A block of mass 2.20 kg isaccelerated across a rough surface by a light cord pas
ID: 1728846 • Letter: A
Question
A block of mass 2.20 kg isaccelerated across a rough surface
by a light cord passing over asmall pulley as shown in the figure
below. The tension T in the cordis maintained at 10.0 N, and the
pulley is 0.100 m above the topof the block. The coefficient of
(a) Determine the accelerationof the block when x = .400m.
(b) Is the acceleration of theblock increasing, decreasing or both as itslides from a location where x is large to x =0?
Describe its changes qualitatively or draw arough graph.
A block of mass 2.20 kg isaccelerated across a rough surface by a light cord passing over asmall pulley as shown in the figure below. The tension T in the cordis maintained at 10.0 N, and the pulley is 0.100 m above the topof the block. The coefficient of kinetic friction is0.400 (a) Determine the accelerationof the block when x = .400m. (b) Is the acceleration of theblock increasing, decreasing or both as itslides from a location where x is large to x =0? Describe its changes qualitatively or draw arough graph.Explanation / Answer
m = 2.20 kg, T = 10.0 N, h =0.100 m, = 0.400, x = 0.400m
net force F = Tcos- (mg - Tsin)
a = F/m = [Tcos - (mg -Tsin)]/m
wheretan = h/x = 1/4, =14.0o
a = 0.931 m/s2
a = T(cos + sin)/m - g =T(x +h)/[m(x2 +h2)] -g
da/dx = Th(h- x)/[m(x2 +h2)3]
when 0 < x <h/, or 0 < x < 0.25 m, da/dx> 0, a is increasing.
when x > 0.25 m, da/dx < 0, a isdecreasing.
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