Question

MEDAL GIVEN TO CORRECT ANSWER.
A mass of 1.5 kg is attached to a spring and placed on a horizontal surface. The spring has a spring constant of 120 N/m, and the spring is compressed 0.25 m past its natural length. If the mass is released from this compressed position, what is the speed of the mass as it passes the natural length of the spring?

A. 3.4 m/s
B. 1.5 m/s
C. 0.99 m/s
D. 2.2 m/s

Answer 1

The mass has maximum velocity when it passes through the origin. The energy stored by a spring is equal to

\[\frac{ 1 }{ 2 }KA ^{2}\] Where K is the spring constant and A is the amplitude.
All that energy stored in the spring is released when let go, all is converted to kinetic energy when it passes through the origin. (mass is fastest when passing through the origin).

Using this fact, we can say the kinetic energy is equal to the maximum energy stored in the spring, given by the equation at the top (1/2kA^2)

\[\frac{ 1 }{ 2 }mv ^{2}=\frac{ 1 }{ 2 }KA ^{2}\]

Reagrange for v, velocity:

\[v=\sqrt{\frac{ KA ^{2} }{ m}}\]

You find v is equal to root 5, 2.2 m/s

Hope this helps!

Answer 2

Yes it should be