- #1
tesla93
- 23
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I have an assignment where I have to build a catapult that is able to launch a bean bag any distance between 8-12 metres. My teacher will give me a random distance on the day it's due, and I have to be able to adjust the catapult in order for it to launch that distance. I'm having a bit of a problem with the calculations. How would I go about solving for the displacement of the spring needed to launch a certain distance?
Relevant Equations:
F=ma
W = Fcosθ(d)
Ek = 1/2mv^2
Eg = mgh
Fx = kx
Ee = 1/2kx^2
d = v1t + 1/2at^2
v2^2 = v1^2 +2ad
Attempting the Calculations:
mass of beanbag = 0.048kg
distance needed to travel = let's say 10m
Fx = 10N (using a spring force gauge)
x = 0.25m
launch angle = 50 degrees
Fx = kx
10 = k(0.25)
k = 40N/m
Ee = 1/2kx^2
= 1/2(40)(.25)^2
= 1.25
In the beginning it has elastic and gravitational potential energy so
Ee = Eg
1.25 = 0.048(9.8)h
h = 2.657m is this the max. height of the bean bag?
I'm thinking I need to solve for acceleration and velocity so that I can use
v2^2 = v1^2 = 2ad and that would be my distance, then I can work backwards using different distances and solve for Fx and x, but then I think I also need to use the launch angle in the calculations, and I don't know where to do that.
Thanks for looking at my post.
Relevant Equations:
F=ma
W = Fcosθ(d)
Ek = 1/2mv^2
Eg = mgh
Fx = kx
Ee = 1/2kx^2
d = v1t + 1/2at^2
v2^2 = v1^2 +2ad
Attempting the Calculations:
mass of beanbag = 0.048kg
distance needed to travel = let's say 10m
Fx = 10N (using a spring force gauge)
x = 0.25m
launch angle = 50 degrees
Fx = kx
10 = k(0.25)
k = 40N/m
Ee = 1/2kx^2
= 1/2(40)(.25)^2
= 1.25
In the beginning it has elastic and gravitational potential energy so
Ee = Eg
1.25 = 0.048(9.8)h
h = 2.657m is this the max. height of the bean bag?
I'm thinking I need to solve for acceleration and velocity so that I can use
v2^2 = v1^2 = 2ad and that would be my distance, then I can work backwards using different distances and solve for Fx and x, but then I think I also need to use the launch angle in the calculations, and I don't know where to do that.
Thanks for looking at my post.