A 4 kg block sitting on a flat table is attached by a string over a cylindrical
ID: 2185735 • Letter: A
Question
A 4 kg block sitting on a flat table is attached by a string over a cylindrical pulley to a 3 kg block which is hanging in the air 4 meters above the ground. The coefficient of the kinetic friction is 0.2. The radius of the wheel is .08 meters and its mass is .07 kg. [Assume the pulley to be a solid cylinder] Find the acceleration (a) of the system. Find the tensions (T1 and T2) in the upper and lower part of the string, respectively. Find the total work done on the wheel by the strings. Find the final angular speed of the wheel.Explanation / Answer
a)(t1-t2)r=.07r^2/2
t1-t2=0.07*.08*/2
a=r=0.08
t1-t2=0.07*a/2
t1-0.2*4*g=4*a
3*g-t2=3*a
solving these 3 equations we get
a)acceleration a=3.16 m/s^2
b)t1=20.635 N
t2=20.524 N
c)4m=r
=4/0.8=5 radians
work done =(t1-t2)=(20.635-20.524)5=0.555 J
d)=sqrt(2)=sqrt(2*5*3.16/0.08)
=19.875 rad/s