Problem 12.69 Part A The two blocks in the figure(Figure 1) are connected by a m
ID: 1500398 • Letter: P
Question
Problem 12.69 Part A The two blocks in the figure(Figure 1) are connected by a massless rope that passes over a pulley. The pulley is 14 cm in diameter and has a mass of 2.4 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.55 N·m If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor? Express your answer to two significant figures and include the appropriate units t=10.782 |s Submit My Answers Give Up Incorrect, Iry Again, 5 attempts remaining Figure 1 of! vide Continue 4.0 kg 1.0 m 2.0 kgExplanation / Answer
let,
mass, m1=4kg
mass, m2=2kg
mass of the pully, m3=2.4 kg
diameter of the pully, d=14cm
radius of the pully, r=7cm
equation of motion of m1,
m1*a=T1-m1*g
T1=m1*(g+a) ------(1)
and
equation of motion of m2,
m2*a=m2*g-T2
T2=m2*(g-a) -------(2)
equation of motion of disk,
I=1/2*m3*R^2
and,
alpa=a/R
net toque, T=I*alpa
T2*R-T1*R-Tf=(1/2*m3*R^2)*(a/R) -----(3)
from equation (1),(2) and (3)
m2*(g-a)*R-m1*(g+a)-Tf=(1/2*m3*R^2)*(a/R)
===>
a=((m2-m1)*g*R-Tf)/R(m2+m1+m3/2)
a=((4-2)*9.8*0.07-0.55)/(0.07(4+2+2.4/2))
a=1.63 m/sec^2
now,
s=u*t+1/2*a*t^2
1=0+1/2*(1.63)*t^2
===> t=1.108 sec ----------------->