What is the speed of the dart as it leaves the toy?

[jbjohnybaker]

Homework Statement

2. A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?

Homework Equations

Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2

The Attempt at a Solution

Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??

 

[Filip Larsen]

In the equation for spring energy, x represents the distance the spring is compressed.

 

[RU2490]

Homework Statement

2. A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?

Homework Equations

Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2

The Attempt at a Solution

Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??

You got the formulas correctly
E= kinetic + potential
Einitial = E final
1/2 kx^2 + 1/2 mv^2 = 1/2 mv^2 + 1/2 kx^2

1/2 * 3.5 x 10^2 * .04m + 0 = 1/2 *.0078 kg v^2 +0

now just solve for V.
I think you just missed the information that tells you the compression (x)