Asked Nov 15, 2019
A spring has a force constant of 18.9 N/m and a rest length of 0.35 m.The spring is stretched to a length of 1.2 m and attached to a mass of 0.45 kg. When the spring is released, what is the speed of the mass when the spring has contracted to 0.70 m long?

Expert Answer

Step 1

The change in potential energy of the spring must be equal to the kinetic energy gained by the mass when it is released. This can be expressed as


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Here, k is the force constant of the spring, is the initial change in length of the spring from its rest length, x, is the final change in length of the spring from its rest length, m is the mass and v is the speed of the mass. The value of x is x =1.2 m 0.35 m 0.85 m The value of x, is x, = 0.70 m -0.35 m = 0.35 m

Step 2

Substitute the values in equ...


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18.9 N/m) (0.85 m-(0.35 m))=(0.45 kg)v 5.67 J 0.225v2 5.67 J 1= 0.225 = 5.02 m/s


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