Three point-like bodies of masses m = 0:20 kg each are connected by weightless r

ID: 2101107 • Letter: T

Question

Three point-like bodies of masses m = 0:20 kg each are connected by weightless rods forming

an equilateral triangle of side a = 0:40 m. The triangle rotates around a xed axis through

its center and perpendicular to triangle's plane. The force of magnitude F = 2:0 N that acts

on each body is constant relative to the triangle, in triangle's plane, making an angle of 30

with the side of the triangle, and directed outside the triangle. Find the total kinetic energy

after 1 second if the system starts from rest. Note that you have to consider two cases: (a)

all three forces oriented clockwise or counterclockwise (b) one force oriented dierently than

the two other.

distance of each mass from centre=a/2Sec30=a/sqrt(3)

I=3*m*a^2/3=ma^2=0.032kgm^2

Casea) Net torque=3*FSin(60)*a/sqrt(3)=sqrt(3)Fa*sqrt(3)/2=3Fa/2=3*2*0.4/2=1.2Nm

alpha=Torque/I=37.5rad/s^2

w=alpha*t=37.5rad/s

Kinetic energy=0.5Iw^2=22.5J

b)Net torque=2*FSin(60)*a/sqrt(3)-FSin(60)*a/sqrt(3)

=FSin(60)*a/sqrt(3)=Fa/2=2*0.4/2=0.4Nm

alpha=Torque/I=12.5rad/s^2

w=alpha*t=12.5rad/s

Kinetic energy=0.5Iw^2=2.5J

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