Practical Investigation - Ballista Project - page 4
Keywords: Physics Practical Investigation Ballista Crossbow
By Jenny on 02/07/2009
Level: A Level (Year 13)
Page Number: 4 of 4 pages: 1 2 3 4
velocity
FAR = Air Resistance Force
g = gravity
H = height
R = range
x = extension of cord
We assume that there has been no energy loss. Therefore all the stored strain energy is converted into kinetic energy:
Es = Ek
We also assume that the cord obeys Hooke’s Law.
F = kx
x = F/k
The formula for elastic stored energy is:
Es = ½Fx
The equation for kinetic energy is:
Ek = ½mv2
The equation for velocity is:
v= r/t
Therefore:
½Fx = ½mv2
Cancelling off the ½s and substituting F/k for x:
F(F/k) = mv2
Multiplying out the brackets and substituting r/t for v:
F2/k = mR2/t2
Therefore:
F2 R2
And:
F R
Measurements
The height of the firing slot off the ground = 24.2 cm.
Force (N) Error in Force Average Range at 10N Tension Error at 10N Tension Average Range at 20N Tension Error at 20N Tension Average Range at 30N Tension Error at 30N Tension
10N 20N 30N
0 0.4 0.0 0.0 0.0 0.0 0.0 0.0
5 0.4 89.3 1.9 110.3 9.3 98.3 9.0
10 0.4 125.1 1.9 151.8 6.3 140.4 5.5
15 0.4 148.8 5.2 174.6 3.4 171.2 13.7
20 0.4 181.2 4.0 211.7 2.7 236.0 11.0
25 0.5 198.0 2.0 260.4 4.6 288.7 4.2
30 0.5 219.6 6.4 296.1 2.9 344.3 7.7
35 1.0 288.2 22.0 332.8 6.3 440.3 10.3
40 1.0 395.6 33.0 368.8 6.2 559.5 60.1
I worked out the errors in these values by using the largest differences between the average and any of the distance values as the Y error bars and the sensitivity of the newtonmeters that I measured the forces with as the X error bars.
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