physics help please....i need the answer?

Question

A 1.1 kg mass is attached to a spring with a force constant of 56 N/m. If the mass is released with a speed of 0.27 m/s at a distance of 9.7 cm from the equilibrium position of the spring, what is its speed when it is halfway to the equilibrium position?

Answer 1

The way you asked the question, do you mean yo want the speed when the mass has traveled halfway from 9.7 cm to the equilibrium, or 4.85 cm?

This can be solved using conservation of energy:
The energy stored in the spring is
.5*56*(9.7/100)^2
The kinetic energy at release is
.5*1.1*0.27^2

after the mass traveles half the distance, the difference in stored energy in the spring gets converted to kinetic energy of the mass.

.5*56*((9.7/100)^2-
(9.7/200)^2)

add the starting kinetic energy

and set equal to the final kinetic energy

.5*1.1*v^2=0.1976+0.04
v=sqrt(2*0.2376/1.1)
v=0.657 m/s

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