- #1
KillerZ
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Homework Statement
At a given instant the 10-lb block A is moving downward with a speed of 6 ft/s. determine its speed 2s later. Block B has a weight of 4-lb, and the coefficient of kinetic friction between it and the horizontal plane is [tex]\o_{k} = 0.2[/tex]. Neglect the mass of the pulleys and cord.
Homework Equations
[tex]v = v_{0} + a_{A}t[/tex]
The Attempt at a Solution
FBD:
Block A:
[tex]+\downarrow \sum F_{y} = ma_{y}[/tex]
[tex]10 - 2T = (0.311)(a_{A})[/tex]
Block B:
[tex]+\rightarrow \sum F_{x} = ma_{x}[/tex]
[tex]T - (0.2)(4) = (0.124)(a_{B})[/tex]
[tex]+\downarrow \sum F_{y} = ma_{y}[/tex]
[tex]4 - N = 0[/tex]
Kinematics:
[tex]2S_{A} + S_{B} = l[/tex]
[tex]2a_{A} + a_{B} = 0[/tex]
[tex]2a_{A} = -a_{B}[/tex]
Solving for T:
[tex]10 - 2T = (0.311)(a_{A})[/tex]
[tex]10 - 2T = -(0.311)(a_{B})[/tex]
[tex]a_{B} = -\frac{10 - 2T}{0.311} = \frac{T - (0.2)(4)}{0.124}[/tex]
[tex]T = -16lb/2 = -8lb[/tex]
[tex]a_{B} = -70.84ft/s^{2}[/tex]
[tex]a_{A} = 83.72ft/s^{2}[/tex]
[tex]v = v_{0} + a_{A}t[/tex]
[tex]v = 6 + (83.72)(2) = 173.44 ft/s[/tex] I am not sure if this is right because that seems fast.