1. The truss shown here is made of five identical, rigid, massless rods and thre

Question

1. The truss shown here is made of five identical, rigid, massless rods and three identical point masses. The truss is attached to a high ceiling support at its left end by a frictionless bolt and at its right end by a massless cable, as shown here in this side view. Initially, everything is at rest, and m, is at the same height as the bolt. Each mass is 4.60 kg. Each rod has a length of 1.35 m ceiling 72 a. Find the tension in the cable when everything is at rest b. Now suppose that the cable suddenly breaks at its lower end (where it attaches to m), so that it swings downward, pivoting clockwise around the bolt like a pendulum Find the net force (magnitude and dircction) acting on m, as it (m) passes directly beneath the bolt Define 0° to the right and L90° vertically upward. Disregard air drag, and use g = 9.80 m/s? m, . Now suppose the bolt breaks as m, passes directly beneath the bolt. (Pathetically shoddy manufacturing here.... As of that moment, the truss becomes a projectile. Find its translational speed at the moment when it has completed 12 revolutions during this free fall. Again, disregard air drag, and use g = 9.80 m/s

Explanation / Answer

1. given, each mass m = 4.6 kg

let tension in the cable be T

let reaction for ecs at the bolt be Fx and Fy

hence from force balance

Fx = Tcos(72)

Fy + Tsin(72) = 3mg

also, from moment balance

Tsin(72)*2l*cos(60) = mg*2l*cos(60) + 2mg*l*cos(60)

Tsin(72) = 2mg

hence

a. T = 94.89656 N

b. so when the truss pivots about the bolt to molve like a pendulum

moment of inertia of the truss about the bolt, I = 2ml^2 + m*(2l*cos(60))^2

where l = 4.35 m

hence

I = 261.1305 kg m^2

let angular speed of the truss at the lowermost point be w

then from conservation of energy

0.5*I*w^2 = mg*2l*cos(60) + mg(2l*cos(60) - l/2) + mg(2l*cos(60) + l/2)

hence

I*w^2 = 12*mgl*cos(60)

w = 2.1237572430 rad/s

hence

net speed of m3 when it passes beneath the bolt = v

v = w*2l*cos(60) = 9.238344 m/s

c. at the givne moment, angular speed, w = 2.12375 rad/s

hence time taken for 12 revolutions = 35.5 s

hence translattinoal speed at this time = vs

vs = sqroot(v^2 + g*t)

vs = 20.819948 m/s

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.