How Does Pulley Friction Affect Block Acceleration?

[unknown_2]

Homework Statement

At a given instant block A of weight 10-lb is moving downward with speed 6 ft/s. Determine its speed at a later time t = 2s. Block B has a weight 4lb and the coefficient of kinetic friction between it and the horizontal plane is μ = 0.2. Neglect the mass of the pulleys and cord.

T = 3.385 a_{A} = 10.403 ft/s^{2} a_{B} = - 20.806 ft/s^{2}

not sure if these are correct seeing i get different answers.

Homework Equations

T - \mu_{k}w_{B} = \frac{-w_{B}}{g}a_{B}

2T - w_{A} = (\frac{-w_{A}}{g}) (-a_{A})

2a_{A} + a_{B} = 0

The Attempt at a Solution

since 2a_{A} + a_{B} = 0 i'd solve for a_{A} and a_{B} in the first 2 equations and sub into the third one

2(\frac{2Tg}{w_{A}} - g) + (\frac{-Tg}{w_{B}} + \mu_{k}g) = 0

then i solve for T

\frac{2g - \mu_{k}g}{g(\frac{4}{w_{A}} - \frac{1}{w_{B}})} = T

T= 12N

then sub back into one of the first 2 equations to solve for either a_{A} or a_{B}.

a_{B} = -90.16ft/s^{2}
a_{A} = 45.08ft/s^{2}

any help would b nice
cheers,

 

[LowlyPion]

ft/sec

lbs

m/s

m/s²

Unit potpourri is never a good recipe.

 

[unknown_2]

ft/sec

lbs

m/s

m/s²

Unit potpourri is never a good recipe.

it was late...i changed the units, i was just used to m/s^{2} from previous physics courses...