Very interesting incline problem

[jakeyboy]

Homework Statement

Find the acceleration of the system. Friction constant of incline is 0.2

Homework Equations

Force of friction = 0.2 * 7 * 9.8 * cos30 = 11.88N
Force of gravity pulling down 7kg weight = 7 * 9.8 * sin30 = 34.3N
Force of gravity pulling down 4kg weight = 4 * 9.8 = 39.2

The Attempt at a Solution

Since F_g4 > F_g7 then the system should accelerate towards the right.

Net Force = F_g4 - F_g7 - F_friction = m₄₊₇a

39.2 - 34.3 - 11.88 = (4+7)a
a = -0.63

It doesn't make sense that a is negative, because that would mean the system would be accelerating towards the left, and friction would change directions.

 

[ehild]

Try to get the acceleration with the assumption that the system moves to the left. You might get a negative value again. It has sense as you assumed that the system moves when equating F_friction =μN, that is, you used kinetic friction. Assuming that the system was in motion at the beginning, negative acceleration means that it decelerates and will stop. After it stopped, the friction is static. See if the system can be in rest assuming static friction.

ehild