Homework9 Fall 2015 Two blocks are connected by inelastic rope over a pulley, as
ID: 1366856 • Letter: H
Question
Homework9 Fall 2015 Two blocks are connected by inelastic rope over a pulley, as shown. Block#1 is on a flat level surface, while Block #2 is on a 50° incline. Both surfaces have the following friction coefficients: , 0.404 Assume the pulley is a solid disk, has a track diameter of 1inch and a totally frictionless axle. The blocks and puiley have the following masses: m1=22 g m2=18g mp = 4g Define Tension T, to be in the Rope between the Pulley and Block #1. Define Tension T, to be in the Rope between the Pulley and Block #2. Based on this information: Problem 4 Determine the acceleration vector of two blocks.Explanation / Answer
on block 1,
T1 - ukm1g = m1a
T1 - (0.282 x 22 x 9.81) = 22a .....(i)
on pulley,
torque (r xF) = I x alpha
(T2 - T1)r = (mr^2/2)(a/r)
T2 - T1 = 4a/2 = 2a .........(ii)
on block 2,
m2gsin50 - T2 - ukm2gcos50 = m2a
(18x9.81 x sin50) - T2 - (0.282 x18x 9.81 x cos50 ) = 18a .........(iii)
from (i), (ii) and (iii),
a = 1.01 m/s^2 ..........Ans
5) T1 - 0.282 x 22 x 9.81 =22 x 1.01
T1 = 83.07 N
6) T2 - T1 = 2a
T2 = 83.07 + (2x1.01) =85.09 N
7) angular accc. = alpha = a/r = 1.01 / (0.5 x 0.0254 m) = 79.53 rad/s^2
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