mass 1 At a certain instant its center of mass has a speed of 9.0 mýs (a) Determ
ID: 2037795 • Letter: M
Question
mass 1 At a certain instant its center of mass has a speed of 9.0 mýs (a) Determine the translational kinetic energy of its center of mass. A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.72 m/s s axle and is initially (a) How much work has been done on the spool when it reaches an angular speed of 6.45 rad/s? (b) How long does it take the spool to reach this angular speed?Explanation / Answer
9) given
m = 12 kg, v = 9 m/s
a) KE_translational = (1/2)*m*v^2
= (1/2)*12*9^2
= 486 J
b) KE_rotational = (1/2)*I*w^2
= (1/2)*(1/2)*m*r^2*w^2
= (1/4)*m*v^2 (since v = r*w)
= (1/4)*12*9^2
= 243 J
c) KE_total = 486 + 243
= 729 J
10)
a) Workdone = gain in kinetic energy
= (1/2)*I*(wf^2 - wi^2)
= (1/2)*(1/2)*m*r^2(wf^2 -wi^2)
= (1/4)*1*0.5^2*(6.45^2 - 0^2)
= 2.60 J
b) alfa = a_tan/r
= 2.72/0.5
= 5.44 rad/s^2
use, t = (wf - wi)/alfa
= (6.45 - 0)/5.44
= 1.186 s
c) s = u*t + (1/2)*a*t^2
= 0 + (1/2)*2.72*1.186^2
= 1.91 m
ramaining cord length = 4 - 1.91
= 2.09 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.