A uniform plank of length 2.00 m and mass 25.5 kg is supported by three ropes, a
ID: 2265014 • Letter: A
Question
A uniform plank of length 2.00 m and mass 25.5 kg is supported by three ropes, as indicated by the blue vectors in the figure below. Find the tension in each rope when a685-N person is d = 0.575 m from the left end.
A 11.0-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 11.9 m/s, determine the following.
(b) the rotational kinetic energy about its center of gravity
J
(c) its total kinetic energy
J
Explanation / Answer
when the system is in equilibrium, net force and net toruqe are zero.
Fnety = 0
T1 + T2*sin(40) - 25*9.8 - 685 = 0
T1 + T2*0.6428 - 245 - 685 = 0
T1 + 0.6428*T2 = 930 --(1)
net torque is zero
T1*cos(40)*2 - 685*0.575 - 25*9.8*1 = 0
T1 = (685*0.575 + 25*9.8*1)/(2*sin(40))
T1 = 497 N
from euqation(1)
T2 = (930-497)/0.6428
T2 = 673.7 N
Fnetx = 0
T3 = T1*cos(40)
= 497*cos(40)
= 380.72 N
2)
b) KE (rotational) = 0.5*I*w^2
= 0.5*0.5*m*r^2*w^2
= 0.25*m*v^2
= 0.25*11*11.9^2
= 389.42 J
c)
KE(total) = o.5*m*v^2 + 0.5*I*w^2
= 0.5*m*v^2 + 0.25*m*v62
= 0.75*m*v^2
= 1168.28 J
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