Overview

Here's a set of physics problems to challenge your knowledge of the concepts of energy and motion. Very few have come up with correct answer to all these problems (question 2 in particular) and I've asked some very smart Maths and Physics phDs! The maths isn't that hard but you have to be very careful about what equations you use and what assumptions you make

Bonus questions are included that any good A-Level physicist should be able to answer but are not part of the main theme to these questions and are arguably not as hard. Usual assumptions can be made in these questions. Partial marks are given for estimates to answers!

 

Updates

• Assume g = 10 and is constant
• This is NOT a trick question!!! It is all pure and simple physics
• Assume Earth is flat

 

The questions

1)

Alice, who weighs 100kg, steadly climbs a ladder at a constant velocity to a height of 10 meters and reaches the top after 100 seconds.

Question: What is the minimum energy needed for Alice to do this?

Bonus: What is the person's power output?

2)

Bob, who also weighs 100kg, straps a rocket pack to his back and follows Alice as she climbs the ladder. That is, Bob also climbs through the air at constant velocity to 10 meters and reachers the top after 100 second.

For this problem, you can assume the mass of the jet fuel consumed is relatively small compared to the mass of Bob. However, if you feel it helps your calculations, you can assume that this is a pie powered jet pack. In 1) Alice eats a 1kg pie before starting uses up all that pie power to climb the lader. Similarly in 2) Bob puts the 1kg pie into his jet pack and uses it all up to get to the top

Question: What is the minimum energy needed for Bob to do this?

Question: Does the energy used in both cases depend on the time taken in getting to the top? If not, why not? If so, by how much?

3) (Bonus problem)

Cain, who also weighs 100kg, puts himself into a human cannon and fires himself up into the air, just reaching the 10 meter height Question: What is the minimum energy needed from the cannon to do this? Bonus: How fast was Cain initially travelling as he left the cannon?

Assumptions:

• All energy conversion is perfectly efficient in terms of useful energy
• Everyone is infinitely short
• Bob's jet fuel is as light as you like and produces no heat
• There is no air friction
• ... other usual assumptions?

For answers, email kevin at glorat dot net!

In developing my extensions, I kept getting the following error:

Got an error: mutiple trigger registration in one add_trigger() call is deprecated. at lib/MT/Entry.pm line 282
Compilation failed in require at lib/MT/Compat/v3.pm line 12.
BEGIN failed--compilation aborted at lib/MT/Compat/v3.pm line 12.
Compilation failed in require at lib/MT.pm line 1210.

The code in MT/Entry.pm is incompatible with Class::Trigger 0.12, which comes with recent versions of perl. If you have set up your paths incorrectly (like $ENV{'MT_HOME'}) or you have plugins that require a version later than the Class::Trigger 0.10 that comes with Movable Type, you will encounter this problem. In my case, I'm linking in external libraries that use the later version.

To fix this, I'm using this patch:

--- lib/MT/Entry.pm     (revision 3196)
+++ lib/MT/Entry.pm     (working copy)
@@ -279,8 +279,12 @@
     );
 }

+# Must use separate statements from Class::Trigger 0.12
 MT::Placement->add_trigger(
     post_save   => \&flush_category_cache,
+);
+
+MT::Placement->add_trigger(
     post_remove => \&flush_category_cache
 );

Issue raised with Six Apart!
http://bugs.movabletype.org/default.asp?85080_etup

I discovered today that my trial has a chance of going beyond the end date of 19th December. This is particularly problematic since I fly out to Hong Kong on the 17th December, as I did tell His Lordship before the trial started.

And I don't call him His Lordship to be pompous, that's really how to address judges. The standard address to a circuit judge in your typical UK criminal court would be "Your Honour" but in the Old Bailey they are one step up and we say "My Lord".

So I have to write a nice little letter to the judge now to plead with him not to cancel my holiday plans! Yes, he does have the power to do that...

References:
It will depend on which How to address a Judge?
Forms of address for the Judiciary

Those who know me personally may be aware that I'm currently on jury service serving at the Central Criminal Court, also known as the "Old Bailey". Being on jury service means you can't talk about your trial at all. Maybe when the trial is over I'll blog about it some day.

I can probably blog about something completely unrelated though. I saw a bunch of kids pass by the court the other day. Lo and behold, it turns out that The Times were reporting on their visit! I won't talk about my experiences but it is interesting to hear about others

http://women.timesonline.co.uk/tol/life_and_style/women/families/article5149502.ece

I don't host my own email, it's not something I want to have to manage given the complexities of hosting your own and the many free email providers out there such as Google's gmail. Nevertheless, webapps still need to be able to send mail and most will either use sendmail or SMTP. Unfortunately, setting up your own SMTP server for sending email is also not straightforward because if you cannot receive email, your server may be regarded as a spam provider by the outside world.

My solution is to set up an SMTP server that routes all outgoing email to Gmail using Exim4's Smarthost facility.

Welcome to my new blog powered by Movable Type. This is the first post on my blog and was created for me automatically when I finished the installation process. But that is ok, because I will soon be creating posts of my own!