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What's the maximum speed?

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

2 Answers by Expert Tutors

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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