(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 10kg mass, attached by means of two springs to the ceiling, is held against the floor and is then released. How fast will it be traveling when it hits the ceiling? The spring constant of each spring is 80 N/m, and each spring has an unstretched length of 1 m. Assume that springs become loose and floppy once they're at their rest length.

distance between ceiling and floor: h_o=4m

horizontal distance from mass to each spring: 2m

Springs are at an angle from mass.

2. Relevant equations

PE(sp)=1/2kx^2

PE(g)=mgh

KE=1/2mv^2

3. The attempt at a solution

I used pythagorean theorem to find stretched length of spring:

s=sqrt(4^2+2^2)=sqrt(20)

I found theta to find h after the mass is released:

tan(theta)=4/2

theta=63.43494

I found h using trig:

h=unstretched length of string*sin(theta)=.8944

The answer is v=9.92m/s

I used this equation to solve for v with my datum at the floor:

PE(sp)=KE+PE(g)

1/2ks^2=1/2mv^2+mgh

1/2(80)(sqrt(20))^2=1/2(10)v^2+(10)(9.81)(.89)

v=11.93m/s

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# Homework Help: Spring Potential Energy involving two springs

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