In the figure below, Block A has mass 3.22 kg and Block B has mass 4.4 kg. Block
ID: 2097353 • Letter: I
Question
In the figure below, Block A has mass 3.22 kg and Block B has mass 4.4 kg. Block A slides on the horizontal table with coefficient of kinetic friction 0.592. The pulley spins with the taut string, so that the string does not slip as it passes over the pulley (what is the relationship between string speed and tangential speed of the outer surface of the pulley?). Treat the pulley as a solid disc with mass 0.549 kg and radius 1.21 cm. What is the speed of Block B after it has fallen by 1.42 m? Assume that both blocks are initially at rest and that the pulley spins without losing energy to friction. Write your answer in SI units to three significant figures.
Explanation / Answer
For Pulley
= I *
I = Mp (r^2)/2
= ( T2 - T1 ) * r = I *
= a/r
For Mass A
Ff ( frictional force ) = M(A) * g *
T1 ( string attached with A havin tension ) = Ff + M(A)*a
T2 ( string attached with B havin tension ) = M(B) * g - M(B) *a
put T1 and T2 in eqn of
( T2 - T1 ) * r = I *
( M(B) * g - M(B) *a - Ff - M(A)*a ) *r = Mp ((r^2)/2) * a/r
a = 3.099 m/s^2
v (final)^2 - v (initial)^2 = 2 * a * s
v (final)^2 = 2 * a * s = 8.791
v (final) = 2.966 m/s