(-1.28s+149.7)(-1.28s+149.7)

+5.7(-1.28s+149.7)+13.85

Therefore

sling length

distance

d=distance

v=velocity

g=gravity

=release angle

Distance Equation

Alrighty,

Lets build a trebuchet!

But how?

How will we make it hit our target?

Change Counterweight ?

move the entire trebuchet?

adjust finger angle?

Adjust sling length?

But sling length only changes release angle? How will that change distance?

counterweight

+ arm

+ rotational power

+ ball

+ Friction

potential energy arm

Potential Energy Counterweight

Friction

potential energy Ball

potential energy Arm

kinetic energy Arm

kinetic energy ball

Before launch

After launch

Potential Energy

Kinetic Energy

= too many variables

Finding Potential energy

mass x height x gravity

1. FRAME/base

(32.174 ft/s )

finding kinetic energy

1/2 x mass x (velocity)

2

2

(8.19 kg)(32.174 ft/s)(2.75 ft)+(40.82 kg)(32.174 Ft/s)(2.39 ft)+ W(F) =

(m3)(32.174 ft/s)(10.52 ft)+(8.19 KG)(32.174 ft/s)(7.25 ft)+(1/2)(8.19 kg)(v2^2)+(1/2)(m3)(v3^2)

724.64 + 3091.21 +W(f) = 338.5 (m3) + 1910.4 + 4.1 (v2)^2 + .5 (m3) (v3)^2

1905.45 + W(F) = 338.5 (m3) +4.1(v2)^2 +.5(m3)(vs)^2

1905.45 + W(F) = 338.5 (m3) +4.1(v2)^2 +.5(m3)(vs)^2

plug in mass of a baseball (0.142 kg) into M3

1905.45 + w(f) = (338.5)(0.142) + (4.1)(v2)^2 +.5(0.12)(v3)^2

1905.45 + w(f) = 48.067 +4.1(v2)^2 + .06(v3)^2

1905.45 + w(f) = 48.067 +4.1(v2

2. Axle

1857.38 + w(f) = 4.1(v2)^2 + .06(v3)^2

1857.38 + w(f) = 4.1(

v2

) + .06(

v3

)

but

v2

and

v3

can be solved for with the same variable

3. Crossbar

4. arm

velocity= (constant(

x

))(radius)

5. Counterweight

v2

= (

x

)(2.5)

v3

= (

x

)(8)

6. Sling and trough

plug in these values

2

2

Thanks mr. Chaffee!

1857.38 + w(f) = 4.1(2.5

x

) + .06(8

x

)

but since this is a theoretical value we pretend friction doesn't exist

2

2

1857.38 = 29.465(

x

)

2

Brad

63=

x

2

x

=7.9

so velocity of baseball =

8

x

= 8 (7.9) = 63.5 ft/s

2

now we take this value for the velocity

63.5 ft/s

and plug it into the distance equation

2

d=-0.067a +5.7a+13.85

R =0.998

2

2

sling length to release angle

Angle of release

movement of trebuchet

different release

tilt of arm

faulty setup

a=-1.28s+149.7

r =0.826

2

some more boring math

So now that we've proven that

And also That

We Can Finally correlate

Or, In Mathematical Terms

Because

d

=-0.067a +5.7a+13.85

2

And

a =

-1.28s+149.7

Then we can say,

d

=-0.067(

-1.28s+149.7

) +5.7(

-1.28s+149.7

)+13.85

2

But that's pretty complex

simplification powers activate!

d=-0.067(-1.28s+149.7) +5.7(-1.28s+149.7)+13.85

2

d=-0.067

(1.6384S-383.232+22,410.09)

+5.7(-1.28s+149.7)+13.85

d=

-0.1097728s +25.676544s-1501.47603

+5.7(-1.285+149.7)+13.85

2

d=-0.1097728s -118.380544S-634.33603

2

2

d=-0.1097728s +25.676544s-1501.47603

-7.296s+853.29

+13.85

Ahh... That's better

2

WE have to account for

friction

(theoretical-experimental) ÷ theoretical

=

% Distance lost to friction

This works out to be about

0.13

, or

13%

distance lost to friction.

For accurate distances, we should multiply our equation by

0.87

to account for this.

d=-0.1097728s -118.380544S-634.33603

• 0.87

d=-0.0955023s -102.9910737S-551.872346

this is our final equation

**HISTORY**

y =release height

0

2

2

**GOAL**

**MATH**

**Correlations**

So to sum it all up...

Because we can relate

sling length

to

distance,

we can accurately hit a target of any distance just by

changing the length of the sling.

A BUNCH OF BORING MATH

**More**

remember this is theoretical Data