What is the Total Energy of a System with Given Values of Mass and Length?

[Clever_name]

(1/2)kl1^(2)+(1/2)mv1^(2) = (1/2)kl2^(2)+(1/2)mv2^(2)

where l1 = 0.5,

and

m*v1*l1*sin(60)=m*v2*l2

 

[voko]

Looking good.

 

[Clever_name]

I'm having trouble solving the two equations however,

i get v2=(4.33/l2) then subbing this into the energy equation i get,

42.5= 50l2^(2) + (11.24934/l2^(2))

i do not know how to go about solving that equation.

 

[voko]

Multiply by l2 squared throughout.

 

[Clever_name]

i get 42.5l2^(2)-50l2^(4) still can't see how to solve this.

 

[voko]

I think you have lost one term. Regardless, this is a called a bi-quadratic equation and I am pretty sure you studied it at some stage.

 

[Clever_name]

my bad yes, 42.5l2^(2)-50l2^(4)-11.2493.
I have not studied bi-quadratic equations before though, i'll have a browse around the internet for information

 

[Clever_name]

ok so i have 42.5l2^(2)-50l2^(4)-11.2493.
let l2^(2) =t

so -50t^(2)+42.5t-11.24934 this is a quadratic with roots of -0.212 or 1.062
so i disregard the negative value here because the root of a negative does not exist

so l2 must equal +- 1.03 m

 

[voko]

I do not think this is correct. The equation for t should have two positive roots.

 

[Clever_name]

ok now i think I've made a mistake somewhere because my b^(2)-4ac term is negative

-50t^(2)+42.5t-11.24934=0

when evaluating (1/2)mv1^(2) am i just using the 10m/s given, i think this is my mistake.

 

[Clever_name]

actually no, disregard that statement..

 

[voko]

The equation you got in #33 seems incorrect. Double check everything.

 

[Clever_name]

so i get l2 = +-0.828 or +-0.405, not sure what to do here with these figures however.

 

[voko]

Can the values of l be negative?

 

[Clever_name]

ah!, so l(min) =0.405 and l(max)=0.828?

 

[voko]

This seems correct.

 

[Clever_name]

thank you voko, for the guidance.