Force and Acceleration

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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.

unknown.jpg


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

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

Homework Equations



T - [tex]\mu_{k}w_{B}[/tex] = [tex]\frac{-w_{B}}{g}a_{B}[/tex]

2T - [tex]w_{A} = (\frac{-w_{A}}{g}) (-a_{A})[/tex]

[tex]2a_{A} + a_{B} = 0[/tex]

The Attempt at a Solution



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

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

then i solve for T

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

T= 12N

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

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

any help would b nice
cheers,
 
Last edited:

Answers and Replies

  • #2
LowlyPion
Homework Helper
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5
ft/sec

lbs

m/s

m/s2

Unit potpourri is never a good recipe.
 
  • #3
29
0
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 [tex]m/s^{2}[/tex] from previous physics courses....
 

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