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## Homework Statement

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In the diagram given, the pulley is frictionless and the force of friction between the .5kg mass and the table is 4.8 N. The force equation for the spring is F = 50x. If the system starts at rest with the spring at its normal length, calculate the maximum speed the 1kg mass will reach.

P.S. I have the answer, I just don't know how to get there.

## Homework Equations

Okay, so here are the equations I have during this unit:

Force of the Spring= kx (k is 50 in this question)

Kinetic Energy = 1/2 mv^2

Potential Energy = mgh

Potential Energy of the spring = 1/2kx^2

Total Energy = sum of all energy

Then from a previous unit, this equation might be needed:

Fnet = Fgravity -T where T is the tension in the string

## The Attempt at a Solution

At Start:

KE = 1/2 mv^2

KE = 0.5kg (0m/s)^

KE = 0Joules

PE(spring) = 1/2 kx^2

PE(spring) = 1/2 (50) 0m^2

PE(spring) = 0 Joules

PE = mgh

PE = 1kg(9.8 N/kg)(0m)

PE = 0

TE= 0Joules

Fnet = Fg + T

1kg(a(1kg object)) = 9.8N/kg (1kg) -T T

A(1kg object) = (9.8N -T)/1kg

Fnet = Fg + T

0.5kg (a(0.5 kg object)) = 0N/kg (0.5kg) -T

a(0.5kg object) = -T/ 0.5kg

I don't know what to do from here, or what I did wrong. I missed a couple of days at school, so I'll admit that I'm a little bit lost.

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