Why does the war-wolf reach its maximum speed at the vertical position?

In summary: I can't follow your reasoning there. You accepted it accelerates until vertical and decelerates thereafter. So when is it rotating fastest? It's a simple enough deduction.
  • #1
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Homework Statement
Pls see below
Relevant Equations
Pls see below
For this problem,
1677041010452.png

For part(a) the solution is,
1677041041534.png

However, how did they know that the max speed is reached in the vertical position?

For part (d) the solution is,
1677041089694.png

However, I thought the solution would be because there is net gravitational torque in clockwise direction (torque due to small mass – torque due big mass) then angular momentum is not conserved.

I don’t understand why they talk only about the lever arm of the 60 kg mass, as there is also a lever arm for the smaller mass. I agree thought about their statement that the lever arm due to the masses on each end changes as the war-wolf rotates.

Many thanks!
 
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  • #2
Callumnc1 said:
then angular momentum is not conserved.
Whether the acceleration is a nonzero constant or varying, angular momentum is not constant. The question is whether the acceleration is constant, so considering angular momentum is not going to help.
 
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  • #3
Callumnc1 said:
I don’t understand why they talk only about the lever arm of the 60 kg mass, as there is also a lever arm for the smaller mass.
I don't see mention of a lever arm in the extracts you posted.
Yes, each weight has its lever arm.
 
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  • #4
Callumnc1 said:
how did they know that the max speed is reached in the vertical position?
Before it reaches vertical, is the system getting faster or slower?
What about after vertical?
 
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  • #5
haruspex said:
Whether the acceleration is a nonzero constant or varying, angular momentum is not constant. The question is whether the acceleration is constant, so considering angular momentum is not going to help.
haruspex said:
I don't see mention of a lever arm in the extracts you posted.
Yes, each weight has its lever arm.
Thank you for your replies @haruspex !
 
  • #6
haruspex said:
Before it reaches vertical, is the system getting faster or slower?
What about after vertical?
Thank you for your reply @haruspex !

The system is getting faster I think because the system as a whole is losing gravitational potential energy (big mass losing GPE at a faster rate than GPE gain by small mass - even though they have same tangential speed)

Many thanks!
 
  • #7
Callumnc1 said:
Thank you for your reply @haruspex !

The system is getting faster I think because the system as a whole is losing gravitational potential energy (big mass losing GPE at a faster rate than GPE gain by small mass - even though they have same tangential speed)

Many thanks!
And what about after passing the vertical position?
 
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  • #8
Callumnc1 said:
even though they have same tangential speed
Actually, no! Since ##v = \omega r## and ##\bf \omega## is the same for both...

##\ ##
 
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  • #9
Callumnc1 said:
... big mass losing GPE at a faster rate than GPE gain by small mass...
Could you explain that a little further?
Can you see a single imaginary mass that is equivalent to both masses and that is located at certain point between the pivot and the big ball?
 
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  • #10
haruspex said:
And what about after passing the vertical position?
Thank you for your reply @haruspex !

I think it slows down since the big mass starts gaining GPE

Many thanks!
 
  • #11
BvU said:
Actually, no! Since ##v = \omega r## and ##\bf \omega## is the same for both...

##\ ##
Thank you for your reply @BvU!

True, good you mentioned that!
 
  • #12
Lnewqban said:
Could you explain that a little further?
Can you see a single imaginary mass that is equivalent to both masses and that is located at certain point between the pivot and the big ball?
Thank you for your reply @Lnewqban !

Do you mean the COM as an imaginary mass equivalent to both masses?

Many thanks!
 
  • #13
Callumnc1 said:
Thank you for your reply @haruspex !

I think it slows down since the big mass starts gaining GPE

Many thanks!
Right again.
If it accelerates all the while before reaching vertical and decelerates thereafter, when is it rotating fastest?
 
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  • #14
haruspex said:
Right again.
If it accelerates all the while before reaching vertical and decelerates thereafter, when is it rotating fastest?
Thank you for your reply @haruspex!

As the war wolf passes the top there is a moment where there is only centripetal acceleration and no tangential acceleration since the war wolf is parallel to gravity. However, since it is still rotating it makes at angle ##d\theta## with the vertical so it has a tangential acceleration again that increases. I guess I could of just said that the top is at unstable equilibrium.

If I reason from mechanical energy conservation, then the system has the least amount of potential energy when the little mass it at the top and the big mass is from the bottom. Therefore, as there is no non-conservative forces acting then the system must have the largest rotational kinetic energy.

Many thanks!
 
  • #15
Callumnc1 said:
However, since it is still rotating it makes at angle dθ with the vertical so it has a tangential acceleration again that increases.
I can't follow your reasoning there. You accepted it accelerates until vertical and decelerates thereafter. So when is it rotating fastest? It's a simple enough deduction.
Callumnc1 said:
the system has the least amount of potential energy when the little mass it at the top and the big mass is from the bottom. Therefore, as there is no non-conservative forces acting then the system must have the largest rotational kinetic energy.
Yes, that's another way to get there.
 
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  • #16
Yes
Or just for understanding the principle on which the system works, you could disregard the little mass.
The little mass induces a CCW moment that is 24.5 times smaller than the CW moment that the big mass induces.

Then, you have a mass oscillating about a pivot after being released from a horizontal position.

Oscillating_pendulum.gif
 
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  • #17
Lnewqban said:
Yes
Or just for understanding the principle on which the system works, you could disregard the little mass.
The little mass induces a CCW moment that is 24.5 times smaller than the CW moment that the big mass induces.

Then, you have a mass oscillating about a pivot after being released from a horizontal position.

View attachment 322757
Thank you for your help @Lnewqban !
 
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  • #18
haruspex said:
I can't follow your reasoning there. You accepted it accelerates until vertical and decelerates thereafter. So when is it rotating fastest? It's a simple enough deduction.

Yes, that's another way to get there.
Thank you for your reply @haruspex!

What was the reasoning you were expecting me to give?

Sorry I think I was meant to say that before it reaches the vertical it is deaccelerating and after it reach's it is accelerating (tangentially).

Many thanks!
 
  • #19
Callumnc1 said:
Sorry I think I was meant to say that before it reaches the vertical it is deaccelerating and after it reach's it is accelerating (tangentially).
Eh? I already agreed with you it is the other way: accelerating until vertical, decelerating thereafter. I am asking what tells you about where it reaches maximum speed.
 
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  • #20
haruspex said:
Eh? I already agreed with you it is the other way: accelerating until vertical, decelerating thereafter. I am asking what tells you about where it reaches maximum speed.
Thank you for your reply @haruspex !

Yes sorry, I agree that it accelerates until vertical an deaccelerates thereafter. The reason it reaches max speed at the vertical is because it keeps accelerating until its reach's the vertical and deaccelerates afterwards. The acceleration = 0 at the vertical.

I think we could also integrate the acceleration graph to find that the velocity is max at the vertical.

Many thanks!
 

Related to Why does the war-wolf reach its maximum speed at the vertical position?

Why does the war-wolf reach its maximum speed at the vertical position?

The war-wolf, or trebuchet, reaches its maximum speed at the vertical position because this is where the gravitational potential energy has been most effectively converted into kinetic energy. The counterweight has fallen the furthest distance, imparting maximum force to the projectile.

What role does gravity play in the war-wolf's speed at the vertical position?

Gravity plays a critical role by pulling the counterweight downwards, which in turn accelerates the arm of the trebuchet. As the arm moves towards the vertical position, the gravitational force maximizes the transfer of energy, resulting in the highest speed.

How does the design of the war-wolf influence its speed at the vertical position?

The design of the war-wolf, particularly the length of the arm and the mass of the counterweight, is optimized to ensure that maximum energy transfer occurs just as the arm reaches the vertical position. This design ensures the projectile achieves its highest velocity at the point of release.

Is air resistance a factor in the war-wolf reaching its maximum speed at the vertical position?

While air resistance does affect the overall motion of the projectile, it is relatively negligible at the moment the arm reaches the vertical position. The primary factors are the gravitational force and the mechanical design of the trebuchet.

Can the war-wolf's maximum speed be increased further by altering its mechanics?

Yes, the maximum speed can be increased by optimizing the arm length, counterweight mass, and pivot point. Enhancements in materials and construction techniques can also reduce energy losses, thereby increasing the efficiency and speed at the vertical position.

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