were mistakes in the question..if you write down your assumption and continue you'll usually still get the marks (assuming you are right of course).

 

[m_c]

Thanks guys. I initially covered that example last week, and thinking I had missed something, I spent a couple nights working through some of the suggested additional/external material, as there were a few areas of the material I was struggling with anyway.
However having revisited that example with a better understanding, it still had the magically appearing radius.

It could be that the question has been taken out of context. If you assume the pendulum revolves once a second then the circumference would be 2m and the radius (2/PI) * 0.5 = 0.32 or 0.3 to 1DP

It's a pretty much standalone example question, with the only details being those in the screenshot I posted.
It's not the first error in the course I've came across, but the rest have been more benign, and easily noticed.

 

[Munkul]

It could be that the question has been taken out of context. If you assume the pendulum revolves once a second then the circumference would be 2m and the radius (2/PI) * 0.5 = 0.32 or 0.3 to 1DP

big assumption though... depends if the examiner is expecting to see a worked assumption like that, or to see the answer in terms of r or arctan like pidgeon droppings said

 

[Robert Weaver]

The displacement, r, seems to be missing from the initial data.

 

[Rannsachair]

There is something almost reassuring that the stuff I studied 40 odd years ago is till being taught, can still recall compound pendulum calculations, I think the textbook was Timoshenko or Timoshenko and Young, probably still have it in my loft.

 

[Rrobson]

HNC maths and thermodynamics was enough for me. Theta this, sigma that…. I had the capacity for it but entirely lacked any real drive to do it. Of course I passed the course but it was enough to put me off hnd and beyond. I do still have nightmares about calculating the bending moment of a beam with a udl and a point load x meters away from a fixed point…

Good luck with your studies!

 

[Seadog]

It was no better at HND. I scraped through, but didn't really have any interest in the complex maths. I had a reasonable ability to cram and regurgitate. I learned the proofs for the Laws of Thermodynamics, and of course they came up in the exam. No idea if I remembered correctly, though.

 

[Pigeon_Droppings2]

It was no better at HND. I scraped through, but didn't really have any interest in the complex maths.

Twas no different at degree level either!...I did a pure and applied maths degree....thermodynamics was not my favourite either...luckily I've forgotten most of it .

Mechanical systems I found very interesting though...sadly I don't use much if any of my degree stuff in my day job

 

[Screwdriver]

You need either the radius of the circle that is being described or the length of the pendulum.

Looks like they forgot to tell you what "r" is or forgot they hadn't stated it and just stuck it into the solution.

Interestingly with pendulums, the mass is irrelevant to the periodicity and is only included because you're supposed to be working out the tension. I assume that's why they mistakenly omitted one of the required parameters.

 

[Agroshield]

Interestingly with pendulums, the mass is irrelevant to the periodicity

True, but it is somewhat tricky to make a massless string fly around in a circle.

 

[addjunkie]

Twas no different at degree level either!...I did a pure and applied maths degree....thermodynamics was not my favourite either...luckily I've forgotten most of it .

Mechanical systems I found very interesting though...sadly I don't use much if any of my degree stuff in my day job

Many of us who have studied use almost none of what was in the course to do the day job we trained for!

 

[Screwdriver]

True, but it is somewhat tricky to make a massless string fly around in a circle.

In a vacuum...

 

[Munkul]

In a vacuum...

it won't have any centripetal force if it's massless though. So it won't have a circular path.

 

[Pigeon_Droppings2]

it won't have any centripetal force if it's massless though. So it won't have a circular path.

I reckon we need an expert in string theory ....any physicists on here

 

[Screwdriver]

it won't have any centripetal force if it's massless though. So it won't have a circular path.

I am agreeing with @Agroshield because he correctly identifies the implicit terms which allow the student to compute an answer to a theoretical scenario. The point he highlights is the length of the "string" in a pendulum is irrelevant to the calculation if and only if it does not change the mass of the system as it's length varies.

<edit> ...and another implicit term is that the experiment takes place in a vacuum for the same reason, length of string vs. aerodynamic drag.