A war - wolf or trebuchet is a device used during the Middle Ages to throw rocks

Question

A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass, d =3.45 m long, joining particles of mass m1 = 0.115 kg and m2 = 73.5 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 13.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation.

A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass, d =3.45 m long, joining particles of mass m1 = 0.115 kg and m2 = 73.5 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 13.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation. Find the maximum speed that the small-mass object attains when it leaves the trebuchet horizontally.

Explanation / Answer

Torque about the pivot
= (73.5*9.8*0.13 - 0.115*9.8*3.32)*cos(?)

So the work done is integral (73.5*9.8*0.13 - 0.115*9.8*3.32)*cos(?)d? (evaluated from 0 to ?/2) =
(73.5*9.8*0.13 - 0.115*9.8*3.32)*(sin(?/2) - sin(0)) = 89.897J

Work = ?K = 1/2*I*?^2 where I = 73.5*0.13^2 + 0.115*3.32^2 = 2.5097kg-m^2

So ? = sqrt(2*W/I) = sqrt(2*89.897/2.5097) = 8.46402rad/s

So v = r*? = 3.32*8.46402 = 28.1m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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