What's the maximum speed?

Question

A compressed spring has 16 J of potential energy. What's the maximum speed it can impart to a 2 kg object?

 

Answer: 4.0 m/s

Answer 1

Use energy conservation. When the object reaches its maximum speed, all the potential energy is converted to kinetic energy. So,

(1/2)mv^2 = 16

Plug in m = 2 kg, and solve for v,

v = 4.0 m/s <==Answer

Answer 2

Hi Sun;

A joule is kg-m²/s².

As Robert explained, the equation is...

kinetic energy=(1/2)mv²

16 kg-m²/s²=(1/2)(2 kg)(x m/s)²

The result we want is m/s.

The unit of kg is in the numerator of both sides of the equation.  These cancel...

16 kg-m²/s²=(1/2)(2 kg)(x m/s)²

16 m²/s²=(1/2)(2)(x m/s)²

16 m²/s²=(x m/s)²

Let's take the square-root of both sides...

4 m/s=x m/s