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## Homework Statement

A box (m

_{2}) with mass 1.0 kg is on a frictionless plane inclined at angle θ = 30

^{o}. It is connected by a cord of negligible mass to a box (m

_{1}) with mass 3.0 kg on a horizontal frictionless surface. Box m

_{1}is pushed with force F. What is the maximum value of F allowed so that the cord does not slack?

## Homework Equations

F

_{net}= ma

## The Attempt at a Solution

I first tried to find the acceleration of the system without the influence of F

_{p}, which turned out to be 1.225 m/s

^{2}. Then I reasoned that if the boxes are moving at that speed, initiated by the m

_{2}from gravity, then that means that F + T (tension) has to equal m

_{1}a, with an "a" larger than 1.225 m/s

^{2}.

Thus, I worked with that equation, which lead to the following:

F + T = m

_{1}a

F = m

_{1}a - T

T = 3.1 N

F = (3.0 kg)(1.225 m/s

^{2}) - 3.1 N

F = 0.575 N

So does this mean that the maximum force allowed is 0.575 N?

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