Trebuchet Energy Conservation Problem Solution Explanation

[RCB]

Homework Statement

http://bit.ly/eLdDK6

Look at this diagram.
Given the following information, can someone help me answer the question
Mass of counter weight = 760 kg
Mass of projectile in arm of trebuchet = 55 kg
distance of counter weight from ground = 5 m
distance projectile rises = 20 m

As the counterweight falls it loses about 37000 J
As the arm rotates to maximum height it gains about 11000 J

What is the total KE of the projectile and the counterweight when the arm is at its maximum height.

Homework Equations

GPE = mgh
KE = 0.5*m*v²

The Attempt at a Solution

I would have said: KE of projectile = 0, KE of counter-weight = 37000 so total KE = 37000 But this was wrong.
How do i do it?
How does it work?
thanks

 

[Ruddie]

This is in fact, part of an assignment I am doing this now, and I am also not sure about this.
I think you forgot about the fact that the arm of the counterweight is not the same as the arm of the projectile.

Think about moment ( M1 = M2 // F1*r1 = F2*r2 ).
http://en.wikipedia.org/wiki/Moment_(physics)"

I found on a couple of websites that Nm = J, however I am not certain.

This would give you:
Egrav = 37000 J

If I assume the arms are in a 1:3 ratio (since I don't know what you are using):

Ekin = 37000/3 = 12333 J

However, I found this on wikipedia:
"It is dimensionally correct to say that 1 joule equals 1 Newton metre (1 J = 1 N·m = 1 kg·m2·s−2); however, these units are not interchangeable in practice"

 

[RCB]

ratio is 4:1 (projectile arm: counterweight arm)
If I presume you are talking about the Physics Revision Guide!

 

[jsmith613]

ye ratio is 4:1 -

 

[Ruddie]

Okay, well since I am not certain if you are allowed to calculate it like this - I can not answer your question with certainty.

If however, my previous assumptions were correct the energy received would be:
Ekin = 37000/4 = 9250J

 

[jsmith613]

It might help if I tell you the actual answer::

about 26000
they got this by subtracting 37000-11000

BUT i don't know why this works?

Here is the exact wording of the question

A medieval siege engine called a trebuchet uses a pivoted lever arm to fire a projectile. The figure (on the link - not exactly the same but will suffice)shows a trebuchet ready to fire. The GPE of the large stone couterweight is converted to Egrav and Ek of the small projectile and Ek of the counterweight.

The loss of Egrav of the counterweight is about 37000 J (I said this was Ek before)
Find the Ek of the projectile and counterweight (show that is is about 26000 J)

 

[Ruddie]

Oh wait, I see what the issue is here..

They simply said:
The energy that the counterweight gives to the projectile is 37000 J, however..
It actually has 11000 J left when the arm is at it's highest point, this means that it 'lost' 37000 - 11000 = 26000 J

Which is the energy given to the projectile (however, I believe they ignored the fact of the arms really.. Since the energy of the counterweight lost is not the same as the energy the projectile gains - and I am pretty certain of that)

 

[jsmith613]

I still don't get why?

 

[Ruddie]

Well, if the counterweight had 37000 Joule of potential energy in the beginning, and then had 11000 J in the end.. how many energy did it lose?

37000-11000 = 26000 J

I presume that's obvious?
Now, this energy was given to something else, in this case - the object on the other side of the beam. This makes it get 26000 J (although this is only correct if the arms had a 1:1 ratio.. which they don't.. so I presume they just ignored that).

What part of that do you not understand?

 

[jsmith613]

I don't understand why the counterweight had 11000 J of energy at the end?

 

[jsmith613]

It says it loses 37000 J?

 

[Ruddie]

Okay, well this is strange indeed, I simply assumed the 37000 J was the answer from E = mgh, which it nearly is..

Sorry - but I believe the variables given are incorrect, or the answer is incorrect.

 

[jsmith613]

yes 37000 is correct for mgh as an approx to nearest thousand
and the question comes from a real exam paper but is just in text-book revision format
so the answer is correct I just can't see why!

 

[jsmith613]

http://s359.photobucket.com/albums/oo40/jsmith613/?action=view&current=Qeu.jpg

In case anything is ambiguous I have attached a photocopy of the question

 

[Ruddie]

Ah I see,
but this explains it all.. The OP formulated the answer incorrectly.

The question is:
a) Show that the Egrav is loses is about 37000 J

This is simply done by filling in Egrav = mgh..

b) Show that the total Ek of the projectile and the counterweight is about 26000 J

Ek_counterweight = Egrav_counterweight - energy lost

I am not sure where it states that you lost 11000 J in the question though?

 

[jsmith613]

so we're saying:
Ek_counterweight = 37000 - energy lost
but what is energy lost?