Solve Trebuchet Efficiency Mystery

In summary, the conversation discusses the calculation of energy efficiency for a trebuchet, with the given values for height, mass, gravity, time, and distance. The theoretical and actual yields are calculated, with the actual yield being 430% of the theoretical yield. An alternative method for finding trebuchet efficiency is also mentioned.
  • #1
thua
9
0

Homework Statement


I've calculated the time, the distance, the height of the counterweight before launch, the mass/weight, and I need to calculate the energy efficiency.
How to go about it?

h = 0.71 m
m = 1.445 kg
g = 9.8 m/s^2
t = 0.7 s
x = 4.44 m

Homework Equations



Eg = mgh
Vix = x/t
y = Viy(t) + (1/2) a(t)^2
Ek = (mv^2)/2

The Attempt at a Solution



THEORETICAL YIELD:
h = 0.71 m
m = 1.445 kg
g = 9.8 m/s^2
Eg = mgh
= (1.445 kg)(9.8 m/s2)(0.71 m)
= 10.05 J

ACTUAL YIELD:
t = 0.7 s
x = 4.44 m
Vix = x/t
= (4.44 m)/(0.7 s)
= 6.34 m/s

y = Viy(t) + (1/2) a(t)^2
0.71 m = Viy(0.7 s) + (1/2) (-9.8 m/s2)(0.7 s)^2
Viy = 4.44 m/s

Vi^2 = (Vx)^2 + (Viy)^2
Vi^ = (6.34 m/s)^2 + (4.44 m/s)^2
Vi= 7.74 m/s

Ek = (1/2) mv^2
= (1/2) (1.445 kg)(7.74 m/s)^2
= 43.28 J

43.28 J / 10.05 J = 430%

I don't think my trebuchet is 430% efficient.
What did I do wrong?
 
Last edited:
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  • #2
Efficiency is work in/work out
 
  • #3
An easier way to find trebuchet efficiency (all credit goes to Rom Toms http://www.trebuchet.com/):
Actual measured range in meters /theoretical range= efficiency

theoretical range in meters= 2 * (counterweight in kg * counterweight drop in meters)/ weight of projectile in kg
 
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FAQ: Solve Trebuchet Efficiency Mystery

1. What is a trebuchet?

A trebuchet is a type of medieval siege weapon that uses a counterweight to launch projectiles over long distances.

2. What is the efficiency of a trebuchet?

The efficiency of a trebuchet is a measure of how effectively it converts the potential energy of the counterweight into the kinetic energy of the projectile. It is typically expressed as a percentage and can vary depending on the design and construction of the trebuchet.

3. Why is the efficiency of a trebuchet important?

The efficiency of a trebuchet is important because it affects the distance and accuracy of the projectile. A more efficient trebuchet will be able to launch projectiles farther and with greater precision, making it a more effective weapon.

4. How can the efficiency of a trebuchet be improved?

The efficiency of a trebuchet can be improved by making adjustments to its design and construction, such as changing the length of the throwing arm, the weight of the counterweight, or the angle of the release mechanism. Experimentation and testing are necessary to determine the most efficient configuration.

5. What is the "Trebuchet Efficiency Mystery" and how can it be solved?

The "Trebuchet Efficiency Mystery" refers to the challenge of finding the optimal design for a trebuchet in order to achieve maximum efficiency. It can be solved through the scientific method, by conducting experiments and analyzing data to determine the most efficient trebuchet design and identifying any factors that may affect its efficiency.

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