Spring launcher equation for x so it hits the target

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SUMMARY

The discussion focuses on calculating the optimal pullback distance for a spring launcher to hit a target, considering factors such as air resistance and projectile motion. Key parameters include a spring mass of 0.024 kg, a spring constant (k) of 25 N/m, and a launch angle of 40 degrees. The conservation of energy equation, specifically 1/2mv² = 1/2kx², is central to the calculations, alongside projectile motion equations. The user seeks guidance on determining the initial velocity required for accurate targeting.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with projectile motion equations
  • Basic knowledge of spring mechanics
  • Ability to perform calculations involving angles and distances
NEXT STEPS
  • Study the relationship between initial velocity and launch angle in projectile motion
  • Learn how to calculate the effects of air resistance on projectile trajectories
  • Explore the use of kinematic equations for vertical motion
  • Investigate the impact of different spring constants on launch distance
USEFUL FOR

Students in physics, engineers designing projectile systems, and hobbyists interested in mechanics and spring-based launchers will benefit from this discussion.

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Homework Statement


I need to find out how far to pull the spring back so it will travel to the target. The launcher and the target is both set on the floor. The spring is the projectile. I will be given the distance on the day of testing. i should take into account air resistance so i will be more accurate.

Mass of spring = 0.024kg
k = 25N/m
launch angle set at 40 degrees
length of spring when not stretched is 0.20m
height of launcher is 0.54m
My trials pulling spring back and recording distance
.25m went .52m
.3m went 1.67m
.34m went 2.2m
.4m went 4.78m
.43m went 5.37m

Homework Equations


conservation of energy
Es = Ek
1/2mv^2 = 1/2kx^2
projectile motion
d = v1xt
v1x = v1cosӨ

The Attempt at a Solution


1/2mv^2 = 1/2kx^2
i get stuck on this part. plugging in numbers but i do not have the velocity. What i do next?
 
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Is the target at floor level?
You need an equation relating to vertical motion, relating initial speed, acceleration, time and height difference.
 
yes it's on the floor
 

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