Suppose you have a spring-loaded projectile launcher. Aim it straight upwards, c

Question

Suppose you have a spring-loaded projectile launcher. Aim it straight upwards, compress the spring 1 cm, then launch a projectile from rest. You find that it rises 20 cm above the end of the spring. If you repeat this experiment, but instead compress the spring by 2 cm, should you expect the projectile to rise more than, less than, or exactly 40 cm above the end of the spring? Explain, assuming the total mechanical energy of the spring + projectile system is conserved.

Explanation / Answer

let "m" be the mass of projectile,"k" be the spring constant projectile rises 20 cm above the end of the spring: by conservation of mechanical energy energy of compressed spring = potential energy of projectile at max height => 1/2*k*x^2 = m*g*h => 1/2*k*0.01*0.01 = m*g*0.2 => k= m*g *0.4*10^4 if spring compressed by 2 cm: energy of compressed spring = potential energy of projectile at max height => 1/2*k*0.02*0.02= m*g*h => h = 1/2*k*0.02*0.02/ m*g but k= m*g *0.4*10^4 => h= 1/2*m*g *0.4*10^4*0.02*0.02/ m*g = 0.8 = 80 cms so projectile rises to 80 cms

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.